bridgesampling/0000755000176200001440000000000015107257542013251 5ustar liggesusersbridgesampling/tests/0000755000176200001440000000000015055304401014400 5ustar liggesusersbridgesampling/tests/testthat/0000755000176200001440000000000015107257542016253 5ustar liggesusersbridgesampling/tests/testthat/test-stan_bridge_sampler_bugs.R0000644000176200001440000001331615060242566024401 0ustar liggesusers context('Stan Bridge Sampler Bugs') test_that("subscript out of bounds error", { ## https://github.com/quentingronau/bridgesampling/issues/26 stan_mod = " data{ int M; int J; int T; int E; int G; int N[G]; int ii[M]; int jj[M]; int gg[M]; int g_all[sum(N)]; int y[M]; matrix[J,J] obs_corr[G]; } transformed data{ int N_all = sum(N); } parameters{ ordered[T] thresholds_raw[G,J]; matrix[E,J] lam[G]; matrix[N_all,E] eta; matrix[N_all,J] ystar_raw; } transformed parameters { ordered[T] thresholds[G,J]; for(g in 1:G) for(j in 1:J) thresholds[g,j] = thresholds_raw[g,j] * 5; } model{ matrix[N_all,J] ystar; int pos = 1; target += std_normal_lpdf(to_vector(ystar_raw)); target += std_normal_lpdf(to_vector(eta)); for(g in 1:G){ int g_ids[N[g]] = segment(g_all,pos,N[g]); target += normal_lpdf(to_vector(eta)| 0,5); for(j in 1:J) target += std_normal_lpdf(thresholds_raw[g,j]); ystar[g_ids,] = eta[g_ids,] * lam[g] + ystar_raw[g_ids,]; pos += N[g]; } for(m in 1:M) target += ordered_logistic_lpmf(y[m] | ystar[ii[m],jj[m]], thresholds[gg[m],jj[m]]); } " testthat::skip_on_cran() testthat::skip_on_ci() testthat::skip_if_not_installed("rstan") library("rstan") # source("tests/testthat/test_dat.txt") source("test_dat.txt") suppressWarnings( mod <- stan(model_code=stan_mod,data=test_dat, chains = 2, refresh = 0) ) expect_warning(object = bridge_sampler(mod, silent=TRUE), regexp = "Infinite value in iterative scheme, returning NA.") }) test_that("bridge_sampler.stanfit multicore works for one-parameter model.", { skip_on_cran() skip_on_ci() skip_on_os("windows") if (require(rstan)) { set.seed(12345) # compute difference scores n <- 10 y <- rnorm(n) # models stancodeH0 <- ' data { int n; // number of observations vector[n] y; // observations } parameters { real sigma2; // variance parameter } model { target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | 0, sqrt(sigma2)); // likelihood } ' # compile models suppressWarnings( stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") ) # fit models stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n), iter = 10000, warmup = 1000, chains = 4, control = list(adapt_delta = 0.95), refresh = 0) ######### bridge sampling ########### suppressWarnings(H0 <- bridge_sampler(stanfitH0, cores = 2, silent = TRUE)) expect_s3_class(H0, "bridge") } }) test_that("turtle example",{ skip_on_cran() skip_on_ci() if (require(rstan)) { data("turtles") ### m1 (model with random intercepts) ### m1_code_nc <- "data { int nobs; int y[nobs]; real x[nobs]; int m; int clutch[nobs]; } parameters { real alpha0_raw; real alpha1_raw; vector[m] b_raw; real sigma2; } transformed parameters { vector[m] b; real sigma = sqrt(sigma2); real alpha0 = sqrt(10.0)*alpha0_raw; real alpha1 = sqrt(10.0)*alpha1_raw; b = b_raw*sigma; } model { // priors target += -2*log(1 + sigma2); // p(sigma2) = 1/(1 + sigma2)^2 target += normal_lpdf(alpha0_raw | 0, 1); target += normal_lpdf(alpha1_raw | 0, 1); // random effects target += normal_lpdf(b_raw | 0, 1); // likelihood for (i in 1:nobs) target += bernoulli_lpmf(y[i] | Phi(alpha0 + alpha1*x[i] + b[clutch[i]])); }" suppressWarnings( stanobject_m1_nc <- stan(model_code = m1_code_nc, data = list(y = turtles$y, x = turtles$x, nobs = nrow(turtles), m = max(turtles$clutch), clutch = turtles$clutch), iter = 10500, warmup = 500, chains = 4, refresh = 0) ) bs_m1_nc <- bridge_sampler(stanobject_m1_nc, method = "warp3", repetitions = 25, silent=TRUE) m0_code_nc <- "data { int nobs; int y[nobs]; real x[nobs]; } parameters { real alpha0_raw; real alpha1_raw; } transformed parameters { real alpha0 = sqrt(10.0)*alpha0_raw; real alpha1 = sqrt(10.0)*alpha1_raw; } model { // priors target += normal_lpdf(alpha0_raw | 0, 1); target += normal_lpdf(alpha1_raw | 0, 1); // likelihood for (i in 1:nobs) target += bernoulli_lpmf(y[i] | Phi(alpha0 + alpha1*x[i])); }" suppressWarnings( stanobject_m0_nc <- stan(model_code = m0_code_nc, data = list(y = turtles$y, x = turtles$x, nobs = nrow(turtles), m = max(turtles$clutch), clutch = turtles$clucth), iter = 10500, warmup = 500, chains = 4, refresh = 0) ) bs_m0_nc <- bridge_sampler(stanobject_m0_nc, method = "warp3", repetitions = 25, silent=TRUE) expect_equal(bf(bs_m0_nc, bs_m1_nc)$bf, rep(1.27, 25), tolerance = 0.02) } }) bridgesampling/tests/testthat/test-bridge_sampler_CmdStanMCMC.R0000644000176200001440000000706415060246656024414 0ustar liggesuserscontext("test bridge_sampler cmdstanmcmc method") testthat::test_that("bridge_sampler() works for CmdStanMCMC and basic sanity checks", { testthat::skip_on_cran() testthat::skip_if_not_installed("cmdstanr") testthat::skip_if_not_installed("bridgesampling") testthat::skip_if_not_installed("posterior") # Require a working CmdStan toolchain if (!file.exists(cmdstanr::cmdstan_path())) { testthat::skip("CmdStan is not installed in the expected path for cmdstanr.") } set.seed(123) N <- 60L sigma <- 1 y <- rnorm(N, mean = 0.5, sd = sigma) data_list <- list(N = N, y = y, sigma = sigma) stan_code <- " data { int N; vector[N] y; real sigma; } parameters { real mu; } model { mu ~ normal(0, 1); y ~ normal(mu, sigma); }" tf <- tempfile(fileext = ".stan") on.exit(unlink(tf), add = TRUE) writeLines(stan_code, tf) mod <- cmdstanr::cmdstan_model(tf, quiet = TRUE, force_recompile = TRUE) fit <- mod$sample( data = data_list, seed = 202, chains = 2, parallel_chains = 2, iter_warmup = 2000, iter_sampling = 4000, refresh = 0, show_messages = FALSE, show_exceptions = FALSE ) bs <- bridgesampling::bridge_sampler(fit, silent = TRUE, use_neff = FALSE) testthat::expect_s3_class(fit, "CmdStanMCMC") testthat::expect_true(is.list(bs)) testthat::expect_true(is.finite(bs$logml)) fit2 <- mod$sample( data = data_list, seed = 203, chains = 4, parallel_chains = 2, iter_warmup = 750, iter_sampling = 2000, refresh = 0, show_messages = FALSE, show_exceptions = FALSE ) bs2 <- bridgesampling::bridge_sampler(fit2, silent = TRUE, use_neff = FALSE) testthat::expect_true(is.finite(bs2$logml)) }) testthat::test_that("CmdStanMCMC bridge estimate roughly agrees with rstan", { testthat::skip_on_cran() testthat::skip_on_ci() testthat::skip_if_not_installed("cmdstanr") testthat::skip_if_not_installed("bridgesampling") if (!requireNamespace("rstan", quietly = TRUE)) testthat::skip("rstan not installed") if (!file.exists(cmdstanr::cmdstan_path())) { testthat::skip("CmdStan is not installed in the expected path for cmdstanr.") } set.seed(456) # Same model/data as above N <- 60L sigma <- 1 y <- rnorm(N, mean = 0.25, sd = sigma) data_list <- list(N = N, y = y, sigma = sigma) stan_code <- " data { int N; vector[N] y; real sigma; } parameters { real mu; } model { mu ~ normal(0, 1); y ~ normal(mu, sigma); }" # --- CmdStanR/RStan fit --- tf <- tempfile(fileext = ".stan") on.exit(unlink(tf), add = TRUE) writeLines(stan_code, tf) mod_cs <- cmdstanr::cmdstan_model(tf, quiet = TRUE) fit_cs <- mod_cs$sample( data = data_list, seed = 777, chains = 4, parallel_chains = 2, iter_warmup = 10000, iter_sampling = 3000, refresh = 0, show_messages = FALSE, show_exceptions = FALSE ) bs_cmd <- bridgesampling::bridge_sampler(fit_cs, silent = TRUE, use_neff = FALSE) testthat::expect_true(is.finite(bs_cmd$logml)) Sys.sleep(2.5) sm <- rstan::stan_model(model_code = stan_code) fit_rs <- rstan::sampling( sm, data = data_list, seed = 777, chains = 4, iter = 10000, warmup = 3000, refresh = 0, cores = 2 ) bs_rstan <- bridgesampling::bridge_sampler(fit_rs, silent = TRUE, use_neff = FALSE) testthat::expect_true(is.finite(bs_rstan$logml)) # Compare the two bridge estimates. Tolerance accounts for MC/bridge variance. testthat::expect_lt(abs(bs_cmd$logml - bs_rstan$logml), 0.5) }) bridgesampling/tests/testthat/test-vignette_example_stan.R0000644000176200001440000001477515060242566023754 0ustar liggesusers context('test vignette bridgesampling_example_stan.Rmd') test_that("bridge sampler yields correct results", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) if (require(rstan)) { ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 # models stancodeH0 <- 'data { int n; // number of observations vector[n] y; // observations real alpha; real beta; real sigma2; } parameters { real tau2; // group-level variance vector[n] theta; // participant effects } model { target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | 0, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' stancodeH1 <- 'data { int n; // number of observations vector[n] y; // observations real mu0; real tau20; real alpha; real beta; real sigma2; } parameters { real mu; real tau2; // group-level variance vector[n] theta; // participant effects } model { target += normal_lpdf(mu | mu0, sqrt(tau20)); target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | mu, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' # compile models stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") # fit models stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 50000, warmup = 1000, chains = 3, cores = 1, refresh = 0) stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 50000, warmup = 1000, chains = 3, cores = 1, refresh = 0) # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(stanfitH0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(stanfitH1, silent = TRUE) # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) # "exact" ml H1 mH1 <- function(data, rel.tol = 1e-10) { y <- data$y n <- data$n mu0 <- data$mu0 tau20 <- data$tau20 alpha <- data$alpha beta <- data$beta sigma2 <- data$sigma2 mH1integrand <- function(tau2, y, sigma2, mu0, tau20, alpha, beta) { (sigma2 + tau2)^(-n/2) * exp(-1/2 * ((n*mean(y)^2 + (n - 1)*sd(y)^2)/(sigma2 + tau2) + mu0^2/tau20 - ((n*mean(y))/(sigma2 + tau2) + mu0/tau20)^2 / (n/(sigma2 + tau2) + 1/tau20))) * (n/(sigma2 + tau2) + 1/tau20)^(-1/2) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * (tau20)^(-1/2) * beta^alpha/gamma(alpha) * integrate(mH1integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta)$value } exact_logmlH1 <- log(mH1(list(y = y, n = n, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2))) # "exact" ml H1 mH0 <- function(data, rel.tol = 1e-10) { y <- data$y n <- data$n alpha <- data$alpha beta <- data$beta sigma2 <- data$sigma2 mH0integrand <- function(tau2, y, sigma2, alpha, beta) { n <- length(y) (sigma2 + tau2)^(-n/2) * exp(-(n*mean(y)^2 + (n - 1)*sd(y)^2)/ (2*(sigma2 + tau2))) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * beta^alpha/gamma(alpha) * integrate(mH0integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, alpha = alpha, beta = beta)$value } exact_logmlH0 <- log(mH0(list(y = y, n = n, alpha = alpha, beta = beta, sigma2 = sigma2))) exact_BF01 <- exp(exact_logmlH0 - exact_logmlH1) H0.bridge.curr <- H0.bridge H1.bridge.curr <- H1.bridge BF01.curr <- BF01 post1.curr <- post1 post2.curr <- post2 load(system.file("extdata/", "vignette_example_stan.RData", package = "bridgesampling")) expect_equal( H0.bridge.curr$logml, expected = exact_logmlH0, tolerance = 0.01 ) expect_equal( H1.bridge.curr$logml, expected = exact_logmlH1, tolerance = 0.01 ) expect_equal( BF01.curr$bf, expected = exact_BF01, tolerance = 0.01 ) expect_equal( H0.bridge.curr$logml, expected = H0.bridge$logml, tolerance = 0.01 ) expect_equal( H1.bridge.curr$logml, expected = H1.bridge$logml, tolerance = 0.01 ) expect_equal( BF01.curr$bf, expected = BF01$bf, tolerance = 0.01 ) expect_equal( post1.curr, expected = post1, tolerance = 0.01 ) expect_equal( post2.curr, expected = post2, tolerance = 0.01 ) } }) bridgesampling/tests/testthat/test-bridge_sampler_Rcpp.R0000644000176200001440000000415715060242566023323 0ustar liggesusers context('basic bridge sampling behavior normal Rcpp') test_that("bridge sampler matches anlytical value normal example", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) library(mvtnorm) if(require(RcppEigen)) { x <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(x) <- c("x1", "x2") lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) Rcpp::sourceCpp("unnormalized_normal_density.cpp") bridge_normal <- bridge_sampler(samples = x, log_posterior = log_densityRcpp, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_densityRcpp, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) expect_equal(bridge_normal$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3$logml, expected = log(2*pi), tolerance = 0.01) # test dots argument mu <- c(1, 2) x <- rmvnorm(1e4, mean = mu, sigma = diag(2)) colnames(x) <- c("x1", "x2") lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) Rcpp::sourceCpp("unnormalized_normal_density_mu.cpp") bridge_normal_dots <- bridge_sampler(samples = x, log_posterior = log_densityRcpp_mu, mu, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3_dots <- bridge_sampler(samples = x, log_posterior = log_densityRcpp_mu, mu, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) expect_equal(bridge_normal_dots$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3_dots$logml, expected = log(2*pi), tolerance = 0.01) } }) bridgesampling/tests/testthat/test-post_prob.R0000644000176200001440000000332415055304401021351 0ustar liggesusers context('post_prob with lists') test_that("post_prob works with lists and with NAs.", { bridge_o <- structure(list(logml = c(4291.14352476047, 4293.29076119542, 4291.96372581169, 4293.02187182362, NA, NA, 4290.9761730488, 4293.32075269401, 4293.5762219227, 4294.02761288449), niter = c(104, 16, 52, 8, 1000, 1000, 167, 16, 21, 44), method = "normal", repetitions = 10), .Names = c("logml", "niter", "method", "repetitions"), class = "bridge_list") H0L <- structure(list(logml = c(-20.8088381186739, -20.8072772698116, -20.808454454621, -20.8083419072281, -20.8087870541247, -20.8084887398113, -20.8086023582344, -20.8079083169745, -20.8083048489095, -20.8090050811436 ), niter = c(4, 4, 4, 4, 4, 4, 4, 4, 4, 4), method = "normal", repetitions = 10), .Names = c("logml", "niter", "method", "repetitions"), class = "bridge_list") H1L <- structure(list(logml = c(-17.961665507006, -17.9611290723151, -17.9607509604499, -17.9608629535992, -17.9602093576442, -17.9600223300432, -17.9610157118017, -17.9615557696561, -17.9608437034849, -17.9606743200309 ), niter = c(4, 4, 4, 4, 4, 4, 4, 4, 3, 4), method = "normal", repetitions = 10), .Names = c("logml", "niter", "method", "repetitions"), class = "bridge_list") H0 <- structure(list(logml = -20.8084543022433, niter = 4, method = "normal"), .Names = c("logml", "niter", "method"), class = "bridge") expect_is(post_prob(H1L, H0L), "matrix") expect_warning(post_prob(H1L, H0L, H0), "recycled") expect_warning(post_prob(H1L, H0L, 4), "ignored") expect_warning(post_prob(H0, H0L, 4), "ignored") expect_warning(post_prob(H1L, H0L, bridge_o), "NA") expect_error(post_prob(H1L, 4, 5, 6), "one object") expect_error(post_prob(H0, 4, 5, 6), "one object") }) bridgesampling/tests/testthat/test-stan_bridge_sampler_basic.R0000644000176200001440000001247215060242566024524 0ustar liggesusers context('bridge_sampler.stanfit works.') ### H0: mu = 0 mH0 <- function(y, sigma2 = 1, alpha = 2, beta = 3, rel.tol = 10^(-10)) { n <- length(y) mH0integrand <- function(tau2, y, sigma2, alpha, beta) { (sigma2 + tau2)^(-n/2) * exp(-(n*mean(y)^2 + (n - 1)*sd(y)^2)/(2*(sigma2 + tau2))) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * beta^alpha/gamma(alpha) * integrate(mH0integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, alpha = alpha, beta = beta)$value } test_that("stan_bridge_sampler", { testthat::skip_on_os("windows") if (require(rstan)) { set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 # models stancodeH0 <- 'data { int n; // number of observations vector[n] y; // observations real alpha; real beta; real sigma2; } parameters { real tau2; // group-level variance vector[n] theta; // participant effects } model { target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | 0, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' # compile models stanmodelH0 <- suppressWarnings( stan_model(model_code = stancodeH0, model_name="stanmodel") ) # fit models stanobjectH0 <- sampling(stanmodelH0, data = list(y = y, n = n, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 3500, warmup = 500, chains = 4, show_messages = FALSE, refresh = 0) expect_is( H0_bridge_norm <- bridge_sampler(samples = stanobjectH0, method = "normal", silent = TRUE) , "bridge") expect_is( H0_bridge_norm_rep <-bridge_sampler(stanobjectH0, method = "normal", repetitions = 2, silent = TRUE) , "bridge_list") expect_is( H0_bridge_warp3 <- bridge_sampler(stanobjectH0, method = "warp3", silent = TRUE) , "bridge") expect_is( H0_bridge_warp3_rep <- bridge_sampler(stanobjectH0, method = "warp3", repetitions = 2, silent = TRUE) , "bridge_list") expect_equal( H0_bridge_norm$logml, log(mH0(y = y, sigma2 = sigma2, alpha = alpha, beta = beta)), tolerance = 0.1) expect_equal( H0_bridge_warp3$logml, log(mH0(y = y, sigma2 = sigma2, alpha = alpha, beta = beta)), tolerance = 0.1) expect_equal( H0_bridge_norm_rep$logml, rep(log(mH0(y = y, sigma2 = sigma2, alpha = alpha, beta = beta)), 2), tolerance = 0.1) expect_equal( H0_bridge_warp3_rep$logml, rep(log(mH0(y = y, sigma2 = sigma2, alpha = alpha, beta = beta)), 2), tolerance = 0.1) } }) test_that("stan_bridge_sampler in multicore", { testthat::skip_on_cran() testthat::skip_on_ci() testthat::skip_on_os("windows") if (require(rstan)) { set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 # models stancodeH0 <- 'data { int n; // number of observations vector[n] y; // observations real alpha; real beta; real sigma2; } parameters { real tau2; // group-level variance vector[n] theta; // participant effects } model { target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | 0, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' # compile models stanmodelH0 <- suppressWarnings( stan_model(model_code = stancodeH0, model_name="stanmodel") ) # fit models stanobjectH0 <- sampling(stanmodelH0, data = list(y = y, n = n, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 2500, warmup = 500, chains = 4, show_messages = FALSE, refresh = 0) expect_is( H0_bridge_norm <- bridge_sampler(stanobjectH0, method = "normal", silent = TRUE, cores = 2) , "bridge") expect_is( H0_bridge_warp3 <- bridge_sampler(stanobjectH0, method = "warp3", silent = TRUE, cores = 2) , "bridge") expect_equal( H0_bridge_norm$logml, log(mH0(y = y, sigma2 = sigma2, alpha = alpha, beta = beta)), tolerance = 0.1) expect_equal( H0_bridge_warp3$logml, log(mH0(y = y, sigma2 = sigma2, alpha = alpha, beta = beta)), tolerance = 0.1) } }) bridgesampling/tests/testthat/unnormalized_normal_density_mu.cpp0000644000176200001440000000116215055304401025263 0ustar liggesusers// load Rcpp #include #include #include using namespace Rcpp; using Eigen::VectorXd; using Eigen::Map; //------------------------------------------------------------------------------ // unnormalized standard multivariate normal density function (log) //------------------------------------------------------------------------------ // [[Rcpp::depends(RcppEigen)]] // [[Rcpp::export]] double log_densityRcpp_mu(NumericVector x, SEXP data, NumericVector mu) { VectorXd xe(as >(x)); VectorXd mue(as >(mu)); return -0.5*(xe - mue).transpose()*(xe - mue); } bridgesampling/tests/testthat/test-iterative-scheme-mcse.R0000644000176200001440000000752415106572257023550 0ustar liggesuserscontext("Iterative scheme MCSE calculations") test_that("MCSE is finite, positive, and returned for normal method", { skip_if_not_installed("Brobdingnag") # Minimal deterministic inputs q11 <- c(0.10, 0.20, 0.30, 0.40) q12 <- c(0.02, 0.09, 0.10, 0.15) q21 <- c(0.05, 0.18, 0.22, 0.28) q22 <- c(0.01, 0.07, 0.11, 0.12) L <- diag(2) out <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21, q22 = q22, r0 = 1, tol = 1e-10, L = L, method = "normal", maxiter = 1000, silent = TRUE, criterion = "r", neff = length(q11), use_ess = FALSE ) expect_type(out, "list") expect_true(is.finite(out$mcse_logml)) expect_gt(out$mcse_logml, 0) # Deterministic value checks for the toy example expect_equal(out$logml, 0.13248979618200290, tolerance = 1e-12) expect_equal(out$mcse_logml, 0.02353233284705807, tolerance = 1e-12) }) test_that("MCSE is invariant to constant shifts (warp3 vs normal)", { skip_if_not_installed("Brobdingnag") # Same base inputs as above q11 <- c(0.10, 0.20, 0.30, 0.40) q12 <- c(0.02, 0.09, 0.10, 0.15) q21 <- c(0.05, 0.18, 0.22, 0.28) q22 <- c(0.01, 0.07, 0.11, 0.12) L <- diag(2) out_normal <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21, q22 = q22, r0 = 1, tol = 1e-10, L = L, method = "normal", maxiter = 1000, silent = TRUE, criterion = "r", neff = length(q11), use_ess = FALSE ) out_warp3 <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21, q22 = q22, r0 = 1, tol = 1e-10, L = L, method = "warp3", maxiter = 1000, silent = TRUE, criterion = "r", neff = length(q11), use_ess = FALSE ) # warp3 adds a constant to both l1 and l2 and shifts l*, the e^(l - l*) terms are invariant expect_equal(out_warp3$mcse_logml, out_normal$mcse_logml, tolerance = 1e-10) }) test_that("MCSE roughly scales like 1/sqrt(n)", { skip_if_not_installed("Brobdingnag") base_q11 <- c(0.10, 0.20, 0.30, 0.40) base_q12 <- c(0.02, 0.09, 0.10, 0.15) base_q21 <- c(0.05, 0.18, 0.22, 0.28) base_q22 <- c(0.01, 0.07, 0.11, 0.12) L <- diag(2) # n out_n <- .run.iterative.scheme( q11 = base_q11, q12 = base_q12, q21 = base_q21, q22 = base_q22, r0 = 1, tol = 1e-10, L = L, method = "normal", maxiter = 1000, silent = TRUE, criterion = "r", neff = length(base_q11), use_ess = FALSE ) # 4n (replicate samples 4x) k <- 4 out_4n <- .run.iterative.scheme( q11 = rep(base_q11, k), q12 = rep(base_q12, k), q21 = rep(base_q21, k), q22 = rep(base_q22, k), r0 = 1, tol = 1e-10, L = L, method = "normal", maxiter = 1000, silent = TRUE, criterion = "r", neff = length(base_q11) * k, use_ess = FALSE ) # Expect MCSE to drop by ~ 1/sqrt(k) expect_lt(out_4n$mcse_logml, out_n$mcse_logml) expect_equal(out_4n$mcse_logml, out_n$mcse_logml / sqrt(k), tolerance = 0.05) # Deterministic value for the 4x replicated case expect_equal(out_4n$mcse_logml, 0.01052514482181162, tolerance = 1e-12) }) test_that("Function runs with use_ess = TRUE (if posterior installed)", { skip_if_not_installed("Brobdingnag") # if (!requireNamespace("posterior", quietly = TRUE)) { # skip("posterior not installed") # } ## uses coda currently q11 <- c(0.10, 0.20, 0.30, 0.40, 0.45, 0.5) q12 <- c(0.02, 0.09, 0.10, 0.15, 0.18, 0.2) q21 <- c(0.05, 0.18, 0.22, 0.28, 0.30, 0.35) q22 <- c(0.01, 0.07, 0.11, 0.12, 0.14, 0.15) L <- diag(2) out <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21, q22 = q22, r0 = 1, tol = 1e-10, L = L, method = "normal", maxiter = 1000, silent = TRUE, criterion = "r", neff = length(q11), use_ess = TRUE ) expect_true(is.finite(out$mcse_logml)) expect_gt(out$mcse_logml, 0) }) bridgesampling/tests/testthat/unnormalized_normal_density.cpp0000644000176200001440000000104515055304401024562 0ustar liggesusers// load Rcpp #include #include #include using namespace Rcpp; using Eigen::VectorXd; using Eigen::Map; //------------------------------------------------------------------------------ // unnormalized standard multivariate normal density function (log) //------------------------------------------------------------------------------ // [[Rcpp::depends(RcppEigen)]] // [[Rcpp::export]] double log_densityRcpp(NumericVector x, SEXP data) { VectorXd xe(as >(x)); return -0.5*xe.transpose()*xe; } bridgesampling/tests/testthat/test-vignette_example_jags.R0000644000176200001440000001707715060242566023731 0ustar liggesusers context('test vignette bridgesampling_example_jags.Rmd') test_that("bridge sampler yields correct results", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) if (require(R2jags)) { ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ### functions to get posterior samples ### # H0: mu = 0 getSamplesModelH0 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(0, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1, progress.bar = "none", quiet = TRUE) return(s) } # H1: mu != 0 getSamplesModelH1 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(mu, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } mu ~ dnorm(mu0, 1/tau20) invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "mu", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1, progress.bar = "none", quiet = TRUE) return(s) } ### get posterior samples ### # create data lists for JAGS data_H0 <- list(y = y, n = length(y), alpha = alpha, beta = beta, sigma2 = sigma2) data_H1 <- list(y = y, n = length(y), mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2) # fit models samples_H0 <- getSamplesModelH0(data_H0) samples_H1 <- getSamplesModelH1(data_H1) ### functions for evaluating the unnormalized posteriors on log scale ### log_posterior_H0 <- function(samples.row, data) { mu <- 0 invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } log_posterior_H1 <- function(samples.row, data) { mu <- samples.row[[ "mu" ]] invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dnorm(mu, data$mu0, sqrt(data$tau20), log = TRUE) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } # specify parameter bounds H0 cn <- colnames(samples_H0$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H0 <- rep(-Inf, length(cn)) ub_H0 <- rep(Inf, length(cn)) names(lb_H0) <- names(ub_H0) <- cn lb_H0[[ "invTau2" ]] <- 0 # specify parameter bounds H1 cn <- colnames(samples_H1$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H1 <- rep(-Inf, length(cn)) ub_H1 <- rep(Inf, length(cn)) names(lb_H1) <- names(ub_H1) <- cn lb_H1[[ "invTau2" ]] <- 0 # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(samples = samples_H0, data = data_H0, log_posterior = log_posterior_H0, lb = lb_H0, ub = ub_H0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(samples = samples_H1, data = data_H1, log_posterior = log_posterior_H1, lb = lb_H1, ub = ub_H1, silent = TRUE) # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) # "exact" ml H1 mH1 <- function(data, rel.tol = 1e-10) { y <- data$y n <- data$n mu0 <- data$mu0 tau20 <- data$tau20 alpha <- data$alpha beta <- data$beta sigma2 <- data$sigma2 mH1integrand <- function(tau2, y, sigma2, mu0, tau20, alpha, beta) { (sigma2 + tau2)^(-n/2) * exp(-1/2 * ((n*mean(y)^2 + (n - 1)*sd(y)^2)/(sigma2 + tau2) + mu0^2/tau20 - ((n*mean(y))/(sigma2 + tau2) + mu0/tau20)^2 / (n/(sigma2 + tau2) + 1/tau20))) * (n/(sigma2 + tau2) + 1/tau20)^(-1/2) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * (tau20)^(-1/2) * beta^alpha/gamma(alpha) * integrate(mH1integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta)$value } exact_logmlH1 <- log(mH1(data_H1)) # "exact" ml H1 mH0 <- function(data, rel.tol = 1e-10) { y <- data$y n <- data$n alpha <- data$alpha beta <- data$beta sigma2 <- data$sigma2 mH0integrand <- function(tau2, y, sigma2, alpha, beta) { n <- length(y) (sigma2 + tau2)^(-n/2) * exp(-(n*mean(y)^2 + (n - 1)*sd(y)^2)/ (2*(sigma2 + tau2))) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * beta^alpha/gamma(alpha) * integrate(mH0integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, alpha = alpha, beta = beta)$value } exact_logmlH0 <- log(mH0(data_H0)) exact_BF01 <- exp(exact_logmlH0 - exact_logmlH1) H0.bridge.curr <- H0.bridge H1.bridge.curr <- H1.bridge BF01.curr <- BF01 post1.curr <- post1 post2.curr <- post2 load(system.file("extdata/", "vignette_example_jags.RData", package = "bridgesampling")) expect_equal( H0.bridge.curr$logml, expected = exact_logmlH0, tolerance = 0.01 ) expect_equal( H1.bridge.curr$logml, expected = exact_logmlH1, tolerance = 0.01 ) expect_equal( BF01.curr$bf, expected = exact_BF01, tolerance = 0.01 ) expect_equal( H0.bridge.curr$logml, expected = H0.bridge$logml, tolerance = 0.01 ) expect_equal( H1.bridge.curr$logml, expected = H1.bridge$logml, tolerance = 0.01 ) expect_equal( BF01.curr$bf, expected = BF01$bf, tolerance = 0.01 ) expect_equal( post1.curr, expected = post1, tolerance = 0.01 ) expect_equal( post2.curr, expected = post2, tolerance = 0.01 ) } }) bridgesampling/tests/testthat/test-vignette_stan_ttest.R0000644000176200001440000001041715060242566023451 0ustar liggesusers context('test vignette bridgesampling_stan_ttest.Rmd') test_that("bridge sampler yields correct results", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) if (require(rstan) && require(BayesFactor)) { set.seed(12345) # Sleep data from t.test example data(sleep) # compute difference scores y <- sleep$extra[sleep$group == 2] - sleep$extra[sleep$group == 1] n <- length(y) # models stancodeH0 <- ' data { int n; // number of observations vector[n] y; // observations } parameters { real sigma2; // variance parameter } model { target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | 0, sqrt(sigma2)); // likelihood } ' stancodeH1 <- ' data { int n; // number of observations vector[n] y; // observations real r; // Cauchy prior scale } parameters { real delta; real sigma2;// variance parameter } model { target += cauchy_lpdf(delta | 0, r); // Cauchy prior on delta target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood } ' # compile models stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") # fit models stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n), iter = 20000, warmup = 1000, chains = 4, cores = 1, control = list(adapt_delta = .99), refresh = 0) stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, r = 1/sqrt(2)), iter = 20000, warmup = 1000, chains = 4, cores = 1, control = list(adapt_delta = .99), refresh = 0) set.seed(12345) suppressWarnings(H0 <- bridge_sampler(stanfitH0, silent = TRUE)) H1 <- bridge_sampler(stanfitH1, silent = TRUE) # compute percentage errors H0.error <- error_measures(H0)$percentage H1.error <- error_measures(H1)$percentage # compute Bayes factor BF10 <- bf(H1, H0) # BayesFactor result BF10.BayesFactor <- extractBF(ttestBF(y), onlybf = TRUE, logbf = FALSE) # one-sided test stancodeHplus <- ' data { int n; // number of observations vector[n] y; // observations real r; // Cauchy prior scale } parameters { real delta; // constrained to be positive real sigma2;// variance parameter } model { target += cauchy_lpdf(delta | 0, r) - cauchy_lccdf(0 | 0, r); // Cauchy prior on delta target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood } ' # compile and fit model stanmodelHplus <- stan_model(model_code = stancodeHplus, model_name="stanmodel") stanfitHplus <- sampling(stanmodelHplus, data = list(y = y, n = n, r = 1/sqrt(2)), iter = 30000, warmup = 1000, chains = 4, control = list(adapt_delta = .99), refresh = 0) Hplus <- bridge_sampler(stanfitHplus, silent = TRUE) Hplus.error <- error_measures(Hplus)$percentage # compute Bayes factor BFplus0 <- bf(Hplus, H0) BFplus0.BayesFactor <- extractBF(ttestBF(y, nullInterval = c(0, Inf)), onlybf = TRUE, logbf = FALSE)[1] H0.curr <- H0 H1.curr <- H1 Hplus.curr <- Hplus BF10.curr <- BF10 BFplus0.curr <- BFplus0 load(system.file("extdata/", "vignette_stan_ttest.RData", package = "bridgesampling")) expect_equal( H0.curr$logml, expected = H0$logml, tolerance = 0.01 ) expect_equal( H1.curr$logml, expected = H1$logml, tolerance = 0.01 ) expect_equal( BF10.curr$bf, expected = BF10$bf, tolerance = 0.01 ) expect_equal( BF10.curr$bf, expected = BF10.BayesFactor, tolerance = 0.03 ) expect_equal( BFplus0.curr$bf, expected = BFplus0$bf, tolerance = 0.01 ) expect_equal( BFplus0.curr$bf, expected = BFplus0.BayesFactor, tolerance = 0.03 ) } }) bridgesampling/tests/testthat/test-bf.R0000644000176200001440000000463215055304401017734 0ustar liggesusers context('bridge sampling bf function') test_that("bf various basic checks", { # library(bridgesampling) library(mvtnorm) x <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data) { -.5*t(s)%*%s } lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) # repetitions = 1 bridge_normal <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) expect_error(bf(bridge_normal, 4), "class 'bridge' or 'bridge_list'") BF <- bf(bridge_normal, bridge_warp3) log_BF <- bf(bridge_normal, bridge_warp3, log = TRUE) expect_output(print(BF), "Estimated Bayes factor") expect_output(print(log_BF), "Estimated log Bayes factor") BF2 <- bayes_factor(bridge_normal, bridge_warp3) log_BF2 <- bayes_factor(bridge_normal, bridge_warp3, log = TRUE) expect_output(print(BF2), "Estimated Bayes factor") expect_output(print(log_BF2), "Estimated log Bayes factor") # repetitions > 1 bridge_normal_mult <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_mult <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE, repetitions = 2) BF_mult <- bf(bridge_normal_mult, bridge_warp3_mult) log_BF_mult <- bf(bridge_normal_mult, bridge_warp3_mult, log = TRUE) expect_output(print(BF_mult), "based on medians") expect_output(print(log_BF_mult), "based on medians") ## bf with multi and singular objects expect_is(suppressWarnings(bf(bridge_normal_mult, bridge_normal)), "bf_bridge_list") expect_is(bf(bridge_normal, bridge_normal_mult), "bf_bridge") expect_error(bf(bridge_normal_mult, 4), "class 'bridge' or 'bridge_list'") # default BF <- bf(1, 2) log_BF <- bf(1, 2, log = TRUE) expect_output(print(BF), "Bayes factor") expect_output(print(log_BF), "Log Bayes factor") }) bridgesampling/tests/testthat/test_dat.txt0000644000176200001440000005616115055304401020621 0ustar liggesuserstest_dat <- list(M = 1500L, J = 5L, T = 3, E = 1, G = 3L, N = c(65, 106, 129), ii = c(276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84), jj = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), gg = c(2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2), g_all = c(116, 122, 251, 268, 72, 274, 215, 200, 106, 293, 57, 182, 31, 128, 142, 240, 138, 10, 267, 91, 266, 18, 247, 163, 271, 201, 29, 150, 51, 237, 20, 149, 139, 64, 48, 89, 109, 233, 288, 289, 99, 63, 5, 60, 133, 114, 199, 286, 78, 250, 115, 76, 100, 55, 154, 23, 43, 24, 234, 83, 73, 211, 75, 144, 280, 276, 179, 68, 90, 145, 261, 245, 8, 192, 74, 104, 207, 131, 290, 157, 61, 26, 81, 124, 174, 135, 93, 292, 143, 92, 32, 194, 140, 28, 12, 101, 253, 195, 4, 158, 298, 291, 282, 236, 9, 79, 86, 205, 184, 25, 137, 147, 198, 188, 213, 134, 127, 255, 7, 296, 180, 193, 120, 272, 129, 15, 259, 226, 181, 42, 80, 70, 222, 203, 35, 117, 126, 285, 110, 191, 177, 208, 283, 153, 56, 40, 187, 224, 162, 173, 130, 2, 22, 161, 221, 167, 209, 166, 17, 227, 156, 59, 33, 231, 13, 295, 186, 257, 225, 235, 84, 220, 65, 82, 284, 37, 146, 6, 27, 204, 254, 41, 218, 281, 275, 95, 45, 196, 297, 260, 248, 98, 165, 38, 206, 88, 228, 269, 278, 85, 136, 216, 151, 159, 175, 52, 3, 102, 77, 212, 16, 189, 256, 172, 229, 210, 223, 103, 141, 44, 71, 54, 277, 238, 123, 111, 19, 1, 34, 14, 96, 299, 241, 66, 49, 87, 21, 176, 243, 202, 160, 148, 185, 125, 113, 119, 263, 230, 94, 170, 155, 265, 264, 270, 249, 242, 279, 258, 183, 171, 50, 67, 168, 132, 169, 190, 262, 178, 287, 39, 217, 273, 152, 69, 219, 246, 53, 47, 97, 107, 46, 294, 58, 244, 108, 197, 300, 105, 112, 118, 164, 36, 252, 214, 11, 239, 62, 121, 30, 232), y = c(4, 3, 1, 2, 2, 2, 4, 4, 3, 2, 4, 1, 3, 2, 3, 2, 1, 2, 4, 4, 1, 3, 1, 2, 4, 2, 3, 4, 1, 3, 3, 3, 3, 2, 4, 4, 4, 4, 3, 3, 4, 2, 1, 2, 2, 3, 3, 3, 4, 2, 1, 4, 4, 4, 3, 4, 3, 2, 2, 3, 3, 4, 4, 2, 1, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 4, 4, 2, 3, 2, 3, 3, 3, 4, 3, 2, 4, 4, 4, 4, 2, 3, 4, 1, 3, 4, 4, 3, 3, 2, 2, 1, 4, 2, 3, 3, 1, 3, 2, 3, 2, 2, 2, 4, 3, 4, 1, 4, 4, 2, 1, 3, 4, 3, 4, 4, 3, 2, 2, 1, 2, 3, 3, 4, 2, 2, 4, 3, 1, 3, 3, 3, 4, 1, 4, 2, 3, 2, 4, 1, 4, 4, 3, 2, 2, 3, 3, 3, 4, 3, 3, 2, 4, 2, 4, 4, 2, 3, 4, 2, 4, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 4, 3, 2, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 2, 4, 4, 2, 2, 4, 3, 2, 3, 4, 4, 3, 1, 3, 2, 3, 3, 1, 3, 2, 2, 3, 3, 3, 1, 3, 4, 2, 4, 4, 4, 4, 2, 3, 3, 4, 3, 1, 4, 3, 3, 4, 4, 4, 4, 3, 2, 2, 3, 3, 4, 1, 2, 2, 3, 1, 4, 2, 2, 4, 3, 2, 3, 3, 3, 3, 1, 2, 3, 4, 3, 3, 1, 2, 3, 4, 2, 3, 4, 3, 2, 1, 4, 3, 3, 4, 3, 3, 4, 3, 3, 2, 4, 4, 1, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 2, 1, 4, 3, 2, 3, 3, 4, 3, 4, 4, 2, 1, 4, 3, 3, 1, 4, 2, 3, 4, 3, 3, 2, 4, 3, 2, 4, 4, 3, 4, 4, 4, 4, 4, 3, 3, 4, 2, 4, 4, 3, 3, 3, 4, 1, 4, 3, 4, 3, 3, 4, 3, 3, 2, 3, 1, 4, 4, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 2, 1, 1, 4, 2, 3, 2, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 2, 4, 3, 2, 4, 4, 4, 2, 3, 1, 1, 3, 4, 4, 3, 4, 3, 3, 3, 2, 4, 2, 3, 3, 3, 4, 1, 4, 3, 3, 1, 4, 4, 3, 4, 4, 3, 3, 4, 2, 3, 2, 1, 3, 4, 3, 3, 4, 4, 3, 3, 3, 4, 3, 4, 4, 4, 3, 3, 2, 4, 4, 2, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 2, 4, 4, 2, 2, 4, 2, 1, 3, 4, 4, 3, 2, 2, 3, 3, 3, 2, 4, 3, 4, 4, 2, 4, 3, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 3, 2, 3, 3, 4, 3, 4, 3, 2, 2, 4, 4, 2, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 2, 2, 4, 4, 3, 4, 4, 4, 4, 4, 2, 4, 4, 4, 3, 2, 3, 3, 3, 2, 2, 2, 4, 4, 4, 4, 3, 3, 4, 4, 2, 3, 4, 4, 3, 3, 4, 3, 4, 3, 3, 2, 3, 4, 3, 2, 4, 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4, 2, 4, 3, 4, 4, 4, 4, 3, 2, 3, 4, 1, 4, 4, 4, 3, 2, 3, 3, 2, 3, 1, 1, 2, 4, 4, 4, 3, 2, 3, 1, 3, 2, 2, 3, 2, 2, 4, 4, 4, 3, 3, 4, 4, 4, 3, 2, 3, 2, 4, 4, 4, 3, 3, 4, 3, 2, 4, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 4, 4, 3, 1, 4, 2, 4, 1, 4, 4, 4, 4, 4, 3, 3, 4, 1, 4, 2, 3, 3, 4, 2, 4, 3, 3, 3, 1, 3, 4, 2, 3, 4, 4, 4, 4, 1, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 2, 2, 3, 3, 4, 4, 3, 3, 4, 3, 3, 2, 4, 3, 2, 3, 3, 3, 3, 2, 3, 4, 3, 3, 4, 3, 4, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 1, 2, 4, 4, 4, 2, 2, 4, 4, 3, 3, 3, 3, 2, 4, 3, 3, 1, 3, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 2, 4, 4, 2, 4, 3, 4, 4, 3, 2, 4, 4, 4, 4, 2, 2, 2, 4, 3, 3, 3, 4, 4, 4, 2, 4, 2, 4, 4, 2, 1, 3, 4, 3, 3, 4, 3, 3, 4, 2, 2, 4, 3, 4, 1, 3, 3, 2, 4, 3, 2, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 3, 4, 4), obs_corr = structure(c(1, 1, 1, 0.51900000000000002, 0.626, 0.38700000000000001, 0.23699999999999999, 0.67900000000000005, 0.22800000000000001, 0.23999999999999999, 0.70999999999999996, 0.28199999999999997, 0.59999999999999998, 0.66000000000000003, 0.45500000000000002, 0.51900000000000002, 0.626, 0.38700000000000001, 1, 1, 1, 0.39400000000000002, 0.58199999999999996, 0.22700000000000001, 0.22700000000000001, 0.53900000000000003, 0.30599999999999999, 0.53700000000000003, 0.52600000000000002, 0.72199999999999998, 0.23699999999999999, 0.67900000000000005, 0.22800000000000001, 0.39400000000000002, 0.58199999999999996, 0.22700000000000001, 1, 1, 1, 0.49099999999999999, 0.68000000000000005, 0.52900000000000003, 0.46899999999999997, 0.56999999999999995, 0.44600000000000001, 0.23999999999999999, 0.70999999999999996, 0.28199999999999997, 0.22700000000000001, 0.53900000000000003, 0.30599999999999999, 0.49099999999999999, 0.68000000000000005, 0.52900000000000003, 1, 1, 1, 0.49299999999999999, 0.57199999999999995, 0.42899999999999999, 0.59999999999999998, 0.66000000000000003, 0.45500000000000002, 0.53700000000000003, 0.52600000000000002, 0.72199999999999998, 0.46899999999999997, 0.56999999999999995, 0.44600000000000001, 0.49299999999999999, 0.57199999999999995, 0.42899999999999999, 1, 1, 1), .Dim = c(3L, 5L, 5L))) bridgesampling/tests/testthat/test-bridge_sampler_print_method.R0000644000176200001440000000400415060242566025102 0ustar liggesusers context('bridge sampling print method') test_that("bridge sampler print method correctly displayed", { # library(bridgesampling) library(mvtnorm) x <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data) { -.5*t(s)%*%s } lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) # repetitions = 1 bridge_normal <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) expect_output(print(bridge_normal), "Bridge sampling estimate of the log marginal likelihood") expect_output(print(bridge_warp3), "Bridge sampling estimate of the log marginal likelihood") # repetitions > 1 bridge_normal <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE, repetitions = 2) expect_output(print(bridge_normal), "Median of") expect_output(print(bridge_warp3), "Median of") }) test_that("prints with NAs with warning.", { bridge_o <- structure(list(logml = c(4291.14352476047, 4293.29076119542, 4291.96372581169, 4293.02187182362, NA, NA, 4290.9761730488, 4293.32075269401, 4293.5762219227, 4294.02761288449), niter = c(104, 16, 52, 8, 1000, 1000, 167, 16, 21, 44), method = "normal", repetitions = 10), .Names = c("logml", "niter", "method", "repetitions"), class = "bridge_list") expect_output(expect_warning(print(bridge_o), "NA")) }) bridgesampling/tests/testthat/test-stanreg_bridge_sampler_basic.R0000644000176200001440000000242615060242566025220 0ustar liggesusers context('bridge_sampler.stanreg works.') test_that("stan_bridge_sampler", { testthat::skip_on_cran() testthat::skip_on_ci() if (require(rstanarm)) { fit_1 <- stan_glm(mpg ~ wt + qsec + am, data = mtcars, chains = 2, cores = 2, iter = 5000, diagnostic_file = file.path(tempdir(), "df.csv"), refresh = 0) bridge_norm <- bridge_sampler(fit_1, silent = TRUE) fit_2 <- update(fit_1, formula = . ~ . + cyl, refresh = 0) bridge_warp <- bridge_sampler(fit_2, method = "warp3", silent = TRUE) expect_true(bridge_norm$logml > bridge_warp$logml) } }) test_that("stan_bridge_sampler in multicore", { testthat::skip_on_cran() testthat::skip_on_ci() #testthat::skip_on_os("windows") if (require(rstanarm)) { fit_1 <- stan_glm(mpg ~ wt + qsec + am, data = mtcars, chains = 2, cores = 2, iter = 5000, diagnostic_file = file.path(tempdir(), "df.csv"), refresh = 0) bridge_norm <- bridge_sampler(fit_1, cores = 2, silent = TRUE) fit_2 <- update(fit_1, formula = . ~ . + cyl, refresh = 0) bridge_warp <- bridge_sampler(fit_2, method = "warp3", cores = 2, silent = TRUE) expect_true(bridge_norm$logml > bridge_warp$logml) } }) bridgesampling/tests/testthat/test-nimble_bridge_sampler.R0000644000176200001440000000335415060242566023663 0ustar liggesusers context('bridge_sampler.nimble works.') test_that("nimble support works", { testthat::skip_on_cran() testthat::skip_on_ci() testthat::skip_if_not_installed("nimble") if (require(nimble)) { set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) # create model codeH1 <- nimbleCode({ mu ~ dnorm(0, sd = 1) invTau2 ~ dgamma(1, 1) tau2 <- 1/invTau2 for (i in 1:20) { theta[i] ~ dnorm(mu, sd = sqrt(tau2)) y[i] ~ dnorm(theta[i], sd = 1) } }) capture.output(suppressMessages({ modelH1 <- nimbleModel(codeH1) modelH1$setData(y = y) # set data # make compiled version from generated C++ cmodelH1 <- compileNimble(modelH1) # build an MCMC, skipping customization of the configuration. mcmcH1 <- buildMCMC(modelH1, monitors = modelH1$getNodeNames(stochOnly = TRUE, includeData = FALSE)) # compile the MCMC via generated C++ cmcmcH1 <- compileNimble(mcmcH1, project = modelH1) # run the MCMC. This is a wrapper for cmcmc$run() and extraction of samples. # the object samplesH1 is actually not needed as the samples are also in cmcmcH1 samplesH1 <- runMCMC(cmcmcH1, niter = 1e5, nburnin = 1000, nchains = 2, progressBar = FALSE) })) # bridge sampling bridge_H1 <- bridge_sampler(samples = cmcmcH1, cores = 1, method = "warp3", repetitions = 2, silent = TRUE) expect_equal(bridge_H1$logml, rep(-37.7983064265064, 2), tolerance = 0.01) } }) bridgesampling/tests/testthat/test-log_posterior_cmdstan.R0000644000176200001440000001677215060116372023761 0ustar liggesuserscontext(".cmdstan_log_posterior helper function for CmdStanMCMC") test_that(".cmdstan_log_posterior and bridge_sampler agree with analytical results on an unconstrained model", { skip_on_cran() skip_if_not_installed("cmdstanr") skip_if_not_installed("posterior") skip_if_not_installed("bridgesampling") if (!file.exists(cmdstanr::cmdstan_path())) { skip("CmdStan is not installed in the expected path for cmdstanr.") } # Access the internal helper from bridgesampling pkg <- "bridgesampling" expect_true( exists(".cmdstan_log_posterior", envir = asNamespace(pkg), inherits = FALSE), info = "Internal function .cmdstan_log_posterior not found in 'bridgesampling'." ) .cmdstan_log_posterior <- get(".cmdstan_log_posterior", envir = asNamespace(pkg)) # Normal - Normal Data Model set.seed(321) N <- 40L sigma <- 1 y <- rnorm(N, 0.25, sigma) data_list <- list(N = N, y = y, sigma = sigma) stan_code <- " data { int N; vector[N] y; real sigma; } parameters { real mu; } model { mu ~ normal(0, 1); y ~ normal(mu, sigma); }" tf <- tempfile(fileext = ".stan") on.exit(unlink(tf), add = TRUE) writeLines(stan_code, tf) mod <- cmdstanr::cmdstan_model(tf, quiet = TRUE, force_recompile = TRUE) fit <- mod$sample( data = data_list, seed = 404, chains = 20, parallel_chains = 4, iter_warmup = 1000, iter_sampling = 10000, refresh = 0, show_messages = FALSE, show_exceptions = FALSE ) # 1) lp__ vs analytical log posterior (up to a constant) # Prior: mu ~ N(0,1); likelihood: y_i | mu ~ N(mu, sigma^2) logpost_mu <- function(mu, y, sigma) { -0.5 * mu^2 - sum((y - mu)^2) / (2 * sigma^2) } # Extract draws lp_df <- fit$draws(variables = "lp__", format = "df") expect_true(nrow(lp_df) > 10) lp_vec_all <- lp_df$lp__ mu_df <- fit$draws(variables = "mu", format = "df") expect_equal(nrow(mu_df), length(lp_vec_all)) mu_vec_all <- mu_df$mu lp_anal_all <- vapply(mu_vec_all, logpost_mu, numeric(1), y = y, sigma = sigma) # Compare up to additive constant: center both and compare lp_cent <- lp_vec_all - mean(lp_vec_all) anal_cent <- lp_anal_all - mean(lp_anal_all) expect_equal(lp_cent, anal_cent, tolerance = 1e-4) expect_gt(stats::cor(lp_vec_all, lp_anal_all), 0.99) # sanity check on correlation # 2) bridgesampling's internal q11 agrees with analytical log posterior bs_out <- bridgesampling::bridge_sampler( samples = fit, repetitions = 1, method = "normal", cores = 1L, use_neff = FALSE, silent = TRUE, verbose = FALSE ) n_all <- length(lp_vec_all) n_fit <- round(n_all / 2) idx_iter <- seq.int(n_fit + 1L, n_all) expect_equal(length(bs_out$q11), length(idx_iter)) # Compute analytical log posterior for the same subset of draws mu_iter <- mu_vec_all[idx_iter] lp_anal_iter <- vapply(mu_iter, logpost_mu, numeric(1), y = y, sigma = sigma) # Compare up to an additive constant by centering both q11_cent <- bs_out$q11 - mean(bs_out$q11) anal_iter_cent <- lp_anal_iter - mean(lp_anal_iter) expect_equal(unname(q11_cent), unname(anal_iter_cent), tolerance = 1e-4) expect_gt(stats::cor(bs_out$q11, lp_anal_iter), 0.99) # additional sanity check # 3) Spot-check the internal helper against lp__ directly upars <- fit$unconstrain_draws(format = "matrix") expect_equal(nrow(upars), length(lp_vec_all)) take <- seq_len(min(100L, nrow(upars))) direct_vals <- apply(upars[take, , drop = FALSE], 1, .cmdstan_log_posterior, data = fit) expect_type(direct_vals, "double") expect_length(direct_vals, length(take)) expect_equal(unname(direct_vals), unname(lp_vec_all[take]), tolerance = 1e-4) # 4) Basic input validation on the helper expect_error( .cmdstan_log_posterior(fit = "not-a-fit", data = list()), info = "Helper should reject invalid input when mis-called with named args." ) expect_error( .cmdstan_log_posterior(x = numeric(), data = fit), info = "Proper signature should reject badly shaped x." ) }) test_that("bridgesampling and .cmdstan_log_posterior handle constrained parameter correctly", { skip_on_cran() skip_if_not_installed("cmdstanr") skip_if_not_installed("posterior") skip_if_not_installed("bridgesampling") if (!file.exists(cmdstanr::cmdstan_path())) { skip("CmdStan is not installed in the expected path for cmdstanr.") } # Access bridgesampling's internal helper pkg <- "bridgesampling" expect_true( exists(".cmdstan_log_posterior", envir = asNamespace(pkg), inherits = FALSE), info = "Internal function .cmdstan_log_posterior not found in 'bridgesampling'." ) .cmdstan_log_posterior <- get(".cmdstan_log_posterior", envir = asNamespace(pkg)) # Stan model with constrained theta and simple Bernoulli likelihood bern_code <- " data { int N; array[N] int y; } parameters { real theta; } model { target += beta_lpdf(theta | 1, 1); // uniform prior on (0,1) target += bernoulli_lpmf(y | theta); // likelihood }" tf <- tempfile(fileext = ".stan") on.exit(unlink(tf), add = TRUE) writeLines(bern_code, tf) mod <- cmdstanr::cmdstan_model(tf, quiet = TRUE, force_recompile = TRUE) # Data data_bern <- list(N = 10L, y = c(1, 1, 1, 0, 1, 1, 1, 0, 1, 0)) fit <- mod$sample( data = data_bern, seed = 777, chains = 8, parallel_chains = 4, iter_warmup = 1000, iter_sampling = 8000, refresh = 0, show_messages = FALSE, show_exceptions = FALSE ) # Analytical log-posterior on the UNCONSTRAINED space y_ <- data_bern$y N_ <- data_bern$N s_ <- sum(y_) logpost_unconstrained <- function(theta, s, N) { # Prior Beta(1,1) contributes only a constant # Likelihood + Jacobian s * log(theta) + (N - s) * log1p(-theta) + log(theta * (1 - theta)) } lp_df <- fit$draws(variables = "lp__", format = "df") expect_true(nrow(lp_df) > 10) lp_vec_all <- lp_df$lp__ th_df <- fit$draws(variables = "theta", format = "df") expect_equal(nrow(th_df), length(lp_vec_all)) theta_all <- th_df$theta lp_anal_all <- vapply(theta_all, logpost_unconstrained, numeric(1), s = s_, N = N_) lp_cent <- lp_vec_all - mean(lp_vec_all) anal_cent <- lp_anal_all - mean(lp_anal_all) expect_equal(lp_cent, anal_cent, tolerance = 1e-4) expect_gt(stats::cor(lp_vec_all, lp_anal_all), 0.99) bs_out <- bridgesampling::bridge_sampler( samples = fit, repetitions = 1, method = "normal", cores = 1L, use_neff = FALSE, silent = TRUE, verbose = FALSE ) n_all <- length(lp_vec_all) n_fit <- round(n_all / 2) idx_iter <- seq.int(n_fit + 1L, n_all) expect_equal(length(bs_out$q11), length(idx_iter)) theta_iter <- theta_all[idx_iter] lp_anal_iter <- vapply(theta_iter, logpost_unconstrained, numeric(1), s = s_, N = N_) q11_cent <- bs_out$q11 - mean(bs_out$q11) anal_iter_cent <- lp_anal_iter - mean(lp_anal_iter) expect_equal(unname(q11_cent), unname(anal_iter_cent), tolerance = 1e-4) expect_gt(stats::cor(bs_out$q11, lp_anal_iter), 0.99) upars <- fit$unconstrain_draws(format = "matrix") expect_equal(nrow(upars), length(lp_vec_all)) take <- seq_len(min(100L, nrow(upars))) direct_vals <- apply(upars[take, , drop = FALSE], 1, .cmdstan_log_posterior, data = fit) expect_type(direct_vals, "double") expect_length(direct_vals, length(take)) expect_equal(unname(direct_vals), unname(lp_vec_all[take]), tolerance = 1e-4) }) bridgesampling/tests/testthat/test-bridge_sampler_summary_method.R0000644000176200001440000000525515055304401025443 0ustar liggesusers context('bridge sampling summary method') test_that("bridge sampler summary method correctly displayed", { # library(bridgesampling) library(mvtnorm) x <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data) { -.5*t(s)%*%s } lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) # repetitions = 1 bridge_normal <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) s_normal <- summary(bridge_normal) s_warp3 <- summary(bridge_warp3) expect_equal(names(s_normal), c("Logml_Estimate", "Relative_Mean_Squared_Error", "Coefficient_of_Variation", "Percentage_Error", "Method", "Repetitions")) expect_equal(names(s_warp3), c("Logml_Estimate", "Method", "Repetitions")) expect_output(print(s_normal), 'All error measures are approximate.') expect_output(print(s_warp3), 'No error measures are available for method = "warp3"') # repetitions > 1 bridge_normal_2 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_2 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE, repetitions = 2) s_normal_2 <- summary(bridge_normal_2) s_warp3_2 <- summary(bridge_warp3_2) expect_equal(names(s_normal_2), c("Logml_Estimate", "Min", "Max", "Interquartile_Range", "Method", "Repetitions")) expect_equal(names(s_warp3_2), c("Logml_Estimate", "Min", "Max", "Interquartile_Range", "Method", "Repetitions")) expect_output(print(s_normal_2), 'All error measures are based on 2 estimates.') expect_output(print(s_warp3_2), 'All error measures are based on 2 estimates.') }) bridgesampling/tests/testthat/test-bridge_sampler_mcmc.list.R0000644000176200001440000003070215060242566024303 0ustar liggesusers context('test bridge_sampler mcmc.list method') test_that("bridge sampler matches analytical value", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) if (require(R2jags) && require(runjags)) { ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ### function to get posterior samples ### # H1: mu != 0 getSamplesModelH1 <- function(data, niter = 12000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(mu, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } mu ~ dnorm(mu0, 1/tau20) invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "mu", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1, progress.bar = "none", quiet = TRUE) return(s) } getSamplesModelH1_runjags <- function(data, niter = 12000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(mu, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } mu ~ dnorm(mu0, 1/tau20) invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" capture_output(s <- suppressWarnings(runjags::run.jags(model = model, data = data, monitor = c("theta", "mu", "invTau2"), n.chains = 3, burnin = 2000, sample = 10000, silent.jags = TRUE))) return(s) } ### get posterior samples ### # create data list for Jags data_H1 <- list(y = y, n = length(y), mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2) # fit model samples_H1 <- getSamplesModelH1(data_H1) samples_runjags <- getSamplesModelH1_runjags(data_H1) ### function for evaluating the unnormalized posterior on log scale ### log_posterior_H1 <- function(samples.row, data) { mu <- samples.row[[ "mu" ]] invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dnorm(mu, data$mu0, sqrt(data$tau20), log = TRUE) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } # specify parameter bounds cn <- colnames(samples_H1$BUGSoutput$sims.matrix) lb_H1 <- rep(-Inf, length(cn) - 1) ub_H1 <- rep(Inf, length(cn) - 1) names(lb_H1) <- names(ub_H1) <- cn[cn != "deviance"] lb_H1[[ "invTau2" ]] <- 0 samples1 <- coda::as.mcmc(samples_H1) samples1 <- samples1[,cn != "deviance"] # mcmc.list bridge_normal <- bridge_sampler(samples = samples1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3 <- bridge_sampler(samples = samples1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2) bridge_normal_m <- bridge_sampler(samples = samples1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2, cores = 2) bridge_warp3_m <- bridge_sampler(samples = samples1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2, cores = 2) # mcmc bridge_normal_s <- bridge_sampler(samples = samples1[[1]], log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_s <- bridge_sampler(samples = samples1[[1]], log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2) bridge_normal_m_s <- bridge_sampler(samples = samples1[[1]], log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2, cores = 2) bridge_warp3_m_s <- bridge_sampler(samples = samples1[[1]], log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2, cores = 2) # rjags bridge_normal_j <- bridge_sampler(samples = samples_H1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_j <- bridge_sampler(samples = samples_H1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2) bridge_normal_jm <- bridge_sampler(samples = samples_H1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2, cores = 2) bridge_warp3_jm <- bridge_sampler(samples = samples_H1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2, cores = 2) # runjags bridge_normal_r <- bridge_sampler(samples = samples_runjags, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_r <- bridge_sampler(samples = samples_runjags, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2) bridge_normal_rm <- bridge_sampler(samples = samples_runjags, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "normal", silent = TRUE, repetitions = 2, cores = 2) bridge_warp3_rm <- bridge_sampler(samples = samples_runjags, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H1, method = "warp3", silent = TRUE, repetitions = 2, cores = 2) # "exact" ml mH1 <- function(data, rel.tol = 1e-10) { y <- data$y n <- data$n mu0 <- data$mu0 tau20 <- data$tau20 alpha <- data$alpha beta <- data$beta sigma2 <- data$sigma2 mH1integrand <- function(tau2, y, sigma2, mu0, tau20, alpha, beta) { (sigma2 + tau2)^(-n/2) * exp(-1/2 * ((n*mean(y)^2 + (n - 1)*sd(y)^2)/(sigma2 + tau2) + mu0^2/tau20 - ((n*mean(y))/(sigma2 + tau2) + mu0/tau20)^2 / (n/(sigma2 + tau2) + 1/tau20))) * (n/(sigma2 + tau2) + 1/tau20)^(-1/2) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * (tau20)^(-1/2) * beta^alpha/gamma(alpha) * integrate(mH1integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta)$value } exact_logml <- log(mH1(data_H1)) expect_equal(class(samples1), expected = "mcmc.list") expect_equal( bridge_normal$logml, expected = rep(exact_logml, length(bridge_normal$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3$logml, expected = rep(exact_logml, length(bridge_warp3$logml)), tolerance = 0.01 ) expect_equal( bridge_normal_m$logml, expected = rep(exact_logml, length(bridge_normal_m$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3_m$logml, expected = rep(exact_logml, length(bridge_warp3_m$logml)), tolerance = 0.01 ) expect_equal(class(samples1[[1]]), expected = "mcmc") expect_equal( bridge_normal_s$logml, expected = rep(exact_logml, length(bridge_normal_s$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3_s$logml, expected = rep(exact_logml, length(bridge_warp3_s$logml)), tolerance = 0.01 ) expect_equal( bridge_normal_m_s$logml, expected = rep(exact_logml, length(bridge_normal_m_s$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3_m_s$logml, expected = rep(exact_logml, length(bridge_warp3_m_s$logml)), tolerance = 0.01 ) expect_equal(class(samples_H1), expected = "rjags") expect_equal( bridge_normal_j$logml, expected = rep(exact_logml, length(bridge_normal_j$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3_j$logml, expected = rep(exact_logml, length(bridge_warp3_j$logml)), tolerance = 0.01 ) expect_equal( bridge_normal_jm$logml, expected = rep(exact_logml, length(bridge_normal_jm$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3_jm$logml, expected = rep(exact_logml, length(bridge_warp3_jm$logml)), tolerance = 0.01 ) expect_equal(class(samples_runjags), expected = "runjags") expect_equal( bridge_normal_r$logml, expected = rep(exact_logml, length(bridge_normal_r$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3_r$logml, expected = rep(exact_logml, length(bridge_warp3_r$logml)), tolerance = 0.01 ) expect_equal( bridge_normal_rm$logml, expected = rep(exact_logml, length(bridge_normal_rm$logml)), tolerance = 0.01 ) expect_equal( bridge_warp3_rm$logml, expected = rep(exact_logml, length(bridge_warp3_rm$logml)), tolerance = 0.01 ) ### check that wrong lb and ub produce errors: ub_H0 <- ub_H1[-2] lb_H0 <- lb_H1[-1] expect_error( bridge_sampler( samples = samples_runjags, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H0 ), "ub does not contain all parameters" ) expect_error( bridge_sampler( samples = samples_runjags, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H0, ub = ub_H1 ), "lb does not contain all parameters" ) expect_error( bridge_sampler( samples = samples1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H0 ), "ub does not contain all parameters" ) expect_error( bridge_sampler( samples = samples1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H0, ub = ub_H1 ), "lb does not contain all parameters" ) expect_error( bridge_sampler( samples = samples_H1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H0, ub = ub_H1 ), "lb does not contain all parameters" ) expect_error( bridge_sampler( samples = samples_H1, log_posterior = log_posterior_H1, data = data_H1, lb = lb_H1, ub = ub_H0 ), "ub does not contain all parameters" ) } }) bridgesampling/tests/testthat/test-bridge_sampler.R0000644000176200001440000002722615055304401022330 0ustar liggesusers context('basic bridge sampling behavior normal') test_that("bridge sampler matches anlytical value normal example", { # library(bridgesampling) library(mvtnorm) x <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data) { -.5*t(s)%*%s } assign(x = "log_density", value = log_density, envir = .GlobalEnv) lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) # check repetitions > 1 bridge_normal <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE, repetitions = 2) bridge_normal_c <- bridge_sampler(samples = x, log_posterior = "log_density", data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_c <- bridge_sampler(samples = x, log_posterior = "log_density", data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE, repetitions = 2) expect_equal(bridge_normal$logml, expected = rep(log(2*pi), length(bridge_normal$logml)), tolerance = 0.01) expect_equal(bridge_warp3$logml, expected = rep(log(2*pi), length(bridge_warp3$logml)), tolerance = 0.01) expect_equal(bridge_normal_c$logml, expected = rep(log(2*pi), length(bridge_normal_c$logml)), tolerance = 0.01) expect_equal(bridge_warp3_c$logml, expected = rep(log(2*pi), length(bridge_warp3_c$logml)), tolerance = 0.01) expect_equal(bf(bridge_normal, bridge_warp3)$bf, expected = rep(1, 2), tolerance = 0.1) # check repetitions = 1 bridge_normal <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) bridge_normal_c <- bridge_sampler(samples = x, log_posterior = "log_density", data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3_c <- bridge_sampler(samples = x, log_posterior = "log_density", data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) expect_equal(bridge_normal$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_normal_c$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3_c$logml, expected = log(2*pi), tolerance = 0.01) # check using dots repetitions > 1 mu <- c(1, 2) x <- rmvnorm(1e4, mean = mu, sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data, ...) { -.5*t(s - mu) %*% (s - mu) } assign(x = "log_density", value = log_density, envir = .GlobalEnv) lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) bridge_normal_dots <- bridge_sampler(samples = x, log_posterior = log_density, mu, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_dots <- bridge_sampler(samples = x, log_posterior = log_density, mu, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_normal_c_dots <- bridge_sampler(samples = x, log_posterior = "log_density", mu, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE, repetitions = 2) bridge_warp3_c_dots <- bridge_sampler(samples = x, log_posterior = "log_density", mu, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE, repetitions = 2) expect_equal(bridge_normal_dots$logml, expected = rep(log(2*pi), length(bridge_normal_dots$logml)), tolerance = 0.01) expect_equal(bridge_warp3_dots$logml, expected = rep(log(2*pi), length(bridge_warp3_dots$logml)), tolerance = 0.01) expect_equal(bridge_normal_c_dots$logml, expected = rep(log(2*pi), length(bridge_normal_c_dots$logml)), tolerance = 0.01) expect_equal(bridge_warp3_c_dots$logml, expected = rep(log(2*pi), length(bridge_warp3_c_dots$logml)), tolerance = 0.01) # check using dots mu <- c(1, 2) x <- rmvnorm(1e4, mean = mu, sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data, ...) { -.5*t(s - mu) %*% (s - mu) } assign(x = "log_density", value = log_density, envir = .GlobalEnv) lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) bridge_normal_dots <- bridge_sampler(samples = x, log_posterior = log_density, mu, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3_dots <- bridge_sampler(samples = x, log_posterior = log_density, mu, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_normal_c_dots <- bridge_sampler(samples = x, log_posterior = "log_density", mu, data = NULL, lb = lb, ub = ub, method = "normal", silent = TRUE) bridge_warp3_c_dots <- bridge_sampler(samples = x, log_posterior = "log_density", mu, data = NULL, lb = lb, ub = ub, method = "warp3", silent = TRUE) expect_equal(bridge_normal_dots$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3_dots$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_normal_c_dots$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3_c_dots$logml, expected = log(2*pi), tolerance = 0.01) # check error_measures err <- error_measures(bridge_normal) expect_equal(names(err), c("re2", "cv", "percentage")) expect_is(unlist(err), "character") expect_error(error_measures(bridge_warp3), "not implemented for warp3") ### these are meant to check the bf and post_prob functions and not as a meaningful comparisons bf <- bf(bridge_normal, bridge_warp3) expect_is(bf$bf, "numeric") # without prior_prob post1 <- post_prob(bridge_normal, bridge_warp3, bridge_normal_c, bridge_warp3_c) expect_equal(sum(post1), 1) # with prior_prob post2 <- post_prob(bridge_normal, bridge_warp3, bridge_normal_c, bridge_warp3_c, prior_prob = c(0.2, 0.1, 0.25, 0.45)) expect_equal(sum(post2), 1) # with incorrect prior_prob expect_error(post_prob(bridge_normal, bridge_warp3, bridge_normal_c, bridge_warp3_c, prior_prob = c(0.2, 0.1, 0.25, 0.55)), "do not sum to one") }) context('non-standard parameter spaces') test_that("bridge sampler functions for non-standard parameter spaces", { # Test with only simplex ru <- replicate(10, runif(10)) theta <- (ru / rowSums(ru))[, -10] colnames(theta) <- paste0("sim", 1:9) theta_t <- .transform2Real(theta, lb = rep(0, 9), ub = rep(1, 9), theta_types = rep("simplex", 9)) expect_equal(theta_t$transTypes[1], c(sim1 = "simplex")) theta_t_t <- .invTransform2Real(theta_t$theta_t, lb = rep(0, 9), ub = rep(1, 9), theta_types = rep("simplex", 9)) expect_equal(theta, theta_t_t) # tranformations work for different input shapes nsimp <- 4 n <- 100 sum_to_one <- function(x) x / sum(x) ru <- t(replicate(n, c(rnorm(2), # unbounded sum_to_one(runif(nsimp)), # simplex runif(3), # double-bounded abs(rnorm(1)), # lower-bounded rnorm(2) %% (2*pi)))) # circular theta_original <- ru[, -(nsimp + 2)] pt <- c(rep("real", 2), rep("simplex", nsimp - 1), rep("real", 4), rep("circular", 2)) lb <- c(rep(-Inf, 2), rep(0, nsimp - 1), rep(0, 4), rep(0, 2)) ub <- c(rep(Inf, 2), rep(1, nsimp - 1), rep(1, 3), rep(Inf, 1), rep(2*pi, 2)) nm <- c(paste0("unbounded", 1:2), paste0("simplex", 1:(nsimp - 1)), paste0("doublebounded", 1:3), paste0("lower", 1), paste0("circular", 1:2)) colnames(theta_original) <- names(lb) <- names(ub) <- names(pt) <- nm theta_t <- .transform2Real(theta_original, lb, ub, pt) theta_t_t <- .invTransform2Real(theta_t$theta_t, lb, ub, pt) # The modulus is to force the circular variables to be equal if they lie on # the same place on the circle. The modulus is also taken for the linear # variables, for simplicity of programming. expect_equal(theta_original %% (2*pi), theta_t_t %% (2*pi)) # Works with one row theta <- theta_original[1, , drop = FALSE] theta_t <- .transform2Real(theta, lb, ub, pt) theta_t_t <- .invTransform2Real(theta_t$theta_t, lb, ub, pt) # The modulus is to force the circular variables to be equal if they lie on # the same place on the circle. expect_equal(theta %% (2*pi), theta_t_t %% (2*pi)) # Test bridge sampler function with non-standard sample spaces bs_ns <- bridge_sampler.matrix( theta_original, data = rnorm(10), log_posterior = function(s, data) -.5*t(s) %*% s, lb = lb, ub = ub, silent = TRUE, verbose = FALSE) expect_true(class(bs_ns) == "bridge") ############ TEST JACOBIAN n <- 2 theta_full <- t(c(.4, .6)) theta <- theta_full[, -n, drop = FALSE] colnames(theta) <- paste0("sim", (1:(n - 1))) y <- bridgesampling:::.transform2Real(theta, lb = rep(0, n - 1), ub = rep(1, n - 1), theta_types = rep("simplex", n - 1))$theta_t tt <- rep("simplex", n - 1) colnames(y) <- paste0("trans_sim", (1:(n - 1))) names(tt) <- paste0("sim", (1:(n - 1))) jacob <- .logJacobian(y, tt, lb = rep(0, n), ub = rep(1, n)) expect_true(is.numeric(jacob)) skip_if_not_installed("MCMCpack") invsimplex <- function(y) { y <- as.matrix(y) n <- length(y) colnames(y) <- paste0("trans_sim", (1:n)) out1 <- .invTransform2Real(y, lb = rep(0, n), ub = rep(1, n), theta_types = rep("simplex", n)) c(out1, 1 - sum(out1)) } invsimplex(100) p_y <- function(y) { y <- as.matrix(y) n <- length(y) tt <- rep("simplex", n) colnames(y) <- paste0("trans_sim", (1:n)) names(tt) <- paste0("sim", (1:n)) MCMCpack::ddirichlet(invsimplex(y), theta_full*10) * exp(.logJacobian(y, tt, lb = rep(0, n), ub = rep(1, n))) } # The jaobian corrects for the transformation expect_equal(integrate(Vectorize(p_y), -100, 100)$value, 1) }) bridgesampling/tests/testthat/test-bridge_sampler_Rcpp_parallel.R0000644000176200001440000000542015060242566025171 0ustar liggesusers context('basic bridge sampling behavior normal Rcpp parallel') test_that("bridge sampler matches anlytical value normal example", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) library(mvtnorm) if(require(RcppEigen)) { x <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(x) <- c("x1", "x2") lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) Rcpp::sourceCpp(file = "unnormalized_normal_density.cpp") Rcpp::sourceCpp(file = "unnormalized_normal_density.cpp", env = .GlobalEnv) bridge_normal <- bridge_sampler(samples = x, log_posterior = "log_densityRcpp", data = NULL, lb = lb, ub = ub, method = "normal", packages = "RcppEigen", rcppFile = "unnormalized_normal_density.cpp", cores = 2, silent = TRUE) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = "log_densityRcpp", data = NULL, lb = lb, ub = ub, method = "warp3", packages = "RcppEigen", rcppFile = "unnormalized_normal_density.cpp", cores = 2, silent = TRUE) expect_equal(bridge_normal$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3$logml, expected = log(2*pi), tolerance = 0.01) # test dots argument mu <- c(1, 2) x <- rmvnorm(1e4, mean = mu, sigma = diag(2)) colnames(x) <- c("x1", "x2") lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) Rcpp::sourceCpp(file = "unnormalized_normal_density_mu.cpp") Rcpp::sourceCpp(file = "unnormalized_normal_density_mu.cpp", env = .GlobalEnv) bridge_normal_dots <- bridge_sampler(samples = x, log_posterior = "log_densityRcpp_mu", mu, data = NULL, lb = lb, ub = ub, method = "normal", packages = "RcppEigen", rcppFile = "unnormalized_normal_density_mu.cpp", cores = 2, silent = TRUE) bridge_warp3_dots <- bridge_sampler(samples = x, log_posterior = "log_densityRcpp_mu", mu, data = NULL, lb = lb, ub = ub, method = "warp3", packages = "RcppEigen", rcppFile = "unnormalized_normal_density_mu.cpp", cores = 2, silent = TRUE) expect_equal(bridge_normal_dots$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3_dots$logml, expected = log(2*pi), tolerance = 0.01) } }) bridgesampling/tests/testthat/test-vignette_example_nimble.R0000644000176200001440000001445715060242566024252 0ustar liggesusers context('test vignette bridgesampling_example_nimble.Rmd') test_that("bridge sampler yields correct results", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) if (require(nimble)) { ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 # models codeH0 <- nimbleCode({ invTau2 ~ dgamma(1, 1) tau2 <- 1/invTau2 for (i in 1:20) { theta[i] ~ dnorm(0, sd = sqrt(tau2)) y[i] ~ dnorm(theta[i], sd = 1) } }) codeH1 <- nimbleCode({ mu ~ dnorm(0, sd = 1) invTau2 ~ dgamma(1, 1) tau2 <- 1/invTau2 for (i in 1:20) { theta[i] ~ dnorm(mu, sd = sqrt(tau2)) y[i] ~ dnorm(theta[i], sd = 1) } }) ## steps for H0: capture.output(suppressMessages(modelH0 <- nimbleModel(codeH0))) modelH0$setData(y = y) # set data cmodelH0 <- compileNimble(modelH0) # make compiled version from generated C++ ## steps for H1: capture.output(suppressMessages(modelH1 <- nimbleModel(codeH1))) modelH1$setData(y = y) # set data cmodelH1 <- compileNimble(modelH1) # make compiled version from generated C++ # build MCMC functions, skipping customization of the configuration. capture.output(suppressMessages({ mcmcH0 <- buildMCMC(modelH0, monitors = modelH0$getNodeNames(stochOnly = TRUE, includeData = FALSE)) mcmcH1 <- buildMCMC(modelH1, monitors = modelH1$getNodeNames(stochOnly = TRUE, includeData = FALSE)) })) # compile the MCMC function via generated C++ cmcmcH0 <- compileNimble(mcmcH0, project = modelH0) cmcmcH1 <- compileNimble(mcmcH1, project = modelH1) # run the MCMC. This is a wrapper for cmcmc$run() and extraction of samples. # the object samplesH1 is actually not needed as the samples are also in cmcmcH1 samplesH0 <- runMCMC(cmcmcH0, niter = 1e5, nburnin = 1000, nchains = 2, progressBar = FALSE) samplesH1 <- runMCMC(cmcmcH1, niter = 1e5, nburnin = 1000, nchains = 2, progressBar = FALSE) # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(cmcmcH0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(cmcmcH1, silent = TRUE) # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) # "exact" ml H1 mH1 <- function(data, rel.tol = 1e-10) { y <- data$y n <- data$n mu0 <- data$mu0 tau20 <- data$tau20 alpha <- data$alpha beta <- data$beta sigma2 <- data$sigma2 mH1integrand <- function(tau2, y, sigma2, mu0, tau20, alpha, beta) { (sigma2 + tau2)^(-n/2) * exp(-1/2 * ((n*mean(y)^2 + (n - 1)*sd(y)^2)/(sigma2 + tau2) + mu0^2/tau20 - ((n*mean(y))/(sigma2 + tau2) + mu0/tau20)^2 / (n/(sigma2 + tau2) + 1/tau20))) * (n/(sigma2 + tau2) + 1/tau20)^(-1/2) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * (tau20)^(-1/2) * beta^alpha/gamma(alpha) * integrate(mH1integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta)$value } exact_logmlH1 <- log(mH1(list(y = y, n = n, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2))) # "exact" ml H1 mH0 <- function(data, rel.tol = 1e-10) { y <- data$y n <- data$n alpha <- data$alpha beta <- data$beta sigma2 <- data$sigma2 mH0integrand <- function(tau2, y, sigma2, alpha, beta) { n <- length(y) (sigma2 + tau2)^(-n/2) * exp(-(n*mean(y)^2 + (n - 1)*sd(y)^2)/ (2*(sigma2 + tau2))) * tau2^(-alpha - 1) * exp(-beta/tau2) } (2*pi)^(-n/2) * beta^alpha/gamma(alpha) * integrate(mH0integrand, 0, Inf, rel.tol = rel.tol, y = y, sigma2 = sigma2, alpha = alpha, beta = beta)$value } exact_logmlH0 <- log(mH0(list(y = y, n = n, alpha = alpha, beta = beta, sigma2 = sigma2))) exact_BF01 <- exp(exact_logmlH0 - exact_logmlH1) H0.bridge.curr <- H0.bridge H1.bridge.curr <- H1.bridge BF01.curr <- BF01 post1.curr <- post1 post2.curr <- post2 # load(system.file("extdata/", "vignette_example_nimble.RData", # package = "bridgesampling")) expect_equal( H0.bridge.curr$logml, expected = exact_logmlH0, tolerance = 0.01 ) expect_equal( H1.bridge.curr$logml, expected = exact_logmlH1, tolerance = 0.01 ) expect_equal( BF01.curr$bf, expected = exact_BF01, tolerance = 0.01 ) expect_equal( H0.bridge.curr$logml, expected = H0.bridge$logml, tolerance = 0.01 ) expect_equal( H1.bridge.curr$logml, expected = H1.bridge$logml, tolerance = 0.01 ) expect_equal( BF01.curr$bf, expected = BF01$bf, tolerance = 0.01 ) expect_equal( post1.curr, expected = post1, tolerance = 0.01 ) expect_equal( post2.curr, expected = post2, tolerance = 0.01 ) } }) bridgesampling/tests/testthat/test-bridge_sampler_parallel.R0000644000176200001440000000712315060242566024207 0ustar liggesusers context('basic bridge sampling behavior normal parallel') test_that("bridge sampler matches anlytical value normal example", { testthat::skip_on_cran() testthat::skip_on_ci() # library(bridgesampling) library(mvtnorm) x <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data) { -.5*t(s)%*%s } assign("log_density", log_density, envir = .GlobalEnv) lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) bridge_normal <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "normal", cores = 2, silent = TRUE) bridge_warp3 <- bridge_sampler(samples = x, log_posterior = log_density, data = NULL, lb = lb, ub = ub, method = "warp3", cores = 2, silent = TRUE) bridge_normal_c <- bridge_sampler(samples = x, log_posterior = "log_density", data = NULL, lb = lb, ub = ub, method = "normal", cores = 2, silent = TRUE, envir = sys.frame(sys.nframe())) bridge_warp3_c <- bridge_sampler(samples = x, log_posterior = "log_density", data = NULL, lb = lb, ub = ub, method = "warp3", cores = 2, silent = TRUE, envir = sys.frame(sys.nframe())) expect_equal(bridge_normal$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_normal_c$logml, expected = log(2*pi), tolerance = 0.01) expect_equal(bridge_warp3_c$logml, expected = log(2*pi), tolerance = 0.01) # test dots argument mu <- c(1, 2) x <- rmvnorm(1e4, mean = mu, sigma = diag(2)) colnames(x) <- c("x1", "x2") log_density <- function(s, data, ...) { -.5*t(s - mu) %*% (s - mu) } assign("log_density", log_density, envir = .GlobalEnv) lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(x) bridge_normal_dots <- bridge_sampler(samples = x, log_posterior = log_density, mu, data = NULL, lb = lb, ub = ub, method = "normal", cores = 2, silent = TRUE) bridge_warp3_dots <- bridge_sampler(samples = x, log_posterior = log_density, mu, data = NULL, lb = lb, ub = ub, method = "warp3", cores = 2, silent = TRUE) bridge_normal_c_dots <- bridge_sampler(samples = x, log_posterior = "log_density", mu, data = NULL, lb = lb, ub = ub, method = "normal", cores = 2, silent = TRUE, envir = sys.frame(sys.nframe())) # ls.str(envir = sys.frame(sys.nframe())) bridge_warp3_c_dots <- bridge_sampler(samples = x, log_posterior = "log_density", mu, data = NULL, lb = lb, ub = ub, method = "warp3", cores = 2, silent = TRUE, envir = sys.frame(sys.nframe())) expect_equal(bridge_normal_dots$logml, expected = log(2*pi), tolerance = 0.01) 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*vignettes/bridgesampling_tutorial.pdf.asis bridgesampling/R/0000755000176200001440000000000015060243416013443 5ustar liggesusersbridgesampling/R/bridge_methods.R0000644000176200001440000001172115060266335016554 0ustar liggesusers#' Methods for bridge and bridge_list objects #' #' Methods defined for objects returned from the generic \code{\link{bridge_sampler}} function. #' #' @param object,x object of class \code{bridge} or \code{bridge_list} as returned from \code{\link{bridge_sampler}}. #' @param na.rm logical. Should NA estimates in \code{bridge_list} objects be removed? Passed to \code{\link{error_measures}}. #' @param ... further arguments, currently ignored. #' #' @return #' The \code{summary} methods return a \code{data.frame} which contains the log marginal likelihood plus the result returned from invoking \code{\link{error_measures}}. #' #' The \code{print} methods simply print and return nothing. #' #' #' @name bridge-methods NULL # summary methods #' @rdname bridge-methods #' @method summary bridge #' @export summary.bridge <- function(object, na.rm = TRUE, ...) { if (!(object$method %in% c("normal", "warp3"))) { stop('object$method needs to be either "normal" or "warp3".', call. = FALSE) } if (object$method == "normal") { em <- error_measures(object) out <- data.frame( "Logml_Estimate" = object$logml, "Relative_Mean_Squared_Error" = em$re2, "Coefficient_of_Variation" = em$cv, "Percentage_Error" = em$percentage, "Method" = object$method, "Repetitions" = 1, stringsAsFactors = FALSE ) } else if (object$method == "warp3") { out <- data.frame( "Logml_Estimate" = object$logml, "Method" = object$method, "Repetitions" = 1 ) } class(out) <- c("summary.bridge", "data.frame") return(out) } #' @rdname bridge-methods #' @method summary bridge_list #' @export summary.bridge_list <- function(object, na.rm = TRUE, ...) { if (!(object$method %in% c("normal", "warp3"))) { stop('object$method needs to be either "normal" or "warp3".', call. = FALSE) } em <- error_measures(object, na.rm = na.rm) out <- data.frame( "Logml_Estimate" = median(object$logml, na.rm = na.rm), "Min" = em$min, "Max" = em$max, "Interquartile_Range" = em$IQR, "Method" = object$method, "Repetitions" = object$repetitions ) class(out) <- c("summary.bridge_list", "data.frame") return(out) } # print summary methods #' @rdname bridge-methods #' @method print summary.bridge #' @export print.summary.bridge <- function(x, ...) { if (x[["Method"]] == "normal") { cat( '\nBridge sampling log marginal likelihood estimate \n(method = "', as.character(x[["Method"]]), '", repetitions = ', x[["Repetitions"]], '):\n\n ', x[["Logml_Estimate"]], '\n\nError Measures:\n\n Relative Mean-Squared Error: ', x[["Relative_Mean_Squared_Error"]], '\n Coefficient of Variation: ', x[["Coefficient_of_Variation"]], '\n Percentage Error: ', x[["Percentage_Error"]], '\n\nNote:\nAll error measures are approximate.\n\n', sep = "" ) } else if (x[["Method"]] == "warp3") { cat( '\nBridge sampling log marginal likelihood estimate \n(method = "', as.character(x[["Method"]]), '", repetitions = ', x[["Repetitions"]], '):\n\n ', x[["Logml_Estimate"]], '\n\nNote:\nNo error measures are available for method = "warp3"', '\nwith repetitions = 1.', '\nWe recommend to run the warp3 procedure multiple times to', '\nassess the uncertainty of the estimate.\n\n', sep = "" ) } } #' @rdname bridge-methods #' @method print summary.bridge_list #' @export print.summary.bridge_list <- function(x, ...) { cat( '\nBridge sampling log marginal likelihood estimate \n(method = "', as.character(x[["Method"]]), '", repetitions = ', x[["Repetitions"]], '):\n\n ', x[["Logml_Estimate"]], '\n\nError Measures:\n\n Min: ', x[["Min"]], '\n Max: ', x[["Max"]], '\n Interquartile Range: ', x[["Interquartile_Range"]], '\n\nNote:\nAll error measures are based on ', x[["Repetitions"]], ' estimates.\n\n', sep = "" ) } # print methods #' @rdname bridge-methods #' @method print bridge #' @export print.bridge <- function(x, ...) { cat( "Bridge sampling estimate of the log marginal likelihood: ", round(x$logml, 5), "\nEstimate obtained in ", x$niter, " iteration(s) via method \"", x$method, "\".\n", sep = "" ) } #' @rdname bridge-methods #' @method print bridge_list #' @export print.bridge_list <- function(x, na.rm = TRUE, ...) { cat( "Median of ", x$repetitions, " bridge sampling estimates\nof the log marginal likelihood: ", round(median(x$logml, na.rm = na.rm), 5), "\nRange of estimates: ", round(range(x$logml, na.rm = na.rm)[1], 5), " to ", round(range(x$logml, na.rm = na.rm)[2], 5), "\nInterquartile range: ", round(stats::IQR(x$logml, na.rm = na.rm), 5), "\nMethod: ", x$method, "\n", sep = "" ) if (any(is.na(x$logml))) { warning( sum(is.na(x$logml)), " bridge sampling estimate(s) are NAs.", call. = FALSE ) } } bridgesampling/R/bridge_sampler_tools.R0000644000176200001440000000251215060266335017772 0ustar liggesusers#-------------------------------------------------------------------------- # functions for Stan support via rstan #-------------------------------------------------------------------------- # taken from rstan: .rstan_relist <- function(x, skeleton) { lst <- utils::relist(x, skeleton) for (i in seq_along(skeleton)) { dim(lst[[i]]) <- dim(skeleton[[i]]) } lst } # taken from rstan: .create_skeleton <- function(pars, dims) { lst <- lapply(seq_along(pars), function(i) { len_dims <- length(dims[[i]]) if (len_dims < 1) { return(0) } return(array(0, dim = dims[[i]])) }) names(lst) <- pars lst } .stan_log_posterior <- function(s.row, data) { out <- tryCatch( rstan::log_prob(object = data$stanfit, upars = s.row), error = function(e) -Inf ) if (is.na(out)) { out <- -Inf } return(out) } .cmdstan_log_posterior <- function(s.row, data) { if ("lp__" %in% names(s.row)) { s.row <- s.row[!names(s.row) %in% "lp__"] } if (!is.numeric(s.row)) { s.row <- as.numeric(s.row) } out <- tryCatch( { log_prob <- data$log_prob(s.row, jacobian = TRUE) log_prob }, error = function(e) { print(e) -Inf } ) if (is.na(out)) { out <- -Inf } result <- data.frame(matrix(s.row, nrow = 1)) result$log_posterior <- out return(out) } bridgesampling/R/logml.R0000644000176200001440000000177415060266335014716 0ustar liggesusers#' Generic function that returns log marginal likelihood from bridge objects. For objects of class \code{"bridge_list"}, which contains multiple log marginal likelihoods, \code{fun} is performed on the vector and its result returned. #' @title Log Marginal Likelihoods from Bridge Objects #' @param x Object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. #' @param fun Function which returns a scalar value and is applied to the \code{logml} vector of \code{"bridge_list"} objects. Default is \code{\link{median}}. #' @param ... Further arguments passed to \code{fun}. #' @return scalar numeric #' @export logml <- function(x, ...) { UseMethod("logml", x) } #' @rdname logml #' @export logml.bridge <- function(x, ...) { x$logml } #' @rdname logml #' @export logml.bridge_list <- function(x, fun = median, ...) { out <- fun(x$logml, ...) if (length(out) != 1) { warning("fun returns results of length != 1, only first used.") out <- out[1] } out } bridgesampling/R/bridge_sampler_normal.R0000644000176200001440000002151715106567446020140 0ustar liggesusers.bridge.sampler.normal <- function( samples_4_fit, # matrix with already transformed samples for fitting the # proposal (rows are samples), colnames are "trans_x" where # x is the parameter name samples_4_iter, # matrix with already transformed samples for the # iterative scheme (rows are samples), colnames are "trans_x" # where x is the parameter name neff, # effective sample size of samples_4_iter (i.e., already transformed samples), scalar log_posterior, ..., data, lb, ub, transTypes, # types of transformations (unbounded/lower/upperbounded) for the different parameters (named character vector) param_types, # Sample space for transformations (real, circular, simplex) cores, repetitions, packages, varlist, envir, rcppFile, maxiter, silent, verbose, use_ess, r0, tol1, tol2 ) { if (is.null(neff)) { neff <- nrow(samples_4_iter) } n_post <- nrow(samples_4_iter) # get mean & covariance matrix and generate samples from proposal m <- apply(samples_4_fit, 2, mean) V_tmp <- cov(samples_4_fit) V <- as.matrix(nearPD(V_tmp)$mat) # make sure that V is positive-definite # sample from multivariate normal distribution and evaluate for posterior samples and generated samples q12 <- dmvnorm(samples_4_iter, mean = m, sigma = V, log = TRUE) gen_samples <- vector(mode = "list", length = repetitions) q22 <- vector(mode = "list", length = repetitions) for (i in seq_len(repetitions)) { gen_samples[[i]] <- rmvnorm(n_post, mean = m, sigma = V) colnames(gen_samples[[i]]) <- colnames(samples_4_iter) q22[[i]] <- dmvnorm(gen_samples[[i]], mean = m, sigma = V, log = TRUE) } # evaluate log of likelihood times prior for posterior samples and generated samples q21 <- vector(mode = "list", length = repetitions) if (cores == 1) { q11 <- apply( .invTransform2Real(samples_4_iter, lb, ub, param_types), 1, log_posterior, data = data, ... ) + .logJacobian(samples_4_iter, transTypes, lb, ub) for (i in seq_len(repetitions)) { q21[[i]] <- apply( .invTransform2Real(gen_samples[[i]], lb, ub, param_types), 1, log_posterior, data = data, ... ) + .logJacobian(gen_samples[[i]], transTypes, lb, ub) } } else if (cores > 1) { if (.Platform$OS.type == "unix") { split1 <- .split_matrix( matrix = .invTransform2Real(samples_4_iter, lb, ub, param_types), cores = cores ) q11 <- parallel::mclapply( split1, FUN = function(x) apply(x, 1, log_posterior, data = data, ...), mc.preschedule = FALSE, mc.cores = cores ) q11 <- unlist(q11) + .logJacobian(samples_4_iter, transTypes, lb, ub) for (i in seq_len(repetitions)) { split2 <- .split_matrix( matrix = .invTransform2Real(gen_samples[[i]], lb, ub, param_types), cores = cores ) q21[[i]] <- parallel::mclapply( split2, FUN = function(x) apply(x, 1, log_posterior, data = data, ...), mc.preschedule = FALSE, mc.cores = cores ) q21[[i]] <- unlist(q21[[i]]) + .logJacobian(gen_samples[[i]], transTypes, lb, ub) } } else { cl <- parallel::makeCluster(cores, useXDR = FALSE) sapply(packages, function(x) { parallel::clusterCall( cl = cl, "require", package = x, character.only = TRUE ) }) parallel::clusterExport(cl = cl, varlist = varlist, envir = envir) if (!is.null(rcppFile)) { parallel::clusterExport( cl = cl, varlist = "rcppFile", envir = parent.frame() ) parallel::clusterCall( cl = cl, "require", package = "Rcpp", character.only = TRUE ) parallel::clusterEvalQ(cl = cl, Rcpp::sourceCpp(file = rcppFile)) } else if (is.character(log_posterior)) { parallel::clusterExport(cl = cl, varlist = log_posterior, envir = envir) } q11 <- parallel::parRapply( cl = cl, x = .invTransform2Real(samples_4_iter, lb, ub, param_types), log_posterior, data = data, ... ) + .logJacobian(samples_4_iter, transTypes, lb, ub) for (i in seq_len(repetitions)) { q21[[i]] <- parallel::parRapply( cl = cl, x = .invTransform2Real(gen_samples[[i]], lb, ub, param_types), log_posterior, data = data, ... ) + .logJacobian(gen_samples[[i]], transTypes, lb, ub) } parallel::stopCluster(cl) } } if (verbose) { print( "summary(q12): (log_dens of proposal (i.e., with dmvnorm) for posterior samples)" ) print(summary(q12)) print( "summary(q22): (log_dens of proposal (i.e., with dmvnorm) for generated samples)" ) print(lapply(q22, summary)) print( "summary(q11): (log_dens of posterior (i.e., with log_posterior) for posterior samples)" ) print(summary(q11)) print( "summary(q21): (log_dens of posterior (i.e., with log_posterior) for generated samples)" ) print(lapply(q21, summary)) .PROPOSALS <- vector("list", repetitions) # for (i in seq_len(repetitions)) { # .PROPOSALS[[i]] <- .invTransform2Real(gen_samples[[i]], lb, ub, param_types) # } # assign(".PROPOSALS", .PROPOSALS, pos = .GlobalEnv) # message("All proposal samples written to .GlobalEnv as .PROPOSALS") } if (any(is.infinite(q11))) { warning( sum(is.infinite(q11)), " of the ", length(q11), " log_prob() evaluations on the posterior draws produced -Inf/Inf.", call. = FALSE ) } for (i in seq_len(repetitions)) { if (any(is.infinite(q21[[i]]))) { warning( sum(is.infinite(q21[[i]])), " of the ", length(q21[[i]]), " log_prob() evaluations on the proposal draws produced -Inf/Inf.", call. = FALSE ) } } if (any(is.na(q11))) { warning( sum(is.na(q11)), " evaluation(s) of log_prob() on the posterior draws produced NA and have been replaced by -Inf.", call. = FALSE ) q11[is.na(q11)] <- -Inf } for (i in seq_len(repetitions)) { if (all(is.na(q21[[i]]))) { stop( "Evaluations of log_prob() on all proposal draws produced NA.\n", "E.g., rounded to 3 digits (use verbose = TRUE for all proposal samples):\n", deparse( round( .invTransform2Real(gen_samples[[i]], lb, ub, param_types)[1, ], 3 ), width.cutoff = 500L ), call. = FALSE ) } if (any(is.na(q21[[i]]))) { warning( sum(is.na(q21[[i]])), " evaluation(s) of log_prob() on the proposal draws produced NA and have been replaced by -Inf.", call. = FALSE ) q21[[i]][is.na(q21[[i]])] <- -Inf } } logml <- numeric(repetitions) niter <- numeric(repetitions) mcse_logmls <- numeric(repetitions) # run iterative updating scheme to compute log of marginal likelihood for (i in seq_len(repetitions)) { tmp <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21[[i]], q22 = q22[[i]], r0 = r0, tol = tol1, L = NULL, method = "normal", maxiter = maxiter, silent = silent, use_ess = use_ess, criterion = "r", neff = neff ) if (is.na(tmp$logml) & !is.null(tmp$r_vals)) { warning( "logml could not be estimated within maxiter, rerunning with adjusted starting value. \nEstimate might be more variable than usual.", call. = FALSE ) lr <- length(tmp$r_vals) # use geometric mean as starting value r0_2 <- sqrt(tmp$r_vals[[lr - 1]] * tmp$r_vals[[lr]]) tmp <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21[[i]], q22 = q22[[i]], r0 = r0_2, tol = tol2, L = NULL, method = "normal", maxiter = maxiter, silent = silent, use_ess = use_ess, criterion = "logml", neff = neff ) tmp$niter <- maxiter + tmp$niter } logml[i] <- tmp$logml mcse_logmls[i] <- tmp$mcse_logml niter[i] <- tmp$niter if (niter[i] == maxiter) { warning( "logml could not be estimated within maxiter, returning NA.", call. = FALSE ) } } if (repetitions == 1) { out <- list( logml = logml, niter = niter, method = "normal", q11 = q11, q12 = q12, q21 = q21[[1]], q22 = q22[[1]], mcse_logml = mcse_logmls ) class(out) <- "bridge" } else if (repetitions > 1) { out <- list( logml = logml, niter = niter, method = "normal", repetitions = repetitions, mcse_logml = mcse_logmls ) class(out) <- "bridge_list" } return(out) } bridgesampling/R/error_measures.R0000644000176200001440000001006215060266335016627 0ustar liggesusers#' Computes error measures for estimated marginal likelihood. #' @export #' @title Error Measures for Estimated Marginal Likelihood #' @param bridge_object an object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. #' @param na.rm a logical indicating whether missing values in logml estimates should be removed. Ignored for the \code{bridge} method. #' @param ... additional arguments (currently ignored). #' @details Computes error measures for marginal likelihood bridge sampling estimates. The approximate errors for a \code{bridge_object} of class \code{"bridge"} that has been obtained with \code{method = "normal"} and \code{repetitions = 1} are based on Fruehwirth-Schnatter (2004). #' Not applicable in case the object of class \code{"bridge"} has been obtained with \code{method = "warp3"} and \code{repetitions = 1}. #' To assess the uncertainty of the estimate in this case, it is recommended to run the \code{"warp3"} procedure multiple times. #' @return If \code{bridge_object} is of class \code{"bridge"} and has been obtained with \code{method = "normal"} and \code{repetitions = 1}, returns a list with components: #' \itemize{ #' \item \code{re2}: approximate relative mean-squared error for marginal likelihood estimate. #' \item \code{cv}: approximate coefficient of variation for marginal likelihood estimate (assumes that bridge estimate is unbiased). #' \item \code{percentage}: approximate percentage error of marginal likelihood estimate. #' } #' If \code{bridge_object} is of class \code{"bridge_list"}, returns a list with components: #' \itemize{ #' \item \code{min}: minimum of the log marginal likelihood estimates. #' \item \code{max}: maximum of the log marginal likelihood estimates. #' \item \code{IQR}: interquartile range of the log marginal likelihood estimates. #' } #' @author Quentin F. Gronau #' @note For examples, see \code{\link{bridge_sampler}} and the accompanying vignettes: \cr \code{vignette("bridgesampling_example_jags")} \cr \code{vignette("bridgesampling_example_stan")} #' #' @seealso The \code{summary} methods for \code{bridge} and \code{bridge_list} objects automatically invoke this function, see \code{\link{bridge-methods}}. #' #' @references #' Fruehwirth-Schnatter, S. (2004). Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques. \emph{The Econometrics Journal, 7}, 143-167. \doi{10.1111/j.1368-423X.2004.00125.x} #' @import Brobdingnag #' @importFrom coda spectrum0.ar #' @export error_measures <- function(bridge_object, ...) { UseMethod("error_measures", bridge_object) } #' @rdname error_measures #' @export error_measures.bridge <- function(bridge_object, ...) { if (bridge_object$method == "warp3") { stop(paste0( "error_measures not implemented for warp3 method with", "\n repetitions = 1.", "\n We recommend to run the warp3 procedure multiple times", "\n to assess the uncertainty of the estimate." )) } e <- as.brob(exp(1)) ml <- e^(bridge_object$logml) g_p <- e^(bridge_object$q12) g_g <- e^(bridge_object$q22) priorTimesLik_p <- e^(bridge_object$q11) priorTimesLik_g <- e^(bridge_object$q21) p_p <- priorTimesLik_p / ml p_g <- priorTimesLik_g / ml N1 <- length(p_p) N2 <- length(g_g) s1 <- N1 / (N1 + N2) s2 <- N2 / (N1 + N2) f1 <- as.numeric(p_g / (s1 * p_g + s2 * g_g)) f2 <- as.numeric(g_p / (s1 * p_p + s2 * g_p)) rho_f2 <- spectrum0.ar(f2)$spec term1 <- 1 / N2 * var(f1) / mean(f1)^2 term2 <- rho_f2 / N1 * var(f2) / mean(f2)^2 re2 <- term1 + term2 # convert to coefficient of variation (assumes that bridge estimate is unbiased) cv <- sqrt(re2) # convert to percentage error percentage <- scales::percent(cv) return(list(re2 = re2, cv = cv, percentage = percentage)) } #' @rdname error_measures #' @export error_measures.bridge_list <- function(bridge_object, na.rm = TRUE, ...) { return(list( min = min(bridge_object$logml, na.rm = na.rm), max = max(bridge_object$logml, na.rm = na.rm), IQR = stats::IQR(bridge_object$logml, na.rm = na.rm) )) } bridgesampling/R/bridge_sampler_internals.R0000644000176200001440000002424515106567166020647 0ustar liggesusers# Helper function to represent circular variables (such as mean directions) as # "gapless" numerical representations. .gaplessCircular <- function(th) { # Mean direction md <- atan2(sum(sin(th)), sum(cos(th))) # Shift th so that it is unlikely to have a gap. ((th - md + pi) %% (2 * pi)) - pi + md } #### for matrix method ###### .transform2Real <- function( theta, lb, ub, theta_types = rep("real", ncol(theta)) ) { ### transform samples to real line theta_t <- theta transTypes <- character(ncol(theta)) cn <- colnames(theta) names(theta_types) <- names(transTypes) <- cn # Because the simplex transform must be done on all simplex parameters at # once, do it before the loop. This transformation follows the Stan reference # manual. For simplex variables, we expect one parameter less than the number # of weights due to the contstraint sum(simplex_theta) == 1. is_simplex_theta <- theta_types == "simplex" if (any(is_simplex_theta)) { # Select the simplex variables simplex_theta <- theta[, is_simplex_theta, drop = FALSE] # Simplex dimensionality simdim <- ncol(simplex_theta) cs <- cbind( 0L, matrix(t(apply(simplex_theta, 1L, cumsum)), ncol = simdim)[, -simdim, drop = FALSE ] ) # Get the break proportions. z_k <- (simplex_theta / (1L - cs)) y_k <- log(z_k) - log(1L - z_k) + matrix(log(simdim:1L), nrow(theta), simdim, byrow = TRUE) theta_t[, is_simplex_theta] <- y_k transTypes[is_simplex_theta] <- "simplex" } for (i in seq_len(ncol(theta))) { p <- cn[i] if (theta_types[[p]] == "circular") { transTypes[[p]] <- "circular" theta_t[, i] <- .gaplessCircular(theta[, i]) } else if (theta_types[[p]] == "real") { if (any(theta[, i] < lb[[p]])) { stop( "Parameter values (samples) cannot be smaller than lb: ", p, call. = FALSE ) } if (any(theta[, i] > ub[[p]])) { stop( "Parameter values (samples) cannot be larger than ub: ", p, call. = FALSE ) } if (lb[[p]] < ub[[p]] && is.infinite(lb[[p]]) && is.infinite(ub[[p]])) { transTypes[[p]] <- "unbounded" theta_t[, i] <- theta[, i] } else if ( lb[[p]] < ub[[p]] && is.finite(lb[[p]]) && is.infinite(ub[[p]]) ) { transTypes[[p]] <- "lower-bounded" theta_t[, i] <- log(theta[, i] - lb[[p]]) } else if ( lb[[p]] < ub[[p]] && is.infinite(lb[[p]]) && is.finite(ub[[p]]) ) { transTypes[[p]] <- "upper-bounded" theta_t[, i] <- log(ub[[p]] - theta[, i]) } else if ( lb[[p]] < ub[[p]] && is.finite(lb[[p]]) && is.finite(ub[[p]]) ) { transTypes[[p]] <- "double-bounded" theta_t[, i] <- qnorm((theta[, i] - lb[[p]]) / (ub[[p]] - lb[[p]])) # Finally, give an error except for simplex variables, which are already # transformed. } else if (theta_types[p] != "simplex") { stop(paste( "Could not transform parameters, possibly due to invalid", "lower and/or upper prior bounds." )) } } } colnames(theta_t) <- paste0("trans_", colnames(theta)) return(list(theta_t = theta_t, transTypes = transTypes)) } .invTransform2Real <- function( theta_t, lb, ub, theta_types = rep("real", ncol(theta)) ) { ### transform transformed samples back to original scales theta <- theta_t colnames(theta) <- stringr::str_sub(colnames(theta), 7) cn <- colnames(theta) names(theta_types) <- cn # Because the simplex transform must be done on all simplex parameters at # once, do it before the loop. This transformation follows the Stan reference # manual. For simplex variables, we expect one parameter less than the number # of weights due to the contstraint sum(simplex_theta) == 1. is_simplex_theta <- theta_types == "simplex" if (any(is_simplex_theta)) { # Select the simplex variables simplex_theta <- theta_t[, is_simplex_theta, drop = FALSE] # Simplex dimensionality simdim <- ncol(simplex_theta) logitz <- simplex_theta - matrix(log(simdim:1L), nrow(theta), simdim, byrow = TRUE) z_k <- exp(logitz) / (1 + exp(logitz)) x_k <- z_k if (simdim > 1) { for (k in 2:simdim) { x_k[, k] <- (1 - rowSums(x_k[, 1:(k - 1), drop = FALSE])) * z_k[, k] } } theta[, is_simplex_theta] <- x_k } # Note that the circular variables are not transformed back, because they are # simply a different numerical representation. for (i in seq_len(ncol(theta_t))) { p <- cn[i] if (theta_types[[p]] == "real") { if (lb[[p]] < ub[[p]] && is.infinite(lb[[p]]) && is.infinite(ub[[p]])) { theta[, i] <- theta_t[, i] } else if ( lb[[p]] < ub[[p]] && is.finite(lb[[p]]) && is.infinite(ub[[p]]) ) { theta[, i] <- exp(theta_t[, i]) + lb[[p]] } else if ( lb[[p]] < ub[[p]] && is.infinite(lb[[p]]) && is.finite(ub[[p]]) ) { theta[, i] <- ub[[p]] - exp(theta_t[, i]) } else if ( lb[[p]] < ub[[p]] && is.finite(lb[[p]]) && is.finite(ub[[p]]) ) { theta[, i] <- pnorm(theta_t[, i]) * (ub[[p]] - lb[[p]]) + lb[[p]] } else { stop( "Could not transform parameters, possibly due to invalid lower and/or upper prior bounds." ) } } } return(theta) } .logJacobian <- function(theta_t, transTypes, lb, ub) { ### compute log of Jacobian logJ <- matrix(nrow = nrow(theta_t), ncol = ncol(theta_t)) cn <- stringr::str_sub(colnames(theta_t), 7) # Separate the computations for the simplex is_simplex_theta <- transTypes == "simplex" if (any(is_simplex_theta)) { # Select the simplex variables simplex_theta <- theta_t[, is_simplex_theta, drop = FALSE] # Simplex dimensionality, this is K - 1 simdim <- ncol(simplex_theta) logitz <- simplex_theta - matrix(log(simdim:1L), nrow(theta_t), simdim, byrow = TRUE) z_k <- exp(logitz) / (1 + exp(logitz)) x_k <- z_k # Sum_x_k is the length of the remaining stick at step k. At the start, the # whole stick is still left sum_x_k <- matrix(nrow = nrow(theta_t), ncol = simdim) sum_x_k[, 1] <- 1 if (simdim > 1) { for (k in 2:simdim) { rsx <- rowSums(x_k[, 1:(k - 1), drop = FALSE]) x_k[, k] <- (1 - rsx) * z_k[, k] sum_x_k[, k] <- (1 - rsx) } } logJ[, is_simplex_theta] <- log(z_k) + log(1 - z_k) + log(sum_x_k) } for (i in seq_len(ncol(theta_t))) { p <- cn[i] if (transTypes[[p]] == "unbounded") { logJ[, i] <- 0 } else if (transTypes[[p]] == "lower-bounded") { logJ[, i] <- theta_t[, i] } else if (transTypes[[p]] == "upper-bounded") { logJ[, i] <- theta_t[, i] } else if (transTypes[[p]] == "double-bounded") { logJ[, i] <- log(ub[[p]] - lb[[p]]) + dnorm(theta_t[, i], log = TRUE) } else if (transTypes[[p]] == "circular") { logJ[, i] <- 0 } } return(.rowSums(logJ, m = nrow(logJ), n = ncol(logJ))) } .split_matrix <- function(matrix, cores) { out <- vector("list", cores) borders <- ceiling(seq(from = 0, to = nrow(matrix), length.out = cores + 1)) for (i in seq_len(cores)) { out[[i]] <- matrix[(borders[i] + 1):borders[i + 1], , drop = FALSE] } out } .run.iterative.scheme <- function( q11, q12, q21, q22, r0, tol, L, method, maxiter, silent, criterion, neff, use_ess ) { ### run iterative updating scheme (using "optimal" bridge function, ### see Meng & Wong, 1996) if (method == "normal") { l1 <- q11 - q12 # log(l) l2 <- q21 - q22 # log(ltilde) } else if (method == "warp3") { l1 <- -log(2) + determinant(L)$modulus + (q11 - q12) # log(l) l2 <- -log(2) + determinant(L)$modulus + (q21 - q22) # log(ltilde) } ## for dbugging: # save( # l1, l2, # r0, tol, L, # method, maxiter, silent, # criterion, neff, # file = "iterative_scheme.rda" # ) lstar <- median(l1) n.1 <- length(l1) n.2 <- length(l2) s1 <- neff / (neff + n.2) s2 <- n.2 / (neff + n.2) r <- r0 r_vals <- r logml <- log(r) + lstar logml_vals <- logml criterion_val <- 1 + tol e <- as.brob(exp(1)) i <- 1 while (i <= maxiter && criterion_val > tol) { if (!silent) { cat(paste0("Iteration: ", i, "\n")) } rold <- r logmlold <- logml numi <- e^(l2 - lstar) / (s1 * e^(l2 - lstar) + s2 * r) deni <- 1 / (s1 * e^(l1 - lstar) + s2 * r) if ( any(is.infinite(as.numeric(numi))) || any(is.infinite(as.numeric((deni)))) ) { warning( "Infinite value in iterative scheme, returning NA.\n Try rerunning with more samples.", call. = FALSE ) return(list(logml = NA, niter = i, mcse_logml = NA_real_)) } mean_numi <- mean(as.numeric(numi)) mean_deni <- mean(as.numeric(deni)) var_numi <- var(as.numeric(numi)) if (use_ess) { var_deni <- tryCatch( var(as.numeric(deni)) * length(deni) / mean(coda::effectiveSize(as.numeric(deni))), error = function(e) { warning( "effective sample size calculation failed in iterative's scheme uncertainty calculation", call. = FALSE ) return(var(as.numeric(deni))) } ) } else { var_deni <- var(as.numeric(deni)) } r <- mean_numi / mean_deni r_vals <- c(r_vals, r) logml <- log(r) + lstar logml_vals <- c(logml_vals, logml) criterion_val <- switch( criterion, "r" = abs((r - rold) / r), "logml" = abs((logml - logmlold) / logml) ) i <- i + 1 var_r <- (mean_numi^2) / (mean_deni^2) * (var_numi / (mean_numi)^2 + var_deni / mean_deni^2) var_r <- var_r / length(numi) ## Compute variance in log scale by match the variance of a ## log-normal approximation ## https://en.wikipedia.org/wiki/Log-normal_distribution#Arithmetic_moments var_logml <- log(1 + var_r / r^2) mcse_logml <- sqrt(var_logml) } if (i >= maxiter) { return(list( logml = NA, niter = i - 1, r_vals = r_vals, mcse_logml = mcse_logml )) } return(list(logml = logml, niter = i - 1, mcse_logml = mcse_logml)) } bridgesampling/R/bf.R0000644000176200001440000001672215060266335014172 0ustar liggesusers#' Generic function that computes Bayes factor(s) from marginal likelihoods. \code{bayes_factor()} is simply an (S3 generic) alias for \code{bf()}. #' @export #' @title Bayes Factor(s) from Marginal Likelihoods #' @param x1 Object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. Additionally, the default method assumes that \code{x1} is a single numeric log marginal likelihood (e.g., from \code{\link{logml}}) and will throw an error otherwise. #' @param x2 Object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. Additionally, the default method assumes that \code{x2} is a single numeric log marginal likelihood (e.g., from \code{\link{logml}}) and will throw an error otherwise. #' @param log Boolean. If \code{TRUE}, the function returns the log of the Bayes factor. Default is \code{FALSE}. #' @param ... currently not used here, but can be used by other methods. #' @details Computes the Bayes factor (Kass & Raftery, 1995) in favor of the model associated with \code{x1} over the model associated with \code{x2}. #' @return For the default method returns a list of class \code{"bf_default"} with components: #' \itemize{ #' \item \code{bf}: (scalar) value of the Bayes factor in favor of the model associated with \code{x1} over the model associated with \code{x2}. #' \item \code{log}: Boolean which indicates whether \code{bf} corresponds to the log Bayes factor. #' } #' #' #' For the method for \code{"bridge"} objects returns a list of class \code{"bf_bridge"} with components: #' \itemize{ #' \item \code{bf}: (scalar) value of the Bayes factor in favor of the model associated with \code{x1} over the model associated with \code{x2}. #' \item \code{log}: Boolean which indicates whether \code{bf} corresponds to the log Bayes factor. #' } #' #' #' For the method for \code{"bridge_list"} objects returns a list of class \code{"bf_bridge_list"} with components: #' \itemize{ #' \item \code{bf}: a numeric vector consisting of Bayes factors where each element gives the Bayes factor for one set of logmls in favor of the model associated with \code{x1} over the model associated with \code{x2}. The length of this vector is given by the \code{"bridge_list"} element with the most \code{repetitions}. Elements with fewer repetitions will be recycled (with warning). #' \item \code{bf_median_based}: (scalar) value of the Bayes factor in favor of the model associated with \code{x1} over the model associated with \code{x2} that is based on the median values of the logml estimates. #' \item \code{log}: Boolean which indicates whether \code{bf} corresponds to the log Bayes factor. #' } #' @author Quentin F. Gronau #' @note For examples, see \code{\link{bridge_sampler}} and the accompanying vignettes: \cr \code{vignette("bridgesampling_example_jags")} \cr \code{vignette("bridgesampling_example_stan")} #' @references #' Kass, R. E., & Raftery, A. E. (1995). Bayes factors. \emph{Journal of the American Statistical Association, 90(430)}, 773-795. \doi{10.1080/01621459.1995.10476572} #' @importFrom methods is bf <- function(x1, x2, log = FALSE, ...) { UseMethod("bf", x1) } #' @rdname bf #' @export bayes_factor <- function(x1, x2, log = FALSE, ...) { UseMethod("bayes_factor", x1) } #' @rdname bf #' @export bayes_factor.default <- function(x1, x2, log = FALSE, ...) { bf(x1, x2, log = log, ...) } .bf_calc <- function(logml1, logml2, log) { bf <- logml1 - logml2 if (!log) { bf <- exp(bf) } return(bf) } #' @rdname bf #' @export bf.bridge <- function(x1, x2, log = FALSE, ...) { if (!inherits(x2, c("bridge", "bridge_list"))) { stop("x2 needs to be of class 'bridge' or 'bridge_list'.", call. = FALSE) } bf <- .bf_calc(logml(x1), logml(x2), log = log) out <- list(bf = bf, log = log) class(out) <- "bf_bridge" try( { mc <- match.call() name1 <- deparse(mc[["x1"]]) name2 <- deparse(mc[["x2"]]) attr(out, "model_names") <- c(name1, name2) }, silent = TRUE ) return(out) } #' @rdname bf #' @export bf.bridge_list <- function(x1, x2, log = FALSE, ...) { if (!inherits(x2, c("bridge", "bridge_list"))) { stop("x2 needs to be of class 'bridge' or 'bridge_list'.", call. = FALSE) } logml1 <- x1$logml logml2 <- x2$logml median1 <- median(logml1, na.rm = TRUE) median2 <- median(logml2, na.rm = TRUE) len1 <- length(logml1) len2 <- length(logml2) max_len <- max(c(len1, len2)) if (!all(c(len1, len2) == max_len)) { warning( "Not all objects provide ", max_len, " logmls. Some values are recycled.", call. = FALSE ) logml1 <- rep(logml1, length.out = max_len) logml2 <- rep(logml2, length.out = max_len) } bf <- .bf_calc(logml1, logml2, log = log) bf_median_based <- .bf_calc(median1, median2, log = log) out <- list(bf = bf, bf_median_based = bf_median_based, log = log) class(out) <- "bf_bridge_list" try( { mc <- match.call() name1 <- deparse(mc[["x1"]]) name2 <- deparse(mc[["x2"]]) attr(out, "model_names") <- c(name1, name2) }, silent = TRUE ) return(out) } #' @rdname bf #' @export bf.default <- function(x1, x2, log = FALSE, ...) { if (!is.numeric(c(x1, x2))) { stop("logml values need to be numeric", call. = FALSE) } if (length(x1) > 1 || length(x2) > 1) { stop("Both logmls need to be scalar values.", call. = FALSE) } bf <- .bf_calc(x1, x2, log = log) out <- list(bf = bf, log = log) class(out) <- "bf_default" try( { mc <- match.call() name1 <- deparse(mc[["x1"]]) name2 <- deparse(mc[["x2"]]) attr(out, "model_names") <- c(name1, name2) }, silent = TRUE ) return(out) } ######## Methods for bf objects: #' @method print bf_bridge #' @export print.bf_bridge <- function(x, ...) { if (!is.null(attr(x, "model_names"))) { model_names <- attr(x, "model_names") } else { model_names <- c("x1", "x2") } cat( "Estimated ", if (x$log) "log " else NULL, "Bayes factor in favor of ", model_names[1], " over ", model_names[2], ": ", formatC(x$bf, digits = 5, format = "f"), "\n", sep = "" ) } #' @method print bf_bridge_list #' @export print.bf_bridge_list <- function(x, na.rm = TRUE, ...) { if (!is.null(attr(x, "model_names"))) { model_names <- attr(x, "model_names") } else { model_names <- c("x1", "x2") } cat( "Estimated ", if (x$log) "log " else NULL, "Bayes factor (based on medians of log marginal likelihood estimates)\n", " in favor of ", model_names[1], " over ", model_names[2], ": ", formatC(x$bf_median_based, digits = 5, format = "f"), "\nRange of estimates: ", formatC(range(x$bf, na.rm = na.rm)[1], digits = 5, format = "f"), " to ", formatC(range(x$bf, na.rm = na.rm)[2], digits = 5, format = "f"), "\nInterquartile range: ", formatC(stats::IQR(x$bf, na.rm = na.rm), digits = 5, format = "f"), "\n", sep = "" ) if (any(is.na(x$bf))) { warning( sum(is.na(x$bf)), " log Bayes factor estimate(s) are NAs.", call. = FALSE ) } } #' @method print bf_default #' @export print.bf_default <- function(x, ...) { if (!is.null(attr(x, "model_names"))) { model_names <- attr(x, "model_names") } else { model_names <- c("Model 1", "Model 2") } cat( if (x$log) "Log " else NULL, "Bayes factor in favor of ", model_names[1], " over ", model_names[2], ": ", formatC(x$bf, digits = 5, format = "f"), "\n", sep = "" ) } bridgesampling/R/post_prob.R0000644000176200001440000001300015060266335015574 0ustar liggesusers#' Generic function that computes posterior model probabilities from marginal #' likelihoods. #' @export #' @title Posterior Model Probabilities from Marginal Likelihoods #' @param x Object of class \code{"bridge"} or \code{"bridge_list"} as returned #' from \code{\link{bridge_sampler}}. Additionally, the default method assumes #' that all passed objects are numeric log marginal likelihoods (e.g., from #' \code{\link{logml}}) and will throw an error otherwise. #' @param ... further objects of class \code{"bridge"} or \code{"bridge_list"} #' as returned from \code{\link{bridge_sampler}}. Or numeric values for the #' default method. #' @param prior_prob numeric vector with prior model probabilities. If omitted, #' a uniform prior is used (i.e., all models are equally likely a priori). The #' default \code{NULL} corresponds to equal prior model weights. #' @param model_names If \code{NULL} (the default) will use model names derived #' from deparsing the call. Otherwise will use the passed values as model #' names. #' #' @return For the default method and the method for \code{"bridge"} objects, a #' named numeric vector with posterior model probabilities (i.e., which sum to #' one). #' #' For the method for \code{"bridge_list"} objects, a matrix consisting of #' posterior model probabilities where each row sums to one and gives the #' model probabilities for one set of logmls. The (named) columns correspond #' to the models and the number of rows is given by the \code{"bridge_list"} #' element with the most \code{repetitions}. Elements with fewer repetitions #' will be recycled (with warning). #' @author Quentin F. Gronau and Henrik Singmann #' @note For realistic examples, see \code{\link{bridge_sampler}} and the #' accompanying vignettes: \cr \code{vignette("bridgesampling_example_jags")} #' \cr \code{vignette("bridgesampling_example_stan")} #' @example examples/example.post_prob.R #' @importFrom methods is post_prob <- function(x, ..., prior_prob = NULL, model_names = NULL) { UseMethod("post_prob", x) } #' @rdname post_prob #' @export post_prob.bridge <- function(x, ..., prior_prob = NULL, model_names = NULL) { dots <- list(...) mc <- match.call() modb <- vapply(dots, inherits, NA, what = c("bridge", "bridge_list")) if (is.null(model_names)) { model_names <- c( deparse(mc[["x"]]), vapply(which(modb), function(x) deparse(mc[[x + 2]]), "") ) } if (sum(modb) == 0) { stop( "Only one object of class 'bridge' or 'bridge_list' passed.", call. = FALSE ) } if (sum(modb) != length(dots)) { warning( "Objects not of class 'bridge' or 'bridge_list' are ignored.", call. = FALSE ) } logml <- vapply(c(list(x), dots[modb]), logml, FUN.VALUE = 0) .post_prob_calc( logml = logml, model_names = model_names, prior_prob = prior_prob ) } #' @rdname post_prob #' @export post_prob.bridge_list <- function( x, ..., prior_prob = NULL, model_names = NULL ) { dots <- list(...) mc <- match.call() modb <- vapply(dots, inherits, NA, what = c("bridge", "bridge_list")) if (is.null(model_names)) { model_names <- c( deparse(mc[["x"]]), vapply(which(modb), function(x) deparse(mc[[x + 2]]), "") ) } if (sum(modb) == 0) { stop( "Only one object of class 'bridge' or 'bridge_list' passed.", call. = FALSE ) } if (sum(modb) != length(dots)) { warning( "Objects not of class 'bridge' or 'bridge_list' are ignored.", call. = FALSE ) } logml <- lapply(c(list(x), dots[modb]), "[[", i = "logml") len <- vapply(logml, length, FUN.VALUE = 0) if (!all(len == max(len))) { warning( "Not all objects provide ", max(len), " logmls. Some values are recycled.", call. = FALSE ) logml <- lapply(logml, function(x) rep(x, length.out = max(len))) } t(apply( as.data.frame(logml), 1, .post_prob_calc, model_names = model_names, prior_prob = prior_prob )) } #' @rdname post_prob #' @export post_prob.default <- function(x, ..., prior_prob = NULL, model_names = NULL) { dots <- list(...) mc <- match.call() if (is.null(model_names)) { model_names <- c( rep(deparse(mc[["x"]]), length(x)), rep( vapply(seq_along(dots), function(x) deparse(mc[[x + 2]]), ""), times = vapply(dots, length, 0) ) ) } logml <- c(x, unlist(dots)) if (!is.numeric(logml)) { stop("logml values need to be numeric", call. = FALSE) } .post_prob_calc( logml = logml, model_names = model_names, prior_prob = prior_prob ) } .post_prob_calc <- function(logml, model_names, prior_prob) { e <- as.brob(exp(1)) if (is.null(prior_prob)) { prior_prob <- rep(1 / length(logml), length(logml)) } if (!isTRUE(all.equal(sum(prior_prob), 1))) { stop("Prior model probabilities do not sum to one.", call. = FALSE) } if (length(logml) != length(prior_prob)) { stop( "Number of objects/logml-values needs to match number of elements in prior_prob.", call. = FALSE ) } if (any(is.na(logml))) { post_prob <- rep(NA_real_, length(logml)) warning( "NAs in logml values. No posterior probabilities calculated.", call. = FALSE ) } else { post_prob <- as.numeric(e^logml * prior_prob / sum(e^logml * prior_prob)) if (!isTRUE(all.equal(sum(post_prob), 1))) { warning("Posterior model probabilities do not sum to one.", call. = FALSE) } } names(post_prob) <- make.unique(as.character(model_names)) return(post_prob) } bridgesampling/R/bridge_sampler.R0000644000176200001440000007436115106572100016554 0ustar liggesusers#'Computes log marginal likelihood via bridge sampling. #'@title Log Marginal Likelihood via Bridge Sampling #'@name bridge_sampler #'@param samples an \code{mcmc.list} object, a fitted \code{stanfit} object, a #' \code{stanreg} object, an \code{rjags} object, a \code{runjags} object, or a #' \code{matrix} with posterior samples (\code{colnames} need to correspond to #' parameter names in \code{lb} and \code{ub}) with posterior samples. #'@param log_posterior function or name of function that takes a parameter #' vector and the \code{data} as input and returns the log of the unnormalized #' posterior density (i.e., a scalar value). If the function name is passed, #' the function should exist in the \code{.GlobalEnv}. For special behavior if #' \code{cores > 1} see \code{Details}. #'@param ... additional arguments passed to \code{log_posterior}. Ignored for #' the \code{stanfit} and \code{stanreg} methods. #'@param data data object which is used in \code{log_posterior}. #'@param stanfit_model for the \code{stanfit} method, an additional object of #' class \code{"stanfit"} with the same model as \code{samples}, which will be #' used for evaluating the \code{log_posterior} (i.e., it does not need to #' contain any samples). The default is to use \code{samples}. In case #' \code{samples} was compiled in a different R session or on another computer #' with a different OS or setup, the \code{samples} model usually cannot be #' used for evaluation. In this case, one can compile the model on the current #' computer with \code{iter = 0} and pass it here (this usually needs to be #' done before \code{samples} is loaded). #'@param lb named vector with lower bounds for parameters. #'@param ub named vector with upper bounds for parameters. #'@param repetitions number of repetitions. #'@param method either \code{"normal"} or \code{"warp3"}. #'@param cores number of cores used for evaluating \code{log_posterior}. On #' unix-like systems (where \code{.Platform$OS.type == "unix"} evaluates to #' \code{TRUE}; e.g., Linux and Mac OS) forking via \code{\link{mclapply}} is #' used. Hence elements needed for evaluation should be in the #' \code{\link{.GlobalEnv}}. For other systems (e.g., Windows) #' \code{\link{makeCluster}} is used and further arguments specified below will #' be used. #'@param use_neff Logical. If \code{TRUE}, the effective sample size (compared #' to the nominal sample size) is used in the optimal bridge function and in #' the iterative scheme's uncertainty calculations (making MCSE computation #' take into account autocorrelation in MCMC samples). Default is TRUE. If #' FALSE, the nominal sample size is used instead. If \code{samples} is a #' \code{matrix}, it is assumed that the \code{matrix} contains the samples of #' one chain in order. If \code{samples} come from more than one chain, we #' recommend to use an \code{mcmc.list} object for optimal performance. #'@param packages character vector with names of packages needed for evaluating #' \code{log_posterior} in parallel (only relevant if \code{cores > 1} and #' \code{.Platform$OS.type != "unix"}). #'@param varlist character vector with names of variables needed for evaluating #' \code{log_posterior} (only needed if \code{cores > 1} and #' \code{.Platform$OS.type != "unix"} as these objects will be exported to the #' nodes). These objects need to exist in \code{envir}. #'@param envir specifies the environment for \code{varlist} (only needed if #' \code{cores > 1} and \code{.Platform$OS.type != "unix"} as these objects #' will be exported to the nodes). Default is \code{\link{.GlobalEnv}}. #'@param rcppFile in case \code{cores > 1} and \code{log_posterior} is an #' \code{Rcpp} function, \code{rcppFile} specifies the path to the cpp file #' (will be compiled on all cores). #'@param maxiter maximum number of iterations for the iterative updating scheme. #' Default is 1,000 to avoid infinite loops. #'@param param_types character vector of length \code{ncol(samples)} with #' \code{"real"}, \code{"simplex"} or \code{"circular"}. For all regular #' bounded or unbounded continuous parameters, this should just be #' \code{"real"}. However, if there are parameters which lie on a simplex or on #' the circle, this should be noted here. Simplex parameters are parameters #' which are bounded below by zero and collectively sum to one, such as weights #' in a mixture model. For these, the stick-breaking transformation is #' performed as described in the Stan reference manual. The circular variables #' are given a numerical representation to which the normal distribution is #' most likely a good fit. Only possible to use with #' \code{bridge_sampler.matrix}. #'@param silent Boolean which determines whether to print the number of #' iterations of the updating scheme to the console. Default is FALSE. #'@param verbose Boolean. Should internal debug information be printed to #' console? Default is \code{FALSE}. #'@details Bridge sampling is implemented as described in Meng and Wong (1996, #' see equation 4.1) using the "optimal" bridge function. When \code{method = #' "normal"}, the proposal distribution is a multivariate normal distribution #' with mean vector equal to the sample mean vector of \code{samples} and #' covariance matrix equal to the sample covariance matrix of \code{samples}. #' For a recent tutorial on bridge sampling, see Gronau et al. (in press). #' #' When \code{method = "warp3"}, the proposal distribution is a standard #' multivariate normal distribution and the posterior distribution is "warped" #' (Meng & Schilling, 2002) so that it has the same mean vector, covariance #' matrix, and skew as the samples. \code{method = "warp3"} takes approximately #' twice as long as \code{method = "normal"}. #' #' Note that for the \code{matrix} method, the lower and upper bound of a #' parameter cannot be a function of the bounds of another parameter. #' Furthermore, constraints that depend on multiple parameters of the model are #' not supported. This usually excludes, for example, parameters that #' constitute a covariance matrix or sets of parameters that need to sum to #' one. #' #' However, if the retransformations are part of the model itself and the #' \code{log_posterior} accepts parameters on the real line and performs the #' appropriate Jacobian adjustments, such as done for \code{stanfit} and #' \code{stanreg} objects, such constraints are obviously possible (i.e., we #' currently do not know of any parameter supported within Stan that does not #' work with the current implementation through a \code{stanfit} object). #' #' \subsection{Parallel Computation}{ On unix-like systems forking is used via #' \code{\link{mclapply}}. Hence elements needed for evaluation of #' \code{log_posterior} should be in the \code{\link{.GlobalEnv}}. #' #' On other OSes (e.g., Windows), things can get more complicated. For normal #' parallel computation, the \code{log_posterior} function can be passed as #' both function and function name. If the latter, it needs to exist in the #' environment specified in the \code{envir} argument. For parallel computation #' when using an \code{Rcpp} function, \code{log_posterior} can only be passed #' as the function name (i.e., character). This function needs to result from #' calling \code{sourceCpp} on the file specified in \code{rcppFile}. #' #' Due to the way \code{rstan} currently works, parallel computations with #' \code{stanfit} and \code{stanreg} objects only work with forking (i.e., NOT #' on Windows). } #'@return If \code{repetitions = 1}, returns a list of class \code{"bridge"} #' with components: #' \itemize{ #' \item \code{logml}: estimate of the log marginal likelihood. #' \item \code{niter}: number of iterations of the iterative #' updating scheme. #' \item \code{method}: bridge sampling method that was used #' to obtain the estimate. #' \item \code{q11}: log posterior evaluations for posterior samples. #' \item \code{q12}: log proposal evaluations for posterior samples. #' \item \code{q21}: log posterior evaluations for samples from the proposal. #' \item \code{q22}: log proposal evaluations for samples from the proposal. #' \item \code{mcse_logml}: Monte Carlo standard error of \code{logml} #' on the log-scale (Micaletto & Vehtari, 2025). #' } #' If \code{repetitions > 1}, returns a list of class \code{"bridge_list"} #' with components: #' \itemize{ #' \item \code{logml}: numeric vector of log marginal likelihood estimates. #' \item \code{niter}: numeric vector with the number of iterations of the #' iterative updating scheme for each repetition. #' \item \code{method}: bridge sampling method that was used to obtain #' the estimates. #' \item \code{repetitions}: number of repetitions. #' \item \code{mcse_logml}: numeric vector of Monte Carlo standard errors #' on the log-scale (Micaletto & Vehtari, 2025), one per repetition. #' } #'@section Warning: Note that the results depend strongly on the parameter #' priors. Therefore, it is strongly advised to think carefully about the #' priors before calculating marginal likelihoods. For example, the prior #' choices implemented in \pkg{rstanarm} or \pkg{brms} might not be optimal #' from a testing point of view. We recommend to use priors that have been #' chosen from a testing and not a purely estimation perspective. #' #' Also note that for testing, the number of posterior samples usually needs to #' be substantially larger than for estimation. #'@note To be able to use a \code{stanreg} object for \code{samples}, the user #' crucially needs to have specified the \code{diagnostic_file} when fitting #' the model in \pkg{rstanarm}. #'@author Quentin F. Gronau and Henrik Singmann. Parallel computing (i.e., #' \code{cores > 1}) and the \code{stanfit} method use code from \code{rstan} #' by Jiaqing Guo, Jonah Gabry, and Ben Goodrich. Ben Goodrich added the #' \code{stanreg} method. Kees Mulder added methods for simplex and circular #' variables. Giorgio Micaletto and Aki Vehtari added the \code{CmdStanMCMC} method (for \code{cmdstanr}) and calculation of the Monte Carlo Standard Error (MCSE). #'@references #' Gronau, Q. F., Singmann, H., & Wagenmakers, E.-J. (2020). bridgesampling: An #' R Package for Estimating Normalizing Constants. \emph{Journal of Statistical #' Software, 92}. \doi{10.18637/jss.v092.i10} #' #' Gronau, Q. F., Sarafoglou, A., Matzke, D., Ly, A., Boehm, U., #' Marsman, M., Leslie, D. S., Forster, J. J., Wagenmakers, E.-J., & #' Steingroever, H. (in press). A tutorial on bridge sampling. \emph{Journal of #' Mathematical Psychology}. \url{https://arxiv.org/abs/1703.05984} \cr #' \code{vignette("bridgesampling_tutorial")} #' #' Gronau, Q. F., Wagenmakers, E.-J., Heck, D. W., & Matzke, D. (2019). A #' Simple Method for Comparing Complex Models: Bayesian Model Comparison for #' Hierarchical Multinomial Processing Tree Models Using Warp-III Bridge #' Sampling. \emph{Psychometrika}, 84(1), 261–284. #' \doi{10.1007/s11336-018-9648-3} #' #' Meng, X.-L., & Wong, W. H. (1996). Simulating ratios of normalizing #' constants via a simple identity: A theoretical exploration. \emph{Statistica #' Sinica, 6}, 831-860. #' \url{https://www3.stat.sinica.edu.tw/statistica/j6n4/j6n43/j6n43.htm} #' #' Meng, X.-L., & Schilling, S. (2002). Warp bridge sampling. \emph{Journal of #' Computational and Graphical Statistics, 11(3)}, 552-586. #' \doi{10.1198/106186002457} #' #' Micaletto, G., & Vehtari, A. (2025). Monte Carlo standard errors for bridge #' sampling marginal likelihood estimation. \emph{arXiv preprint}, #' arXiv:2508.14487. \url{https://arxiv.org/abs/2508.14487} #' #' Overstall, A. M., & Forster, J. J. (2010). Default Bayesian model #' determination methods for generalised linear mixed models. #' \emph{Computational Statistics & Data Analysis, 54}, 3269-3288. #' \doi{10.1016/j.csda.2010.03.008} #'@example examples/example.bridge_sampler.R #' #'@seealso \code{\link{bf}} allows the user to calculate Bayes factors and #' \code{\link{post_prob}} allows the user to calculate posterior model #' probabilities from bridge sampling estimates. \code{\link{bridge-methods}} #' lists some additional methods that automatically invoke the #' \code{\link{error_measures}} function. #' #'@importFrom mvtnorm rmvnorm dmvnorm #'@importFrom Matrix nearPD #'@import Brobdingnag #'@importFrom stringr str_sub #'@importFrom stats qnorm pnorm dnorm median cov var #'@export bridge_sampler <- function(samples, ...) { UseMethod("bridge_sampler", samples) } #' @rdname bridge_sampler #' @export bridge_sampler.CmdStanMCMC <- function( samples = NULL, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, maxiter = 1000, silent = FALSE, verbose = FALSE, ... ) { draws <- samples$unconstrain_draws(format = "matrix") parameters <- colnames(draws) lb <- rep(-Inf, length(parameters)) ub <- rep(Inf, length(parameters)) names(lb) <- names(ub) <- parameters bridge_out <- bridge_sampler.matrix( samples = draws, ..., maxiter = maxiter, silent = silent, lb = lb, ub = ub, repetitions = repetitions, method = method, log_posterior = .cmdstan_log_posterior, cores = cores, data = samples, use_neff = use_neff, verbose = verbose ) return(bridge_out) } #' @rdname bridge_sampler #' @export bridge_sampler.stanfit <- function( samples = NULL, stanfit_model = samples, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, maxiter = 1000, silent = FALSE, verbose = FALSE, ... ) { # cores > 1 only for unix: if (!(.Platform$OS.type == "unix") & (cores != 1)) { warning( "cores > 1 only possible on Unix/MacOs. Uses 'core = 1' instead.", call. = FALSE ) cores <- 1L } # convert samples into matrix if (!requireNamespace("rstan")) { stop("package rstan required") } ex <- rstan::extract(samples, permuted = FALSE) skeleton <- .create_skeleton( samples@sim$pars_oi, samples@par_dims[samples@sim$pars_oi] ) upars <- apply(ex, 1:2, FUN = function(theta) { rstan::unconstrain_pars(stanfit_model, .rstan_relist(theta, skeleton)) }) if (length(dim(upars)) == 2) { # for one parameter models dim(upars) <- c(1, dim(upars)) } nr <- dim(upars)[2] samples4fit_index <- seq_len(nr) %in% seq_len(round(nr / 2)) # split samples in two parts samples_4_fit <- apply(upars[, samples4fit_index, , drop = FALSE], 1, rbind) samples_4_iter_stan <- upars[, !samples4fit_index, , drop = FALSE] samples_4_iter_tmp <- vector("list", dim(upars)[3]) for (i in seq_along(samples_4_iter_tmp)) { samples_4_iter_tmp[[i]] <- coda::as.mcmc(t(samples_4_iter_stan[,, i])) } samples_4_iter_tmp <- coda::as.mcmc.list(samples_4_iter_tmp) if (use_neff) { neff <- tryCatch( median(coda::effectiveSize(samples_4_iter_tmp)), error = function(e) { warning( "effective sample size cannot be calculated, has been replaced by number of samples.", call. = FALSE ) return(NULL) } ) } else { neff <- NULL } samples_4_iter <- apply(samples_4_iter_stan, 1, rbind) parameters <- paste0("x", (seq_len(dim(upars)[1]))) transTypes <- rep("unbounded", length(parameters)) names(transTypes) <- parameters # prepare lb and ub lb <- rep(-Inf, length(parameters)) ub <- rep(Inf, length(parameters)) names(lb) <- names(ub) <- parameters colnames(samples_4_iter) <- paste0("trans_", parameters) colnames(samples_4_fit) <- paste0("trans_", parameters) # run bridge sampling if (cores == 1) { bridge_output <- do.call( what = paste0(".bridge.sampler.", method), args = list( samples_4_fit = samples_4_fit, samples_4_iter = samples_4_iter, neff = neff, use_ess = use_neff, log_posterior = .stan_log_posterior, data = list(stanfit = stanfit_model), lb = lb, ub = ub, param_types = rep("real", ncol(samples_4_fit)), transTypes = transTypes, repetitions = repetitions, cores = cores, packages = "rstan", maxiter = maxiter, silent = silent, verbose = verbose, r0 = 0.5, tol1 = 1e-10, tol2 = 1e-4 ) ) } else { bridge_output <- do.call( what = paste0(".bridge.sampler.", method), args = list( samples_4_fit = samples_4_fit, samples_4_iter = samples_4_iter, neff = neff, use_ess = use_neff, log_posterior = .stan_log_posterior, data = list(stanfit = stanfit_model), lb = lb, ub = ub, param_types = rep("real", ncol(samples_4_fit)), transTypes = transTypes, repetitions = repetitions, varlist = "stanfit", envir = sys.frame(sys.nframe()), cores = cores, packages = "rstan", maxiter = maxiter, silent = silent, verbose = verbose, r0 = 0.5, tol1 = 1e-10, tol2 = 1e-4 ) ) } return(bridge_output) } #' @rdname bridge_sampler #' @export bridge_sampler.mcmc.list <- function( samples = NULL, log_posterior = NULL, ..., data = NULL, lb = NULL, ub = NULL, repetitions = 1, param_types = rep("real", ncol(samples[[1]])), method = "normal", cores = 1, use_neff = TRUE, packages = NULL, varlist = NULL, envir = .GlobalEnv, rcppFile = NULL, maxiter = 1000, silent = FALSE, verbose = FALSE ) { # split samples in two parts nr <- nrow(samples[[1]]) samples4fit_index <- seq_len(nr) %in% seq_len(round(nr / 2)) samples_4_fit_tmp <- samples[samples4fit_index, , drop = FALSE] samples_4_fit_tmp <- do.call("rbind", samples_4_fit_tmp) # check lb and ub if (!is.numeric(lb)) { stop("lb needs to be numeric", call. = FALSE) } if (!is.numeric(ub)) { stop("ub needs to be numeric", call. = FALSE) } if (!all(colnames(samples_4_fit_tmp) %in% names(lb))) { stop("lb does not contain all parameters.", call. = FALSE) } if (!all(colnames(samples_4_fit_tmp) %in% names(ub))) { stop("ub does not contain all parameters.", call. = FALSE) } # transform parameters to real line tmp <- .transform2Real(samples_4_fit_tmp, lb, ub) samples_4_fit <- tmp$theta_t transTypes <- tmp$transTypes samples_4_iter_tmp <- lapply( samples[!samples4fit_index, , drop = FALSE], function(x) .transform2Real(x, lb = lb, ub = ub)$theta_t ) # compute effective sample size if (use_neff) { samples_4_iter_tmp <- coda::mcmc.list(lapply( samples_4_iter_tmp, coda::mcmc )) neff <- tryCatch( median(coda::effectiveSize(samples_4_iter_tmp)), error = function(e) { warning( "effective sample size cannot be calculated, has been replaced by number of samples.", call. = FALSE ) return(NULL) } ) } else { neff <- NULL } # convert to matrix samples_4_iter <- do.call("rbind", samples_4_iter_tmp) # run bridge sampling out <- do.call( what = paste0(".bridge.sampler.", method), args = list( samples_4_fit = samples_4_fit, samples_4_iter = samples_4_iter, neff = neff, use_ess = use_neff, log_posterior = log_posterior, "..." = ..., data = data, lb = lb, ub = ub, transTypes = transTypes, repetitions = repetitions, cores = cores, packages = packages, varlist = varlist, envir = envir, param_types = param_types, rcppFile = rcppFile, maxiter = maxiter, silent = silent, verbose = verbose, r0 = 0.5, tol1 = 1e-10, tol2 = 1e-4 ) ) return(out) } #' @rdname bridge_sampler #' @export bridge_sampler.mcmc <- function( samples = NULL, log_posterior = NULL, ..., data = NULL, lb = NULL, ub = NULL, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, packages = NULL, varlist = NULL, envir = .GlobalEnv, rcppFile = NULL, maxiter = 1000, param_types = rep("real", ncol(samples)), silent = FALSE, verbose = FALSE ) { samples <- as.matrix(samples) bridge_output <- bridge_sampler( samples = samples, log_posterior = log_posterior, ..., data = data, lb = lb, ub = ub, repetitions = repetitions, method = method, cores = cores, use_neff = use_neff, packages = packages, varlist = varlist, envir = envir, rcppFile = rcppFile, maxiter = maxiter, param_types = param_types, silent = silent, verbose = verbose ) return(bridge_output) } #' @export #' @rdname bridge_sampler bridge_sampler.matrix <- function( samples = NULL, log_posterior = NULL, ..., data = NULL, lb = NULL, ub = NULL, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, packages = NULL, varlist = NULL, envir = .GlobalEnv, rcppFile = NULL, maxiter = 1000, param_types = rep("real", ncol(samples)), silent = FALSE, verbose = FALSE ) { # see Meng & Wong (1996), equation 4.1 # Check simplex computation is_simplex_param <- param_types == "simplex" if (any(is_simplex_param)) { simplex_samples <- samples[, is_simplex_param] if (any(!(round(rowSums(simplex_samples), 6) == 1L))) { stop(paste( "Simplex parameters do not sum to one. This could be due to having multiple separate sets of simplex parameters, which are not supported. " )) } # Remove the last simplex variable because it is superfluous. last_sim <- which(is_simplex_param)[sum(is_simplex_param)] samples <- samples[, -last_sim, drop = FALSE] param_types <- param_types[-last_sim] lb <- lb[-last_sim] ub <- ub[-last_sim] } # transform parameters to real line tmp <- .transform2Real(samples, lb, ub, theta_types = param_types) theta_t <- tmp$theta_t transTypes <- tmp$transTypes # split samples for proposal/iterative scheme nr <- nrow(samples) samples4fit_index <- seq_len(nr) %in% seq_len(round(nr / 2)) # split samples in two parts samples_4_fit <- theta_t[samples4fit_index, , drop = FALSE] samples_4_iter <- theta_t[!samples4fit_index, , drop = FALSE] # compute effective sample size if (use_neff) { neff <- tryCatch( median(coda::effectiveSize(coda::mcmc(samples_4_iter))), error = function(e) { warning( "effective sample size cannot be calculated, has been replaced by number of samples.", call. = FALSE ) return(NULL) } ) } else { neff <- NULL } out <- do.call( what = paste0(".bridge.sampler.", method), args = list( samples_4_fit = samples_4_fit, samples_4_iter = samples_4_iter, neff = neff, use_ess = use_neff, log_posterior = log_posterior, "..." = ..., data = data, lb = lb, ub = ub, transTypes = transTypes, param_types = param_types, repetitions = repetitions, cores = cores, packages = packages, varlist = varlist, envir = envir, rcppFile = rcppFile, maxiter = maxiter, silent = silent, verbose = verbose, r0 = 0.5, tol1 = 1e-10, tol2 = 1e-4 ) ) return(out) } #' @rdname bridge_sampler #' @export #' @importFrom utils read.csv bridge_sampler.stanreg <- function( samples, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, maxiter = 1000, silent = FALSE, verbose = FALSE, ... ) { df <- eval(samples$call$diagnostic_file) if (is.null(df)) { stop( "the 'diagnostic_file' option must be specified in the call to ", samples$stan_function, " to use the 'bridge_sampler'" ) } sf <- samples$stanfit chains <- ncol(sf) if (chains > 1) { df <- sapply(1:chains, FUN = function(j) { sub("\\.csv$", paste0("_", j, ".csv"), df) }) } samples_list <- lapply(df, FUN = function(f) { d <- read.csv(f, comment.char = "#") excl <- c( "lp__", "accept_stat__", "stepsize__", "treedepth__", "n_leapfrog__", "divergent__", "energy__" ) d <- d[, !(colnames(d) %in% excl), drop = FALSE] coda::as.mcmc(as.matrix(d[, 1:rstan::get_num_upars(sf), drop = FALSE])) }) samples <- coda::as.mcmc.list(samples_list) lb <- rep(-Inf, ncol(samples[[1]])) ub <- rep(Inf, ncol(samples[[1]])) names(lb) <- names(ub) <- colnames(samples[[1]]) # cores > 1 only for unix: if (!(.Platform$OS.type == "unix") & (cores != 1)) { warning( "cores > 1 only possible on Unix/MacOs. Uses 'core = 1' instead.", call. = FALSE ) cores <- 1L } if (cores == 1) { bridge_output <- bridge_sampler( samples = samples, log_posterior = .stan_log_posterior, data = list(stanfit = sf), lb = lb, ub = ub, repetitions = repetitions, method = method, cores = cores, use_neff = use_neff, packages = "rstan", maxiter = maxiter, silent = silent, verbose = verbose ) } else { bridge_output <- bridge_sampler( samples = samples, log_posterior = .stan_log_posterior, data = list(stanfit = sf), lb = lb, ub = ub, repetitions = repetitions, varlist = "stanfit", envir = sys.frame(sys.nframe()), method = method, cores = cores, use_neff = use_neff, packages = "rstan", maxiter = maxiter, silent = silent, verbose = verbose ) } return(bridge_output) } #' @rdname bridge_sampler #' @export bridge_sampler.rjags <- function( samples = NULL, log_posterior = NULL, ..., data = NULL, lb = NULL, ub = NULL, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, packages = NULL, varlist = NULL, envir = .GlobalEnv, rcppFile = NULL, maxiter = 1000, silent = FALSE, verbose = FALSE ) { # convert to mcmc.list samples <- coda::as.mcmc(samples) cn <- coda::varnames(samples) samples <- samples[, cn != "deviance", drop = FALSE] # run bridge sampling out <- bridge_sampler( samples = samples, log_posterior = log_posterior, ..., data = data, lb = lb, ub = ub, repetitions = repetitions, method = method, cores = cores, use_neff = use_neff, packages = packages, varlist = varlist, envir = envir, rcppFile = rcppFile, maxiter = maxiter, silent = silent, verbose = verbose ) return(out) } #' @rdname bridge_sampler #' @export bridge_sampler.runjags <- function( samples = NULL, log_posterior = NULL, ..., data = NULL, lb = NULL, ub = NULL, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, packages = NULL, varlist = NULL, envir = .GlobalEnv, rcppFile = NULL, maxiter = 1000, silent = FALSE, verbose = FALSE ) { # convert to mcmc.list samples <- coda::as.mcmc.list(samples) # run bridge sampling out <- bridge_sampler( samples = samples, log_posterior = log_posterior, ..., data = data, lb = lb, ub = ub, repetitions = repetitions, method = method, cores = cores, use_neff = use_neff, packages = packages, varlist = varlist, envir = envir, rcppFile = rcppFile, maxiter = maxiter, silent = silent, verbose = verbose ) return(out) } #' @rdname bridge_sampler #' @export bridge_sampler.MCMC_refClass <- function( samples, repetitions = 1, method = "normal", cores = 1, use_neff = TRUE, maxiter = 1000, silent = FALSE, verbose = FALSE, ... ) { if (!requireNamespace("nimble")) { stop("package nimble required") } ## functions for nimble support .log_posterior_nimble <- ".log_posterior_nimble <- nimble::nimbleFunction( # based on code by Perry de Valpine ## setup code is executed in R and specializes an instance ## of the nimbleFunction to a particular model or nodes setup = function(model, nodes) { calcNodes <- model$getDependencies(nodes) }, ## run code is called repeatedly and can be converted into C++ run = function(sample = double(1)) { values(model, nodes) <<- sample out <- model$calculate(calcNodes) return(out) returnType(double(0)) } )" eval(parse(text = .log_posterior_nimble)) ## trick for avoiding R CMD check NOTEs .nimble_bounds <- function(samples, model, which) { if (!(which %in% c("lower", "upper"))) { stop('"which" needs to be either "lower" or "upper"\n', call. = FALSE) } cn <- colnames(samples) bounds <- numeric(length(cn)) names(bounds) <- cn for (i in seq_along(cn)) { bounds[[cn[i]]] <- model$getBound(cn[i], which) } return(bounds) } # cores > 1 only for unix: if (!(.Platform$OS.type == "unix") & (cores != 1)) { warning( "cores > 1 only possible on Unix/MacOs. Uses 'core = 1' instead.", call. = FALSE ) cores <- 1L } mcmc_samples <- as.matrix(samples$mvSamples) if (all(is.na(mcmc_samples))) { stop( "nimble object does not contain samples. Call runMCMC() first.", call. = FALSE ) } # make sure that samples is a list if (is.matrix(mcmc_samples)) { # TRUE in case nchains = 1 mcmc_samples <- list(mcmc_samples) } # convert samples to mcmc.list samples_mcmc <- lapply(mcmc_samples, FUN = coda::as.mcmc) samples_mcmc_list <- coda::as.mcmc.list(samples_mcmc) ## get model name from MCMC_refClass object mod_name <- ls(samples$nimbleProject$models)[1] nimble_model <- samples$nimbleProject$models[[mod_name]] # compile log_posterior for bridge sampling log_posterior_tmp <- .log_posterior_nimble( model = nimble_model, nodes = colnames(mcmc_samples[[1]]) ) suppressMessages( clog_posterior <- nimble::compileNimble( log_posterior_tmp, project = nimble_model ) ) # wrapper to match required format for log_posterior log_posterior <- function(x, data) { clog_posterior$run(x) } out <- bridge_sampler( samples = samples_mcmc_list, log_posterior = log_posterior, ..., data = NULL, lb = .nimble_bounds(mcmc_samples[[1]], nimble_model, "lower"), ub = .nimble_bounds(mcmc_samples[[1]], nimble_model, "upper"), repetitions = repetitions, method = method, cores = cores, use_neff = use_neff, packages = "nimble", maxiter = maxiter, silent = silent, verbose = verbose ) return(out) } bridgesampling/R/turtles-data.R0000644000176200001440000000260215055304401016173 0ustar liggesusers#' Turtles Data from Janzen, Tucker, and Paukstis (2000) #' #' This data set contains information about 244 newborn turtles from 31 #' different clutches. For each turtle, the data set includes information about #' survival status (column \code{y}; 0 = died, 1 = survived), birth weight in #' grams (column \code{x}), and clutch (family) membership (column #' \code{clutch}; an integer between one and 31). The clutches have been ordered #' according to mean birth weight. #' #' @docType data #' @keywords dataset #' @name turtles #' @usage turtles #' @format A data.frame with 244 rows and 3 variables. #' @source Janzen, F. J., Tucker, J. K., & Paukstis, G. L. (2000). Experimental #' analysis of an early life-history stage: Selection on size of hatchling #' turtles. \emph{Ecology, 81(8)}, 2290-2304. #' \doi{10.2307/177115} #' #' Overstall, A. M., & Forster, J. J. (2010). Default Bayesian model #' determination methods for generalised linear mixed models. #' \emph{Computational Statistics & Data Analysis, 54}, 3269-3288. #' \doi{10.1016/j.csda.2010.03.008} #' #' Sinharay, S., & Stern, H. S. (2005). An empirical comparison of methods for #' computing Bayes factors in generalized linear mixed models. \emph{Journal #' of Computational and Graphical Statistics, 14(2)}, 415-435. #' \doi{10.1198/106186005X47471} #' @encoding UTF-8 #' #' @example examples/example.turtles.R NULL bridgesampling/R/ier-data.R0000644000176200001440000000201615055304401015247 0ustar liggesusers#' Standardized International Exchange Rate Changes from 1975 to 1986 #' #' This data set contains the changes in monthly international exchange rates for pounds sterling from January 1975 to December 1986 obtained from West and Harrison (1997, pp. 612-615). Currencies tracked are US Dollar (column \code{us_dollar}), Canadian Dollar (column \code{canadian_dollar}), Japanese Yen (column \code{yen}), French Franc (column \code{franc}), Italian Lira (column \code{lira}), and the (West) German Mark (column \code{mark}). Each series has been standardized with respect to its sample mean and standard deviation. #' #' @docType data #' @keywords dataset #' @name ier #' @usage ier #' @format A matrix with 143 rows and 6 columns. #' @source West, M., Harrison, J. (1997). \emph{Bayesian forecasting and dynamic models} (2nd ed.). Springer-Verlag, New York. #' #' Lopes, H. F., West, M. (2004). Bayesian model assessment in factor analysis. \emph{Statistica Sinica, 14}, 41-67. #' @encoding UTF-8 #' #' @example examples/example.ier.R NULL bridgesampling/R/bridge_sampler_warp3.R0000644000176200001440000003161515106567454017703 0ustar liggesusers.bridge.sampler.warp3 <- function( samples_4_fit, # matrix with already transformed samples for fitting the # proposal (rows are samples), colnames are "trans_x" where # x is the parameter name samples_4_iter, # matrix with already transformed samples for the # iterative scheme (rows are samples), colnames are "trans_x" # where x is the parameter name neff, # effective sample size of samples_4_iter (i.e., already transformed samples), scalar log_posterior, ..., data, lb, ub, transTypes, # types of transformations (unbounded/lower/upperbounded) for the different parameters (named character vector) param_types, # Sample space for transformations (real, circular, simplex) cores, repetitions, packages, varlist, envir, rcppFile, maxiter, silent, verbose, use_ess, r0, tol1, tol2 ) { if (is.null(neff)) { neff <- nrow(samples_4_iter) } n_post <- nrow(samples_4_iter) # get mean & covariance matrix and generate samples from proposal m <- apply(samples_4_fit, 2, mean) V_tmp <- cov(samples_4_fit) V <- as.matrix(nearPD(V_tmp)$mat) # make sure that V is positive-definite L <- t(chol(V)) # sample from multivariate normal distribution and evaluate for posterior samples and generated samples q12 <- dmvnorm( (samples_4_iter - matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE)) %*% t(solve(L)), sigma = diag(ncol(samples_4_fit)), log = TRUE ) q22 <- vector(mode = "list", length = repetitions) gen_samples <- vector(mode = "list", length = repetitions) for (i in seq_len(repetitions)) { gen_samples[[i]] <- rmvnorm(n_post, sigma = diag(ncol(samples_4_fit))) colnames(gen_samples[[i]]) <- colnames(samples_4_iter) q22[[i]] <- dmvnorm( gen_samples[[i]], sigma = diag(ncol(samples_4_fit)), log = TRUE ) } e <- as.brob(exp(1)) # evaluate log of likelihood times prior for posterior samples and generated samples q21 <- vector(mode = "list", length = repetitions) if (cores == 1) { q11 <- log( e^(apply( .invTransform2Real(samples_4_iter, lb, ub, param_types), 1, log_posterior, data = data, ... ) + .logJacobian(samples_4_iter, transTypes, lb, ub)) + e^(apply( .invTransform2Real( matrix(2 * m, nrow = n_post, ncol = length(m), byrow = TRUE) - samples_4_iter, lb, ub, param_types ), 1, log_posterior, data = data, ... ) + .logJacobian( matrix(2 * m, nrow = n_post, ncol = length(m), byrow = TRUE) - samples_4_iter, transTypes, lb, ub )) ) for (i in seq_len(repetitions)) { q21[[i]] <- log( e^(apply( .invTransform2Real( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) - gen_samples[[i]] %*% t(L), lb, ub, param_types ), 1, log_posterior, data = data, ... ) + .logJacobian( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) - gen_samples[[i]] %*% t(L), transTypes, lb, ub )) + e^(apply( .invTransform2Real( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) + gen_samples[[i]] %*% t(L), lb, ub, param_types ), 1, log_posterior, data = data, ... ) + .logJacobian( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) + gen_samples[[i]] %*% t(L), transTypes, lb, ub )) ) } } else if (cores > 1) { if (.Platform$OS.type == "unix") { split1a <- .split_matrix( matrix = .invTransform2Real(samples_4_iter, lb, ub, param_types), cores = cores ) split1b <- .split_matrix( matrix = .invTransform2Real( matrix(2 * m, nrow = n_post, ncol = length(m), byrow = TRUE) - samples_4_iter, lb, ub, param_types ), cores = cores ) q11a <- parallel::mclapply( split1a, FUN = function(x) apply(x, 1, log_posterior, data = data, ...), mc.preschedule = FALSE, mc.cores = cores ) q11b <- parallel::mclapply( split1b, FUN = function(x) apply(x, 1, log_posterior, data = data, ...), mc.preschedule = FALSE, mc.cores = cores ) q11 <- log( e^(unlist(q11a) + .logJacobian(samples_4_iter, transTypes, lb, ub)) + e^(unlist(q11b) + .logJacobian( matrix(2 * m, nrow = n_post, ncol = length(m), byrow = TRUE) - samples_4_iter, transTypes, lb, ub )) ) for (i in seq_len(repetitions)) { tmp_mat2 <- gen_samples[[i]] %*% t(L) split2a <- .split_matrix( matrix = .invTransform2Real( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) - tmp_mat2, lb, ub, param_types ), cores = cores ) split2b <- .split_matrix( matrix = .invTransform2Real( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) + tmp_mat2, lb, ub, param_types ), cores = cores ) q21a <- parallel::mclapply( split2a, FUN = function(x) apply(x, 1, log_posterior, data = data, ...), mc.preschedule = FALSE, mc.cores = cores ) q21b <- parallel::mclapply( split2b, FUN = function(x) apply(x, 1, log_posterior, data = data, ...), mc.preschedule = FALSE, mc.cores = cores ) q21[[i]] <- log( e^(unlist(q21a) + .logJacobian( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) - tmp_mat2, transTypes, lb, ub )) + e^(unlist(q21b) + .logJacobian( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) + tmp_mat2, transTypes, lb, ub )) ) } } else { cl <- parallel::makeCluster(cores, useXDR = FALSE) sapply(packages, function(x) { parallel::clusterCall( cl = cl, "require", package = x, character.only = TRUE ) }) parallel::clusterExport(cl = cl, varlist = varlist, envir = envir) if (!is.null(rcppFile)) { parallel::clusterExport( cl = cl, varlist = "rcppFile", envir = parent.frame() ) parallel::clusterCall( cl = cl, "require", package = "Rcpp", character.only = TRUE ) parallel::clusterEvalQ(cl = cl, Rcpp::sourceCpp(file = rcppFile)) } else if (is.character(log_posterior)) { parallel::clusterExport(cl = cl, varlist = log_posterior, envir = envir) } q11 <- log( e^(parallel::parRapply( cl = cl, x = .invTransform2Real(samples_4_iter, lb, ub, param_types), log_posterior, data = data, ... ) + .logJacobian(samples_4_iter, transTypes, lb, ub)) + e^(parallel::parRapply( cl = cl, x = .invTransform2Real( matrix(2 * m, nrow = n_post, ncol = length(m), byrow = TRUE) - samples_4_iter, lb, ub, param_types ), log_posterior, data = data, ... ) + .logJacobian( matrix(2 * m, nrow = n_post, ncol = length(m), byrow = TRUE) - samples_4_iter, transTypes, lb, ub )) ) for (i in seq_len(repetitions)) { q21[[i]] <- log( e^(parallel::parRapply( cl = cl, x = .invTransform2Real( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) - gen_samples[[i]] %*% t(L), lb, ub, param_types ), log_posterior, data = data, ... ) + .logJacobian( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) - gen_samples[[i]] %*% t(L), transTypes, lb, ub )) + e^(parallel::parRapply( cl = cl, x = .invTransform2Real( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) + gen_samples[[i]] %*% t(L), lb, ub, param_types ), log_posterior, data = data, ... ) + .logJacobian( matrix(m, nrow = n_post, ncol = length(m), byrow = TRUE) + gen_samples[[i]] %*% t(L), transTypes, lb, ub )) ) } parallel::stopCluster(cl) } } if (any(is.infinite(q11))) { warning( sum(is.infinite(q11)), " of the ", length(q11), " log_prob() evaluations on the warp-transformed posterior draws produced -Inf/Inf.", call. = FALSE ) } for (i in seq_len(repetitions)) { if (any(is.infinite(q21[[i]]))) { warning( sum(is.infinite(q21[[i]])), " of the ", length(q21[[i]]), " log_prob() evaluations on the warp-transformed proposal draws produced -Inf/Inf.", call. = FALSE ) } } if (any(is.na(q11))) { warning( sum(is.na(q11)), " evaluation(s) of log_prob() on the warp-transformed posterior draws produced NA and have been replaced by -Inf.", call. = FALSE ) q11[is.na(q11)] <- -Inf } for (i in seq_len(repetitions)) { if (any(is.na(q21[[i]]))) { warning( sum(is.na(q21[[i]])), " evaluation(s) of log_prob() on the warp-transformed proposal draws produced NA nd have been replaced by -Inf.", call. = FALSE ) q21[[i]][is.na(q21[[i]])] <- -Inf } } if (verbose) { print("summary(q12): (log_dens of proposal for posterior samples)") print(summary(q12)) print("summary(q22): (log_dens of proposal for generated samples)") print(lapply(q22, summary)) print("summary(q11): (log_dens of posterior for posterior samples)") print(summary(q11)) print("summary(q21): (log_dens of posterior for generated samples)") print(lapply(q21, summary)) } logml <- numeric(repetitions) niter <- numeric(repetitions) mcse_logmls <- numeric(repetitions) # run iterative updating scheme to compute log of marginal likelihood for (i in seq_len(repetitions)) { tmp <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21[[i]], q22 = q22[[i]], r0 = r0, tol = tol1, L = L, method = "warp3", maxiter = maxiter, silent = silent, criterion = "r", neff = neff, use_ess = use_ess ) if (is.na(tmp$logml) & !is.null(tmp$r_vals)) { warning( "logml could not be estimated within maxiter, rerunning with adjusted starting value. \nEstimate might be more variable than usual.", call. = FALSE ) lr <- length(tmp$r_vals) # use geometric mean as starting value r0_2 <- sqrt(tmp$r_vals[[lr - 1]] * tmp$r_vals[[lr]]) tmp <- .run.iterative.scheme( q11 = q11, q12 = q12, q21 = q21[[i]], q22 = q22[[i]], r0 = r0_2, tol = tol2, L = L, method = "warp3", maxiter = maxiter, silent = silent, criterion = "logml", neff = neff, use_ess = use_ess ) tmp$niter <- maxiter + tmp$niter } logml[i] <- tmp$logml niter[i] <- tmp$niter mcse_logmls[i] <- tmp$mcse_logml if (niter[i] == maxiter) { warning( "logml could not be estimated within maxiter, returning NA.", call. = FALSE ) } } if (repetitions == 1) { out <- list( logml = logml, niter = niter, method = "warp3", q11 = q11, q12 = q12, q21 = q21[[1]], q22 = q22[[1]], mcse_logml = mcse_logmls ) class(out) <- "bridge" } else if (repetitions > 1) { out <- list( logml = logml, niter = niter, method = "warp3", repetitions = repetitions, mcse_logml = mcse_logmls ) class(out) <- "bridge_list" } return(out) } bridgesampling/vignettes/0000755000176200001440000000000015107052017015247 5ustar liggesusersbridgesampling/vignettes/bridgesampling_tutorial.pdf.asis0000644000176200001440000000012215055304401023604 0ustar liggesusers%\VignetteIndexEntry{A Tutorial on Bridge Sampling} %\VignetteEngine{R.rsp::asis} bridgesampling/vignettes/bridgesampling_stan_ttest.Rmd0000644000176200001440000002073515055304401023160 0ustar liggesusers--- title: "Bayesian One-Sample T-Test (Stan)" author: "Quentin F. Gronau" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Bayesian One-Sample T-Test Stan} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how we can compute the (log) marginal likelihood and the Bayes factor for models fitted in `Stan`. This approach has the advantage that the user only needs to pass the fitted `stanfit` object which contains all information that is necessary to compute the (log) marginal likelihood. Here we show how one can conduct a Bayesian one-sample t-test as implemented in the `BayesFactor` package (Morey & Rouder, 2015). ## Model The Bayesian one-sample t-test makes the assumption that the observations are normally distributed with mean $\mu$ and variance $\sigma^2$. The model is then reparametrized in terms of the standardized effect size $\delta = \mu/\sigma$. For the standardized effect size, a Cauchy prior with location zero and scale $r = 1/\sqrt{2}$ is used. For the variance $\sigma^2$, Jeffreys's prior is used: $p(\sigma^2) \propto 1/\sigma^2$. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the effect size $\delta$ is zero, to the alternative hypothesis $\mathcal{H}_1$, which assigns $\delta$ the above described Cauchy prior. ## Data In this example, we will analyze the `sleep` data set from the `t.test` example. This data set shows the effect of two soporific drugs (increase in hours of sleep compared to control) on 10 patients. These data can be analyzed via a one-sample t-test by first computing the difference scores and then conducting the t-test using these difference scores as data. The difference scores are calculated as follows: ```{r} library(bridgesampling) set.seed(12345) # Sleep data from t.test example data(sleep) # compute difference scores y <- sleep$extra[sleep$group == 2] - sleep$extra[sleep$group == 1] n <- length(y) ``` ## Specifying the Models Next, we implement the models in `Stan`. Note that to compute the (log) marginal likelihood for a `Stan` model, we need to specify the model in a certain way. Instad of using `"~"` signs for specifying distributions, we need to directly use the (log) density functions. The reason for this is that when using the `"~"` sign, constant terms are dropped which are not needed for sampling from the posterior. However, for computing the marginal likelihood, these constants need to be retained. For instance, instead of writing `y ~ normal(mu, sigma)` we would need to write `target += normal_lpdf(y | mu, sigma)`. The models can then be specified and compiled as follows (note that it is necessary to install `rstan` for this): ```{r, eval=FALSE} library(rstan) # models stancodeH0 <- ' data { int n; // number of observations vector[n] y; // observations } parameters { real sigma2; // variance parameter } model { target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | 0, sqrt(sigma2)); // likelihood } ' stancodeH1 <- ' data { int n; // number of observations vector[n] y; // observations real r; // Cauchy prior scale } parameters { real delta; real sigma2;// variance parameter } model { target += cauchy_lpdf(delta | 0, r); // Cauchy prior on delta target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood } ' # compile models stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") ``` ## Fitting the Models Now we can fit the null and the alternative model in `Stan`. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models. ```{r, eval=FALSE} # fit models stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n), iter = 20000, warmup = 1000, chains = 4, cores = 1, control = list(adapt_delta = .99)) stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, r = 1/sqrt(2)), iter = 20000, warmup = 1000, chains = 4, cores = 1, control = list(adapt_delta = .99)) ``` ## Computing the (Log) Marginal Likelihoods Computing the (log) marginal likelihoods via the `bridge_sampler` function is now easy: we only need to pass the `stanfit` objects which contain all information necessary. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_stan_ttest.RData", package = "bridgesampling")) ``` ```{r, eval=FALSE} H0 <- bridge_sampler(stanfitH0, silent = TRUE) H1 <- bridge_sampler(stanfitH1, silent = TRUE) ``` We obtain: ```{r} print(H0) print(H1) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0)$percentage H1.error <- error_measures(H1)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Computing the Bayes Factor To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{10}$, that is, the Bayes factor which quantifies how much more likely the data are under the alternative versus the null hypothesis: ```{r} # compute Bayes factor BF10 <- bf(H1, H0) print(BF10) ``` We can compare the bridge sampling result to the `BayesFactor` package result: ```{r, eval=FALSE} library(BayesFactor) BF10.BayesFactor <- extractBF(ttestBF(y), onlybf = TRUE) ``` We obtain: ```{r, message=FALSE} print(BF10.BayesFactor) ``` ## One-sided Test We can also conduct one-sided tests. For instance, we could test the hypothesis that the effect size is positive versus the null hypothesis. Since we already fitted the null model and computed its marginal likelihood, we only need to slightly adjust the alternative model to reflect the directed hypothesis. To achieve this, we need to truncate the Cauchy prior distribution for $\delta$ at zero and then renormalize the (log) density. This is easily achieved via the `Stan` function `cauchy_lccdf` which corresponds to the log of the complementary cumulative distribution function of the Cauchy distribution. Thus, `cauchy_lccdf(0 | 0, r)` gives us the log of the area greater than zero which is required for renormalizing the truncated Cauchy prior. The model can then be specified and fitted as follows: ```{r, eval=FALSE} stancodeHplus <- ' data { int n; // number of observations vector[n] y; // observations real r; // Cauchy prior scale } parameters { real delta; // constrained to be positive real sigma2;// variance parameter } model { target += cauchy_lpdf(delta | 0, r) - cauchy_lccdf(0 | 0, r); // Cauchy prior on delta target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood } ' # compile and fit model stanmodelHplus <- stan_model(model_code = stancodeHplus, model_name="stanmodel") stanfitHplus <- sampling(stanmodelHplus, data = list(y = y, n = n, r = 1/sqrt(2)), iter = 30000, warmup = 1000, chains = 4, control = list(adapt_delta = .99)) ``` The (log) marginal likelihood is then computed as follows: ```{r,eval=FALSE} Hplus <- bridge_sampler(stanfitHplus, silent = TRUE) ``` We obtain: ```{r} print(Hplus) ``` We can again use the `error_measures` function to compute an approximate percentage error of the estimate: ```{r,eval=FALSE} Hplus.error <- error_measures(Hplus)$percentage ``` We obtain: ```{r} print(Hplus.error) ``` The one-sided Bayes factor in favor of a positive effect versus the null hypothesis can be computed as follows: ```{r} # compute Bayes factor BFplus0 <- bf(Hplus, H0) print(BFplus0) ``` We can compare the bridge sampling result to the `BayesFactor` package result: ```{r, eval=FALSE} BFplus0.BayesFactor <- extractBF(ttestBF(y, nullInterval = c(0, Inf)), onlybf = TRUE)[1] ``` We obtain: ```{r} print(BFplus0.BayesFactor) ``` ## References Richard D. Morey and Jeffrey N. Rouder (2015). BayesFactor: Computation of Bayes Factors for Common Designs. R package version 0.9.12-2. \url{https://CRAN.R-project.org/package=BayesFactor} bridgesampling/vignettes/bridgesampling_example_nimble.Rmd0000644000176200001440000001606115060116372023752 0ustar liggesusers--- title: "Hierarchical Normal Example (nimble)" author: "Quentin F. Gronau, Henrik Singmann & Perry de Valpine" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Hierarchical Normal Example Nimble} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in `nimble`. The [`nimble` documentation](https://r-nimble.org/manual/cha-welcome-nimble.html) provides a comprehensive overview. This vignette uses the same models and data as the [`Stan` vignette](bridgesampling_example_stan.html) and [`Jags` vignette](bridgesampling_example_jags.html). ## Model and Data The model that we will use assumes that each of the $n$ observations $y_i$ (where $i$ indexes the observation, $i = 1,2,...,n$) is normally distributed with corresponding mean $\theta_i$ and a common known variance $\sigma^2$: $y_i \sim \mathcal{N}(\theta_i, \sigma^2)$. Each $\theta_i$ is drawn from a normal group-level distribution with mean $\mu$ and variance $\tau^2$: $\theta_i \sim \mathcal{N}(\mu, \tau^2)$. For the group-level mean $\mu$, we use a normal prior distribution of the form $\mathcal{N}(\mu_0, \tau^2_0)$. For the group-level variance $\tau^2$, we use an inverse-gamma prior of the form $\text{Inv-Gamma}(\alpha, \beta)$. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the group-level mean $\mu = 0$, to the alternative model $\mathcal{H}_1$, which allows $\mu$ to be different from zero. First, we generate some data from the null model: ```{r} library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ``` Next, we specify the prior parameters $\mu_0$, $\tau^2_0$, $\alpha$, and $\beta$: ```{r,eval=FALSE} ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ``` ## Specifying the Models Next, we implement the models in `nimble`. This requires to first transform the code into a `nimbleModel`, then we need to set the data, and then we can compile the model. Given that `nimble` is build on BUGS, the similarity between the `nimble` code and the [`Jags` code](bridgesampling_example_jags.html) is not too surprising. ```{r, eval=FALSE} library("nimble") # models codeH0 <- nimbleCode({ invTau2 ~ dgamma(1, 1) tau2 <- 1/invTau2 for (i in 1:20) { theta[i] ~ dnorm(0, sd = sqrt(tau2)) y[i] ~ dnorm(theta[i], sd = 1) } }) codeH1 <- nimbleCode({ mu ~ dnorm(0, sd = 1) invTau2 ~ dgamma(1, 1) tau2 <- 1/invTau2 for (i in 1:20) { theta[i] ~ dnorm(mu, sd = sqrt(tau2)) y[i] ~ dnorm(theta[i], sd = 1) } }) ## steps for H0: modelH0 <- nimbleModel(codeH0) modelH0$setData(y = y) # set data cmodelH0 <- compileNimble(modelH0) # make compiled version from generated C++ ## steps for H1: modelH1 <- nimbleModel(codeH1) modelH1$setData(y = y) # set data cmodelH1 <- compileNimble(modelH1) # make compiled version from generated C++ ``` ## Fitting the Models Fitting a model with `nimble` requires one to first create an MCMC function from the (compiled or uncompiled) model. This function then needs to be compiled again. With this object we can then create the samples. Note that nimble uses a reference object semantic so we do not actually need the samples object, as the samples will be saved in the MCMC function objects. But as `runMCMC` returns them anyway, we nevertheless save them. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models. ```{r, eval=FALSE} # build MCMC functions, skipping customization of the configuration. mcmcH0 <- buildMCMC(modelH0, monitors = modelH0$getNodeNames(stochOnly = TRUE, includeData = FALSE)) mcmcH1 <- buildMCMC(modelH1, monitors = modelH1$getNodeNames(stochOnly = TRUE, includeData = FALSE)) # compile the MCMC function via generated C++ cmcmcH0 <- compileNimble(mcmcH0, project = modelH0) cmcmcH1 <- compileNimble(mcmcH1, project = modelH1) # run the MCMC. This is a wrapper for cmcmc$run() and extraction of samples. # the object samplesH1 is actually not needed as the samples are also in cmcmcH1 samplesH0 <- runMCMC(cmcmcH0, niter = 1e5, nburnin = 1000, nchains = 2, progressBar = FALSE) samplesH1 <- runMCMC(cmcmcH1, niter = 1e5, nburnin = 1000, nchains = 2, progressBar = FALSE) ``` ## Computing the (Log) Marginal Likelihoods Computing the (log) marginal likelihoods via the `bridge_sampler` function is now easy: we only need to pass the compiled MCMC function objects (of class `"MCMC_refClass"`) which contain all information necessary. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_example_nimble.RData", package = "bridgesampling")) ``` ```{r,eval=FALSE} # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(cmcmcH0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(cmcmcH1, silent = TRUE) ``` We obtain: ```{r} print(H0.bridge) print(H1.bridge) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Bayesian Model Comparison To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{01}$, that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model: ```{r} # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ``` In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the `post_prob` function: ```{r} # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ``` When the argument `prior_prob` is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the `prior_prob` argument to specify different prior model probabilities: ```{r} # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) ``` bridgesampling/vignettes/bridgesampling_example_jags.Rmd0000644000176200001440000002477215055304401023434 0ustar liggesusers--- title: "Hierarchical Normal Example (JAGS)" author: "Quentin F. Gronau" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Hierarchical Normal Example JAGS} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in `JAGS`. This vignette uses the same models and data as the [`Stan` vignette](bridgesampling_example_stan.html). ## Model and Data The model that we will use assumes that each of the $n$ observations $y_i$ (where $i$ indexes the observation, $i = 1,2,...,n$) is normally distributed with corresponding mean $\theta_i$ and a common known variance $\sigma^2$: $y_i \sim \mathcal{N}(\theta_i, \sigma^2)$. Each $\theta_i$ is drawn from a normal group-level distribution with mean $\mu$ and variance $\tau^2$: $\theta_i \sim \mathcal{N}(\mu, \tau^2)$. For the group-level mean $\mu$, we use a normal prior distribution of the form $\mathcal{N}(\mu_0, \tau^2_0)$. For the group-level variance $\tau^2$, we use an inverse-gamma prior of the form $\text{Inv-Gamma}(\alpha, \beta)$. We will use `JAGS` to fit the model which parametrizes the normal distribution in terms of the precision (i.e., one over the variance). Consequently, we implement this inverse-gamma prior on $\tau^2$ by placing a gamma prior of the form $\text{Gamma}(\alpha, \beta)$ on the precision; we call this precision parameter `invTau2` in the code. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the group-level mean $\mu = 0$, to the alternative model $\mathcal{H}_1$, which allows $\mu$ to be different from zero. First, we generate some data from the null model: ```{r} library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ``` Next, we specify the prior parameters $\mu_0$, $\tau^2_0$, $\alpha$, and $\beta$: ```{r,eval=FALSE} ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ``` ## Fitting the Models Now we can fit the null and the alternative model in `JAGS` (note that it is necessary to install `JAGS` for this). One usually requires a larger number of posterior sample for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples (i.e., 50,000 post burn-in samples per chain) for this comparatively simple model. ```{r, eval=FALSE} library(R2jags) ### functions to get posterior samples ### # H0: mu = 0 getSamplesModelH0 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(0, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1) return(s) } # H1: mu != 0 getSamplesModelH1 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(mu, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } mu ~ dnorm(mu0, 1/tau20) invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "mu", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1) return(s) } ### get posterior samples ### # create data lists for JAGS data_H0 <- list(y = y, n = length(y), alpha = alpha, beta = beta, sigma2 = sigma2) data_H1 <- list(y = y, n = length(y), mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2) # fit models samples_H0 <- getSamplesModelH0(data_H0) samples_H1 <- getSamplesModelH1(data_H1) ``` ## Specifying the Unnormalized Log Posterior Function The next step is to write the corresponding `log_posterior` (i.e., unnormalized posterior) function for both models. This function takes one draw from the joint posterior and the data object as input and returns the log of the unnormalized joint posterior density. When using MCMC software such as `JAGS` or `Stan`, specifying this function is relatively simple. As a rule of thumb, one only needs to look for all places where a "`~`" sign appears in the model code. The log of the densities on the right-hand side of these "`~`" symbols needs to be evaluated for the relevant quantities and then these log densities values are summed. For example, in the null model, there are three "`~`" signs. Starting at the data-level, we need to evaluate the log of the normal density with mean $\theta_i$ and variance $\sigma^2$ for all $y_i$ and then sum the resulting log density values. Next, we move one step up in the model and evaluate the log of the group-level density for all $\theta_i$. Hence, we evaluate the log of the normal density for $\theta_i$ with mean $\mu = 0$ and variance $\tau^2$ (remember that `JAGS` parametrizes the normal distribution in terms of the precision `invTau2` = $1/\tau^2$; in contrast, `R` parametrizes it in terms of the standard deviation) and sum the resulting log density values. The result of this summation is added to the result of the previous summation for the data-level normal distribution. Finally, we need to evaluate the log of the prior density for `invTau2`. This means that we compute the log density of the gamma distribution with parameters $\alpha$ and $\beta$ for the sampled `invTau2` value and add the resulting log density value to the result of summing the data-level and group-level log densities. The unnormalized log posterior for the alternative model can be obtained in a similar fashion. The resulting functions look as follows: ```{r,eval=FALSE} ### functions for evaluating the unnormalized posteriors on log scale ### log_posterior_H0 <- function(samples.row, data) { mu <- 0 invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } log_posterior_H1 <- function(samples.row, data) { mu <- samples.row[[ "mu" ]] invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dnorm(mu, data$mu0, sqrt(data$tau20), log = TRUE) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } ``` ## Specifying the Parameter Bounds The final step before computing the log marginal likelihoods is to specify the parameter bounds. In this example, for both models, all parameters can range from $-\infty$ to $\infty$ except the precision `invTau2` which has a lower bound of zero. These boundary vectors need to be named and the names need to match the order of the parameters. ```{r,eval=FALSE} # specify parameter bounds H0 cn <- colnames(samples_H0$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H0 <- rep(-Inf, length(cn)) ub_H0 <- rep(Inf, length(cn)) names(lb_H0) <- names(ub_H0) <- cn lb_H0[[ "invTau2" ]] <- 0 # specify parameter bounds H1 cn <- colnames(samples_H1$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H1 <- rep(-Inf, length(cn)) ub_H1 <- rep(Inf, length(cn)) names(lb_H1) <- names(ub_H1) <- cn lb_H1[[ "invTau2" ]] <- 0 ``` Note that currently, the lower and upper bound of a parameter cannot be a function of the bounds of another parameter. Furthermore, constraints that depend on multiple parameters of the model are not supported. This excludes, for example, parameters that constitute a covariance matrix or sets of parameters that need to sum to one. ## Computing the (Log) Marginal Likelihoods Now we are ready to compute the log marginal likelihoods using the `bridge_sampler` function. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_example_jags.RData", package = "bridgesampling")) ``` ```{r,eval=FALSE} # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(samples = samples_H0, data = data_H0, log_posterior = log_posterior_H0, lb = lb_H0, ub = ub_H0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(samples = samples_H1, data = data_H1, log_posterior = log_posterior_H1, lb = lb_H1, ub = ub_H1, silent = TRUE) ``` We obtain: ```{r} print(H0.bridge) print(H1.bridge) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Bayesian Model Comparison To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{01}$, that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model: ```{r} # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ``` In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the `post_prob` function: ```{r} # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ``` When the argument `prior_prob` is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the `prior_prob` argument to specify different prior model probabilities: ```{r} # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) ``` bridgesampling/vignettes/bridgesampling_paper_extended.pdf.asis0000644000176200001440000000020115055304401024726 0ustar liggesusers%\VignetteIndexEntry{bridgesampling: An R Package for Estimating Normalizing Constants (Extended)} %\VignetteEngine{R.rsp::asis} bridgesampling/vignettes/bridgesampling_paper.pdf.asis0000644000176200001440000000020415055304401023051 0ustar liggesusers%\VignetteIndexEntry{bridgesampling: An R Package for Estimating Normalizing Constants (JSS version)} %\VignetteEngine{R.rsp::asis} bridgesampling/vignettes/bridgesampling_example_stan.Rmd0000644000176200001440000001607515055304401023452 0ustar liggesusers--- title: "Hierarchical Normal Example (Stan)" author: "Quentin F. Gronau" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Hierarchical Normal Example Stan} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in `Stan`. This vignette uses the same models and data as the [`Jags` vignette](bridgesampling_example_jags.html). ## Model and Data The model that we will use assumes that each of the $n$ observations $y_i$ (where $i$ indexes the observation, $i = 1,2,...,n$) is normally distributed with corresponding mean $\theta_i$ and a common known variance $\sigma^2$: $y_i \sim \mathcal{N}(\theta_i, \sigma^2)$. Each $\theta_i$ is drawn from a normal group-level distribution with mean $\mu$ and variance $\tau^2$: $\theta_i \sim \mathcal{N}(\mu, \tau^2)$. For the group-level mean $\mu$, we use a normal prior distribution of the form $\mathcal{N}(\mu_0, \tau^2_0)$. For the group-level variance $\tau^2$, we use an inverse-gamma prior of the form $\text{Inv-Gamma}(\alpha, \beta)$. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the group-level mean $\mu = 0$, to the alternative model $\mathcal{H}_1$, which allows $\mu$ to be different from zero. First, we generate some data from the null model: ```{r} library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ``` Next, we specify the prior parameters $\mu_0$, $\tau^2_0$, $\alpha$, and $\beta$: ```{r,eval=FALSE} ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ``` ## Specifying the Models Next, we implement the models in `Stan`. Note that to compute the (log) marginal likelihood for a `Stan` model, we need to specify the model in a certain way. Instad of using `"~"` signs for specifying distributions, we need to directly use the (log) density functions. The reason for this is that when using the `"~"` sign, constant terms are dropped which are not needed for sampling from the posterior. However, for computing the marginal likelihood, these constants need to be retained. For instance, instead of writing `y ~ normal(mu, sigma)` we would need to write `target += normal_lpdf(y | mu, sigma)`. The models can then be specified and compiled as follows (note that it is necessary to install `rstan` for this): ```{r, eval=FALSE} library(rstan) # models stancodeH0 <- 'data { int n; // number of observations vector[n] y; // observations real alpha; real beta; real sigma2; } parameters { real tau2; // group-level variance vector[n] theta; // participant effects } model { target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | 0, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' stancodeH1 <- 'data { int n; // number of observations vector[n] y; // observations real mu0; real tau20; real alpha; real beta; real sigma2; } parameters { real mu; real tau2; // group-level variance vector[n] theta; // participant effects } model { target += normal_lpdf(mu | mu0, sqrt(tau20)); target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | mu, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' # compile models stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") ``` ## Fitting the Models Now we can fit the null and the alternative model in `Stan`. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models. ```{r, eval=FALSE} # fit models stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 50000, warmup = 1000, chains = 3, cores = 1) stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 50000, warmup = 1000, chains = 3, cores = 1) ``` ## Computing the (Log) Marginal Likelihoods Computing the (log) marginal likelihoods via the `bridge_sampler` function is now easy: we only need to pass the `stanfit` objects which contain all information necessary. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_example_stan.RData", package = "bridgesampling")) ``` ```{r,eval=FALSE} # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(stanfitH0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(stanfitH1, silent = TRUE) ``` We obtain: ```{r} print(H0.bridge) print(H1.bridge) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Bayesian Model Comparison To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{01}$, that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model: ```{r} # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ``` In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the `post_prob` function: ```{r} # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ``` When the argument `prior_prob` is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the `prior_prob` argument to specify different prior model probabilities: ```{r} # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) ``` bridgesampling/data/0000755000176200001440000000000015055304401014147 5ustar liggesusersbridgesampling/data/ier.rda0000644000176200001440000000777415055304401015435 0ustar liggesusers‹uYw8–ÝxÌ BihèÕx‹7iè<YES);Y 7T4$JDF‰×¬¼çA©ì=Ëz²Gö¦Ÿ«ûœó^ž®ß®ï}Ÿû;>ßÏçsÔu9¨|LnÖ±Y4“Fçâ¤qÒ§§#ÆAã¢ñOGº…™ýô×ÙÓOÇA[y34K†ŠóawÓÔ°”"Š¾°%ߘ¶€1'Ÿm³°W=‡nÙ_8ÃGÎKvh¬8*² &lW¬Š1„õI™üËL@…¶E„•DÈ`œ°¥eT“zq=5ÇÍ£úè¿Äç(ÿîzΫžÈ)’Çùäü×t±£{ yŸŠôPOöÀ}Ñ^·`ßTþyŽ Åøô£ê‘>lç˜WrŽùþµ¯ž*Û^ÿ£z†Àû¢³x’)¾…ïþ(<­˜0.™ µ=°EˆçÁ11+ëaÝÃhŸ`´_í̹Ó>˜ÉK>©Ç:ã=.&§^盿æôØ?”n!L.éÒu½ÞXGÌßoz û4Lñ&|ãyÔž¹d_1nâ¬öÛ _Nû‰òíbÌ+©cïËæÒG¶9¿ÍÃýpöæ‘í;Á‡}ÅîŒ ×ãsÌ7âÏaðXÖ…š“û€Ï9ëDBtþÙ@ð²ù‹èÀæwÒ‡ýÞa<ïo<°ññÛ=ýá-eÇ/M5 Vm±=R K5¡’ LÿôµúÔ†0&MòìúNæás¼?îƒ÷Ã}°¾è;òÇ68b~˜tI¾¥Ãí{HæÒ=Ì¥¢ÃLý0ÓûïÛ÷aåÇWu¤kä̾bâÄ—lþ#ý±¿fú0è†|EîÕg)Ùóûá<Œå³é½šôAù¤ãÀõ3õ5EºÜAç 1¿ÄçÈ¿Ø'ì÷ƒAk¼ŵšôA¼’}gê >¤;ñëŒû4}ŽùÇû³Gì;v¾ê# uÄd€çÅæ›K¯ƒWQ&ÏÊOç+ í7ƒeãϾâ¼Gtõ·‹gñ¾!“‰ KÚáÇ£åJÚñ_Á3!nÛSªU Ý.oµÍ=C²0¢H ªæ~˜¿+3M.yuÁŸÁãukÏ 2é;ÎéJ[›+žÕññ퀭?·®É¹´d˜:Êñ+ÀÊåzÿZ;Ï‚#nåo¾OZÂ!§”Ê.¸´–îÓswý±YéÝG+I}Ÿ ¦ü>0åöÃ~ºl}cžL<¬ÖØÐÅ >ñ4µ2[X•>[‘&r¶¾UÝ%/|t؉Ì×ܪÎl“‘–0‡]þ'^·WΆyCòvú^[A_ñ¹¦;L½}m°æ%E:™ŸT–nƒãö{Þž… üóAÙ"ÁÛëaÿßjF“Fð‡m®hí™Ó¾NX^'ZÞQT{Î×χ#ÿ–\ö ŽV$ܺNÛ¯rûz4÷F36º¥€ÉŽ²P} Wìü„CPÃג϶DêËIbps+{Ðf ˜úî‚•'k|»Bx*‹Áݤ[u`+hazNŒ}JýôSѪ.€ŸÞ×%Í!«A®ÌmÏÂ¥ÇfØ{,Î=èz<ÉËל»2´Ûs.ú!™{NàãÚþLL¼Ö¯š„y¿ñ8„ÃA©1µþûðƒò¬]Ã`¿cMê˜;z• Gõn›þwOCí@b¬ HºÝîóÖ¶Œæ¨©fÁ†Ô@¯ä¢y°ÆÆù½½fIòr;•A†g@~¡V¬.­ª5αYÄûÚ½KýV½µÜ_C¬lõ Eß·ýÎñ¬ 0(;5ê¥- ÊSÿå]—õ㬵']j¬ï‚^¯?ŸO9§1iÌÂekÒ„™|zÁ§•Îߢbã÷£`ª}ß|¤Xý rùw2¯+wÝ‚aP×È!dåˆó@ᮑ¥,3 Ç<.Øý\æÈ^¿ðŽ§^Jßψ¿ˆ^± –­ vY1öP5­ž™×6À á»âiê ¨þåcÇÉ,P‘çsçŠÈÓ¸­È âÂëÚÓ]F𽄜:¶?.Åy°2f×Ýà#`ùÕ(åêúyàín%©‚ýœ 9:Uç‘`ƒÃÄ‘Whn¨UÖö¯j܇ü‘†7,*º|ûŒŸX»~ËQQøÙˇF)Ø¿íHÓgŸ7°y_š@…l-(°_h&\CðGO,ŒÛMÝoÿ@±åëÈê ¢ßçqƒDÉØC°cU‘³O,lôrP¹"µéé@xëq0åx’V*ÚþÍ4ˆ€…7{-íÛ˘ ›«5Ú`ÛƳEÉOï19ô\-BÃd`ož[Ò£d6xwµ3¿=ì0üv§Ò꼪 ©OñŽÝzEõ2ŒfÚ1ëž(i2Q óÆï$oøEy­ðM)Rß`²/HòYè «h X¾t9ß öW?‡NDʆÜÅ<ιf˜o:×ïXþ¥|×SHº–gLÎ3†S7Éï׃·—.ҸƠð¨8‘ùõ¢‹Ú¢–ŸM/OY íÍEš´…ðð>TßlŒô¼™ýÕŽÕzuž+¬ £Ožv(dï`Ò„Õ“ä–¿‡é.-§B­©bApà~µZ-Ewƒ›0¯ Jr%½$t3Á‰ø 8š‡¤ÌrA¿†ÝníÆtrÞ^¦ý<ÿÍ=ùá¢áôÿûW,ß;ë»Íÿzê´‹ì‡ñã}Ÿ€%ÌC_°oè7H·ßxÀ¯½ÀÙ«5 Ý´¤7‡ÚÀþtåÌtÁ·°Ïa¾ÈÛÚÔœ=&Wƒ¬¢qæ ~/zµ¾!´×ÊnNÐxOüFí¯NtÌz­¯ø>X ²&b飡‘ îÝvþV§ ¾<ã…±ÿñ‰æÁÁD¡ÂVÍ &w{ø·ç 8ñíQTžWòa¬xf„t‘Æü? 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This bug should now be removed. See: https://github.com/quentingronau/bridgesampling/issues/18 * For older news see NEWS.old file on GitHub: https://github.com/quentingronau/bridgesampling/blob/master/NEWS.old bridgesampling/inst/0000755000176200001440000000000015107052015014212 5ustar liggesusersbridgesampling/inst/CITATION0000644000176200001440000000156215055304401015354 0ustar liggesusersbibentry(bibtype = "Article", title = "{bridgesampling}: An {R} Package for Estimating Normalizing Constants", author = c(person(given = c("Quentin", "F."), family = "Gronau", email = "Quentin.F.Gronau@gmail.com"), person(given = "Henrik", family = "Singmann", email = "Henrik.Singmann@warwick.ac.uk"), person(given = "Eric-Jan", family = "Wagenmakers", email = "EJ.Wagenmakers@gmail.com")), journal = "Journal of Statistical Software", year = "2020", volume = "92", number = "10", pages = "1--29", doi = "10.18637/jss.v092.i10", header = "To cite bridgesampling in publications use:" ) bridgesampling/inst/doc/0000755000176200001440000000000015107052015014757 5ustar liggesusersbridgesampling/inst/doc/bridgesampling_tutorial.pdf.asis0000644000176200001440000000012215055304401023316 0ustar liggesusers%\VignetteIndexEntry{A Tutorial on Bridge Sampling} %\VignetteEngine{R.rsp::asis} bridgesampling/inst/doc/bridgesampling_paper.pdf0000644000176200001440000135054315107052016021644 0ustar liggesusers%PDF-1.5 %¿÷¢þ 1 0 obj << /Type /ObjStm /Length 5316 /Filter /FlateDecode /N 89 /First 751 >> stream xœÕ\Yw¹’~Ÿ_¡·ážLíKŸ;}ÆlnÀ€Û6 Í=<å´P‹»* ¦ýýBRÖ^v¹ºèËS(W)Š=B)gŠ á™fFf˜ó‚Y&¸ÖÌ1¡8gž k Lep‡IÍñ„`ÒÍ„dJŽG™ Ïj¦5†içÑ·e†É„cF\÷Ì8‰ëY¡ “œYã%“6HǤdŽ{Íðˆ“-àÐ.0 Ðþ“–yqð¨Wçžy£L`ÞÇöÀbÎS’À YPDiÃT‚ʼn²,¸€ëŽ… qSà‚ãL˜K+™æ„ïFÜ1Óáž ¦1Ç”Ø0#´˜·&i¼«Fa€)t.D +èYJLŒÐ& h W8  =+ƒn1Ìx „æ@œAÏZÑ-ô¬ `0èY;thí36èÙôli:´èÙàÃD„±Î1‹žÇ=[Ž€a% ·èÙjZ GkÔXZ|×hÁd… ‡žæ-®áX'ôì,]AÏÎ;ËzÆ$<ñð8ÂkZ\ôì -X[g5óDë f²XsɈŽ‚ÆÜA"XZ{ô<ˆÏ£ç@uX É9ÝqpšŽÕp°'¹–þ¿þùOV¾¬šÎi§é€,@üG¬|}Y öºM=°ⵧuÃ>àÖUÓ«Õ¤“®vΫ—ÃÓŠ•oÆÕän¼< ÅgN¾]âþ# Ñž³ŸŽ£î]5û÷ëU5hê{Z°ýÑpйºÏ~©£ú3;®çýÎ`pŸ=ÕÝÏ;öÝúÏÕhüô8ª:åãNS±{Â$ ˆÎãǹ}Ïùã_ûuÐ9©Þ±¯usÁ.ÓhT±ËN÷3zÅc/ªo_‡£Ó1»÷qTŸžWlÜé_b>ç÷Ù`8êwzõŸ8aÝá`ÜtÍ}ÖǼ{l\õªˆ¬ûìaçf}Öéb´ûvtùàÙ³gèº ÈÃÑðôª[Êýö17ãlÀP7…À3ÇW?a,vÇ'uÓ«ZP[Hb{`ü0͉aÒOÆMÝšù«™Y<ʳó‚<^ ’å‹HhW^¦E”S±…8Š­kÛDJçç\j••¹M÷µHÄ¥!Žb«E¾Ÿž×6ß7é= ZMçé}#xnÓóF¥û‚§û ©5©µ •Ncå.ÓÙ‡–0­¶d9 š½¹›[—[ŸÛ<~†KäùAÖå6Õá…ÄË­mGÇ4 ý13àÄÓºópxá©WLAÒ\‹Øø@ŽðBËVGÕxx5êvüÉu³Ü‘ á2Ïb€¨Ê§Ž†ÝãªAßåá㧘|uM,ýóϳxXFƒI°É¼.2¯i¢Ôf21ãÆå6Ó‹Ix’–çV¬˜¿Üåüe&½4iÕóØWñõòà÷§‡/þÏ£—±Òå“AwxJüS¾­{ƒq=½ð´›Gi±8öã*q0¸0¯ÁA'?"@^ÄÎM™Æ-iØ·õis¹svóŸ¤rd<&M༹ÌÌ“X  ZiMooÓ3 [è@5—àÎųt䡛躗úÕ_A‡©®‚'ÂFG&ä5îÒB:¼½pùKUŸ_4ŒIè¡eºW>,•OËýòeyT—oÊNù±ì–§eUž•çe]~*{e¿”Ãò²•ã²)›¯ÃòªüR~-¿ABúi”†Iù´×9“ñü0QÙJ¼„‰Ð|H·ŸÖ½ SÓjJH¯:ýj‘žA£ÕݽÁ9$1N_Öã1H!.]ÄIyÜTýß`·¸ÙÅ!‹ò]žº®–HïèhÿäÑ1 öReJ{Þ¶:¹¥8™Å®³\š%9¹!Éån!¹öÏx±òº‚£D"I¯úå'…œ{ÓÃt¦k´d`úÂütœl2hôˆÏ£Z²¥8 3ºìÉ:·>¶rÞ’uìS×¹r%Äæ=HK[2Ù£=)ãy‚Í+ñ©|Äv"L·w‚ŠpS‘ n$ùt:!ù½HôË'‘ð)Ÿ•ÏË0À«òuyXþá¤|›Y¡;ì ™!ÎÎêò¬þ‚CÈD°ÇE 碀O>Oød8¨À+0|êáiùÇÕ°©N?özÕY39T‘›Æõ5qÔŨªføêºüVþ¹†·ìkñtz0¬â,½ÈY ľ)k¡£[YË.³ÖËý‡¿ÓhGsRÝ·šsÂY~™±äc¹ «•ÒÆg¹‰ÉÐ$Mã[¤ýô¾ÃQ{3WÐ#µQ*oø“ùÝÔK«-8yžj-j=y¦8+Ò=UN,CoùëLïйO­SI›Ä>LêSOÒžØè6» í[•2QCh[5Dç­""µ²J™¨ˆDRF@Ϭ2¢–~±ïÙñVñ«™çWÌñ~}1ñ‡õ„kß”¿sß•¿—ïÁ¿îUS•0ÛáÊt§àç#XíUÙ1'n£×£îUÿ¬W]gžïûý8ÿ´®FÕ¸—§C¼,ˆ€–Õà´3¾(«?®:½(²„ÈB¢·BN|šHŠœ¸©¸ £+BLY†\ö®Æå7‰’x6#Uª~¦0®¾`T’2ãA:‘5uïtIâ”V£áœØ‰6Ö ±ó@ótWP¬ƒVoAð´þìDðÌ‹‚MåÜ‚[åŽZ–;Ož½9y˜¤Üœàñ‹‚G. ½$x65"}Э~U|éè®ÓÞ²÷¤!É 4ÐÉ›üú‹Æh ‹N´+‰Ž8EPàoÅøÕìkù Ž_%*¡-¬xÛ©%‰o&ŸàMm€¯ŸÀj)D¥âúiíâ½@úŸ~Ë:ÝÌ›±~^F;£ÉûÕy§<®ÏÁÁ'åÉEÕt¢FŸ•ÉÌMœ|6¯×[n]Å©‰)ŸµÜµ¨Ã#?-rÓ­J^:Ír—Z;tÂK ä½)3™ ˜i…}üö`ï÷ýß0Úññƾ™5Ë|eùŠ„üF|eí¬«emRÚÉZ´ÚdiÝŸö7(}1; 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Gronau" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Bayesian One-Sample T-Test Stan} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how we can compute the (log) marginal likelihood and the Bayes factor for models fitted in `Stan`. This approach has the advantage that the user only needs to pass the fitted `stanfit` object which contains all information that is necessary to compute the (log) marginal likelihood. Here we show how one can conduct a Bayesian one-sample t-test as implemented in the `BayesFactor` package (Morey & Rouder, 2015). ## Model The Bayesian one-sample t-test makes the assumption that the observations are normally distributed with mean $\mu$ and variance $\sigma^2$. The model is then reparametrized in terms of the standardized effect size $\delta = \mu/\sigma$. For the standardized effect size, a Cauchy prior with location zero and scale $r = 1/\sqrt{2}$ is used. For the variance $\sigma^2$, Jeffreys's prior is used: $p(\sigma^2) \propto 1/\sigma^2$. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the effect size $\delta$ is zero, to the alternative hypothesis $\mathcal{H}_1$, which assigns $\delta$ the above described Cauchy prior. ## Data In this example, we will analyze the `sleep` data set from the `t.test` example. This data set shows the effect of two soporific drugs (increase in hours of sleep compared to control) on 10 patients. These data can be analyzed via a one-sample t-test by first computing the difference scores and then conducting the t-test using these difference scores as data. The difference scores are calculated as follows: ```{r} library(bridgesampling) set.seed(12345) # Sleep data from t.test example data(sleep) # compute difference scores y <- sleep$extra[sleep$group == 2] - sleep$extra[sleep$group == 1] n <- length(y) ``` ## Specifying the Models Next, we implement the models in `Stan`. Note that to compute the (log) marginal likelihood for a `Stan` model, we need to specify the model in a certain way. Instad of using `"~"` signs for specifying distributions, we need to directly use the (log) density functions. The reason for this is that when using the `"~"` sign, constant terms are dropped which are not needed for sampling from the posterior. However, for computing the marginal likelihood, these constants need to be retained. For instance, instead of writing `y ~ normal(mu, sigma)` we would need to write `target += normal_lpdf(y | mu, sigma)`. The models can then be specified and compiled as follows (note that it is necessary to install `rstan` for this): ```{r, eval=FALSE} library(rstan) # models stancodeH0 <- ' data { int n; // number of observations vector[n] y; // observations } parameters { real sigma2; // variance parameter } model { target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | 0, sqrt(sigma2)); // likelihood } ' stancodeH1 <- ' data { int n; // number of observations vector[n] y; // observations real r; // Cauchy prior scale } parameters { real delta; real sigma2;// variance parameter } model { target += cauchy_lpdf(delta | 0, r); // Cauchy prior on delta target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood } ' # compile models stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") ``` ## Fitting the Models Now we can fit the null and the alternative model in `Stan`. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models. ```{r, eval=FALSE} # fit models stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n), iter = 20000, warmup = 1000, chains = 4, cores = 1, control = list(adapt_delta = .99)) stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, r = 1/sqrt(2)), iter = 20000, warmup = 1000, chains = 4, cores = 1, control = list(adapt_delta = .99)) ``` ## Computing the (Log) Marginal Likelihoods Computing the (log) marginal likelihoods via the `bridge_sampler` function is now easy: we only need to pass the `stanfit` objects which contain all information necessary. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_stan_ttest.RData", package = "bridgesampling")) ``` ```{r, eval=FALSE} H0 <- bridge_sampler(stanfitH0, silent = TRUE) H1 <- bridge_sampler(stanfitH1, silent = TRUE) ``` We obtain: ```{r} print(H0) print(H1) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0)$percentage H1.error <- error_measures(H1)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Computing the Bayes Factor To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{10}$, that is, the Bayes factor which quantifies how much more likely the data are under the alternative versus the null hypothesis: ```{r} # compute Bayes factor BF10 <- bf(H1, H0) print(BF10) ``` We can compare the bridge sampling result to the `BayesFactor` package result: ```{r, eval=FALSE} library(BayesFactor) BF10.BayesFactor <- extractBF(ttestBF(y), onlybf = TRUE) ``` We obtain: ```{r, message=FALSE} print(BF10.BayesFactor) ``` ## One-sided Test We can also conduct one-sided tests. For instance, we could test the hypothesis that the effect size is positive versus the null hypothesis. Since we already fitted the null model and computed its marginal likelihood, we only need to slightly adjust the alternative model to reflect the directed hypothesis. To achieve this, we need to truncate the Cauchy prior distribution for $\delta$ at zero and then renormalize the (log) density. This is easily achieved via the `Stan` function `cauchy_lccdf` which corresponds to the log of the complementary cumulative distribution function of the Cauchy distribution. Thus, `cauchy_lccdf(0 | 0, r)` gives us the log of the area greater than zero which is required for renormalizing the truncated Cauchy prior. The model can then be specified and fitted as follows: ```{r, eval=FALSE} stancodeHplus <- ' data { int n; // number of observations vector[n] y; // observations real r; // Cauchy prior scale } parameters { real delta; // constrained to be positive real sigma2;// variance parameter } model { target += cauchy_lpdf(delta | 0, r) - cauchy_lccdf(0 | 0, r); // Cauchy prior on delta target += log(1/sigma2); // Jeffreys prior on sigma2 target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood } ' # compile and fit model stanmodelHplus <- stan_model(model_code = stancodeHplus, model_name="stanmodel") stanfitHplus <- sampling(stanmodelHplus, data = list(y = y, n = n, r = 1/sqrt(2)), iter = 30000, warmup = 1000, chains = 4, control = list(adapt_delta = .99)) ``` The (log) marginal likelihood is then computed as follows: ```{r,eval=FALSE} Hplus <- bridge_sampler(stanfitHplus, silent = TRUE) ``` We obtain: ```{r} print(Hplus) ``` We can again use the `error_measures` function to compute an approximate percentage error of the estimate: ```{r,eval=FALSE} Hplus.error <- error_measures(Hplus)$percentage ``` We obtain: ```{r} print(Hplus.error) ``` The one-sided Bayes factor in favor of a positive effect versus the null hypothesis can be computed as follows: ```{r} # compute Bayes factor BFplus0 <- bf(Hplus, H0) print(BFplus0) ``` We can compare the bridge sampling result to the `BayesFactor` package result: ```{r, eval=FALSE} BFplus0.BayesFactor <- extractBF(ttestBF(y, nullInterval = c(0, Inf)), onlybf = TRUE)[1] ``` We obtain: ```{r} print(BFplus0.BayesFactor) ``` ## References Richard D. Morey and Jeffrey N. Rouder (2015). BayesFactor: Computation of Bayes Factors for Common Designs. R package version 0.9.12-2. \url{https://CRAN.R-project.org/package=BayesFactor} bridgesampling/inst/doc/bridgesampling_example_stan.html0000644000176200001440000003006715107052015023402 0ustar liggesusers Hierarchical Normal Example (Stan)

Hierarchical Normal Example (Stan)

Quentin F. Gronau

2025-11-18

In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in Stan. This vignette uses the same models and data as the Jags vignette.

Model and Data

The model that we will use assumes that each of the \(n\) observations \(y_i\) (where \(i\) indexes the observation, \(i = 1,2,...,n\)) is normally distributed with corresponding mean \(\theta_i\) and a common known variance \(\sigma^2\): \(y_i \sim \mathcal{N}(\theta_i, \sigma^2)\). Each \(\theta_i\) is drawn from a normal group-level distribution with mean \(\mu\) and variance \(\tau^2\): \(\theta_i \sim \mathcal{N}(\mu, \tau^2)\). For the group-level mean \(\mu\), we use a normal prior distribution of the form \(\mathcal{N}(\mu_0, \tau^2_0)\). For the group-level variance \(\tau^2\), we use an inverse-gamma prior of the form \(\text{Inv-Gamma}(\alpha, \beta)\).

In this example, we are interested in comparing the null model \(\mathcal{H}_0\), which posits that the group-level mean \(\mu = 0\), to the alternative model \(\mathcal{H}_1\), which allows \(\mu\) to be different from zero. First, we generate some data from the null model:

library(bridgesampling)

### generate data ###
set.seed(12345)

mu <- 0
tau2 <- 0.5
sigma2 <- 1

n <- 20
theta <- rnorm(n, mu, sqrt(tau2))
y <- rnorm(n, theta, sqrt(sigma2))

Next, we specify the prior parameters \(\mu_0\), \(\tau^2_0\), \(\alpha\), and \(\beta\):

### set prior parameters ###
mu0 <- 0
tau20 <- 1
alpha <- 1
beta <- 1

Specifying the Models

Next, we implement the models in Stan. Note that to compute the (log) marginal likelihood for a Stan model, we need to specify the model in a certain way. Instad of using "~" signs for specifying distributions, we need to directly use the (log) density functions. The reason for this is that when using the "~" sign, constant terms are dropped which are not needed for sampling from the posterior. However, for computing the marginal likelihood, these constants need to be retained. For instance, instead of writing y ~ normal(mu, sigma) we would need to write target += normal_lpdf(y | mu, sigma). The models can then be specified and compiled as follows (note that it is necessary to install rstan for this):

library(rstan)

# models
stancodeH0 <- 'data {
  int<lower=1> n; // number of observations
  vector[n] y; // observations
  real<lower=0> alpha;
  real<lower=0> beta;
  real<lower=0> sigma2;
}
parameters {
  real<lower=0> tau2; // group-level variance
  vector[n] theta; // participant effects
}
model {
  target += inv_gamma_lpdf(tau2 | alpha, beta);
  target += normal_lpdf(theta | 0, sqrt(tau2));
  target += normal_lpdf(y | theta, sqrt(sigma2));
}
'
stancodeH1 <- 'data {
  int<lower=1> n; // number of observations
  vector[n] y; // observations
  real mu0;
  real<lower=0> tau20;
  real<lower=0> alpha;
  real<lower=0> beta;
  real<lower=0> sigma2;
}
parameters {
  real mu;
  real<lower=0> tau2; // group-level variance
  vector[n] theta; // participant effects
}
model {
  target += normal_lpdf(mu | mu0, sqrt(tau20));
  target += inv_gamma_lpdf(tau2 | alpha, beta);
  target += normal_lpdf(theta | mu, sqrt(tau2));
  target += normal_lpdf(y | theta, sqrt(sigma2));
}
'
# compile models
stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel")
stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel")

Fitting the Models

Now we can fit the null and the alternative model in Stan. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models.

# fit models
stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n,
                                               alpha = alpha,
                                               beta = beta,
                                               sigma2 = sigma2),
                      iter = 50000, warmup = 1000, chains = 3, cores = 1)
stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n,
                                               mu0 = mu0,
                                               tau20 = tau20,
                                               alpha = alpha,
                                               beta = beta,
                                               sigma2 = sigma2),
                      iter = 50000, warmup = 1000, chains = 3, cores = 1)

Computing the (Log) Marginal Likelihoods

Computing the (log) marginal likelihoods via the bridge_sampler function is now easy: we only need to pass the stanfit objects which contain all information necessary. We use silent = TRUE to suppress printing the number of iterations to the console:

# compute log marginal likelihood via bridge sampling for H0
H0.bridge <- bridge_sampler(stanfitH0, silent = TRUE)

# compute log marginal likelihood via bridge sampling for H1
H1.bridge <- bridge_sampler(stanfitH1, silent = TRUE)

We obtain:

print(H0.bridge)
## Bridge sampling estimate of the log marginal likelihood: -37.53183
## Estimate obtained in 5 iteration(s) via method "normal".
print(H1.bridge)
## Bridge sampling estimate of the log marginal likelihood: -37.79683
## Estimate obtained in 4 iteration(s) via method "normal".

We can use the error_measures function to compute an approximate percentage error of the estimates:

# compute percentage errors
H0.error <- error_measures(H0.bridge)$percentage
H1.error <- error_measures(H1.bridge)$percentage

We obtain:

print(H0.error)
## [1] "0.143%"
print(H1.error)
## [1] "0.164%"

Bayesian Model Comparison

To compare the null model and the alternative model, we can compute the Bayes factor by using the bf function. In our case, we compute \(\text{BF}_{01}\), that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model:

# compute Bayes factor
BF01 <- bf(H0.bridge, H1.bridge)
print(BF01)
## Estimated Bayes factor in favor of H0.bridge over H1.bridge: 1.30343

In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the post_prob function:

# compute posterior model probabilities (assuming equal prior model probabilities)
post1 <- post_prob(H0.bridge, H1.bridge)
print(post1)
## H0.bridge H1.bridge 
## 0.5658657 0.4341343

When the argument prior_prob is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the prior_prob argument to specify different prior model probabilities:

# compute posterior model probabilities (using user-specified prior model probabilities)
post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4))
print(post2)
## H0.bridge H1.bridge 
## 0.6616079 0.3383921
bridgesampling/inst/doc/bridgesampling_example_nimble.Rmd0000644000176200001440000001606115060116372023464 0ustar liggesusers--- title: "Hierarchical Normal Example (nimble)" author: "Quentin F. Gronau, Henrik Singmann & Perry de Valpine" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Hierarchical Normal Example Nimble} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in `nimble`. The [`nimble` documentation](https://r-nimble.org/manual/cha-welcome-nimble.html) provides a comprehensive overview. This vignette uses the same models and data as the [`Stan` vignette](bridgesampling_example_stan.html) and [`Jags` vignette](bridgesampling_example_jags.html). ## Model and Data The model that we will use assumes that each of the $n$ observations $y_i$ (where $i$ indexes the observation, $i = 1,2,...,n$) is normally distributed with corresponding mean $\theta_i$ and a common known variance $\sigma^2$: $y_i \sim \mathcal{N}(\theta_i, \sigma^2)$. Each $\theta_i$ is drawn from a normal group-level distribution with mean $\mu$ and variance $\tau^2$: $\theta_i \sim \mathcal{N}(\mu, \tau^2)$. For the group-level mean $\mu$, we use a normal prior distribution of the form $\mathcal{N}(\mu_0, \tau^2_0)$. For the group-level variance $\tau^2$, we use an inverse-gamma prior of the form $\text{Inv-Gamma}(\alpha, \beta)$. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the group-level mean $\mu = 0$, to the alternative model $\mathcal{H}_1$, which allows $\mu$ to be different from zero. First, we generate some data from the null model: ```{r} library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ``` Next, we specify the prior parameters $\mu_0$, $\tau^2_0$, $\alpha$, and $\beta$: ```{r,eval=FALSE} ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ``` ## Specifying the Models Next, we implement the models in `nimble`. This requires to first transform the code into a `nimbleModel`, then we need to set the data, and then we can compile the model. Given that `nimble` is build on BUGS, the similarity between the `nimble` code and the [`Jags` code](bridgesampling_example_jags.html) is not too surprising. ```{r, eval=FALSE} library("nimble") # models codeH0 <- nimbleCode({ invTau2 ~ dgamma(1, 1) tau2 <- 1/invTau2 for (i in 1:20) { theta[i] ~ dnorm(0, sd = sqrt(tau2)) y[i] ~ dnorm(theta[i], sd = 1) } }) codeH1 <- nimbleCode({ mu ~ dnorm(0, sd = 1) invTau2 ~ dgamma(1, 1) tau2 <- 1/invTau2 for (i in 1:20) { theta[i] ~ dnorm(mu, sd = sqrt(tau2)) y[i] ~ dnorm(theta[i], sd = 1) } }) ## steps for H0: modelH0 <- nimbleModel(codeH0) modelH0$setData(y = y) # set data cmodelH0 <- compileNimble(modelH0) # make compiled version from generated C++ ## steps for H1: modelH1 <- nimbleModel(codeH1) modelH1$setData(y = y) # set data cmodelH1 <- compileNimble(modelH1) # make compiled version from generated C++ ``` ## Fitting the Models Fitting a model with `nimble` requires one to first create an MCMC function from the (compiled or uncompiled) model. This function then needs to be compiled again. With this object we can then create the samples. Note that nimble uses a reference object semantic so we do not actually need the samples object, as the samples will be saved in the MCMC function objects. But as `runMCMC` returns them anyway, we nevertheless save them. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models. ```{r, eval=FALSE} # build MCMC functions, skipping customization of the configuration. mcmcH0 <- buildMCMC(modelH0, monitors = modelH0$getNodeNames(stochOnly = TRUE, includeData = FALSE)) mcmcH1 <- buildMCMC(modelH1, monitors = modelH1$getNodeNames(stochOnly = TRUE, includeData = FALSE)) # compile the MCMC function via generated C++ cmcmcH0 <- compileNimble(mcmcH0, project = modelH0) cmcmcH1 <- compileNimble(mcmcH1, project = modelH1) # run the MCMC. This is a wrapper for cmcmc$run() and extraction of samples. # the object samplesH1 is actually not needed as the samples are also in cmcmcH1 samplesH0 <- runMCMC(cmcmcH0, niter = 1e5, nburnin = 1000, nchains = 2, progressBar = FALSE) samplesH1 <- runMCMC(cmcmcH1, niter = 1e5, nburnin = 1000, nchains = 2, progressBar = FALSE) ``` ## Computing the (Log) Marginal Likelihoods Computing the (log) marginal likelihoods via the `bridge_sampler` function is now easy: we only need to pass the compiled MCMC function objects (of class `"MCMC_refClass"`) which contain all information necessary. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_example_nimble.RData", package = "bridgesampling")) ``` ```{r,eval=FALSE} # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(cmcmcH0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(cmcmcH1, silent = TRUE) ``` We obtain: ```{r} print(H0.bridge) print(H1.bridge) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Bayesian Model Comparison To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{01}$, that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model: ```{r} # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ``` In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the `post_prob` function: ```{r} # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ``` When the argument `prior_prob` is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the `prior_prob` argument to specify different prior model probabilities: ```{r} # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) ``` bridgesampling/inst/doc/bridgesampling_example_jags.Rmd0000644000176200001440000002477215055304401023146 0ustar liggesusers--- title: "Hierarchical Normal Example (JAGS)" author: "Quentin F. Gronau" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Hierarchical Normal Example JAGS} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in `JAGS`. This vignette uses the same models and data as the [`Stan` vignette](bridgesampling_example_stan.html). ## Model and Data The model that we will use assumes that each of the $n$ observations $y_i$ (where $i$ indexes the observation, $i = 1,2,...,n$) is normally distributed with corresponding mean $\theta_i$ and a common known variance $\sigma^2$: $y_i \sim \mathcal{N}(\theta_i, \sigma^2)$. Each $\theta_i$ is drawn from a normal group-level distribution with mean $\mu$ and variance $\tau^2$: $\theta_i \sim \mathcal{N}(\mu, \tau^2)$. For the group-level mean $\mu$, we use a normal prior distribution of the form $\mathcal{N}(\mu_0, \tau^2_0)$. For the group-level variance $\tau^2$, we use an inverse-gamma prior of the form $\text{Inv-Gamma}(\alpha, \beta)$. We will use `JAGS` to fit the model which parametrizes the normal distribution in terms of the precision (i.e., one over the variance). Consequently, we implement this inverse-gamma prior on $\tau^2$ by placing a gamma prior of the form $\text{Gamma}(\alpha, \beta)$ on the precision; we call this precision parameter `invTau2` in the code. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the group-level mean $\mu = 0$, to the alternative model $\mathcal{H}_1$, which allows $\mu$ to be different from zero. First, we generate some data from the null model: ```{r} library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ``` Next, we specify the prior parameters $\mu_0$, $\tau^2_0$, $\alpha$, and $\beta$: ```{r,eval=FALSE} ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ``` ## Fitting the Models Now we can fit the null and the alternative model in `JAGS` (note that it is necessary to install `JAGS` for this). One usually requires a larger number of posterior sample for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples (i.e., 50,000 post burn-in samples per chain) for this comparatively simple model. ```{r, eval=FALSE} library(R2jags) ### functions to get posterior samples ### # H0: mu = 0 getSamplesModelH0 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(0, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1) return(s) } # H1: mu != 0 getSamplesModelH1 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(mu, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } mu ~ dnorm(mu0, 1/tau20) invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "mu", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1) return(s) } ### get posterior samples ### # create data lists for JAGS data_H0 <- list(y = y, n = length(y), alpha = alpha, beta = beta, sigma2 = sigma2) data_H1 <- list(y = y, n = length(y), mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2) # fit models samples_H0 <- getSamplesModelH0(data_H0) samples_H1 <- getSamplesModelH1(data_H1) ``` ## Specifying the Unnormalized Log Posterior Function The next step is to write the corresponding `log_posterior` (i.e., unnormalized posterior) function for both models. This function takes one draw from the joint posterior and the data object as input and returns the log of the unnormalized joint posterior density. When using MCMC software such as `JAGS` or `Stan`, specifying this function is relatively simple. As a rule of thumb, one only needs to look for all places where a "`~`" sign appears in the model code. The log of the densities on the right-hand side of these "`~`" symbols needs to be evaluated for the relevant quantities and then these log densities values are summed. For example, in the null model, there are three "`~`" signs. Starting at the data-level, we need to evaluate the log of the normal density with mean $\theta_i$ and variance $\sigma^2$ for all $y_i$ and then sum the resulting log density values. Next, we move one step up in the model and evaluate the log of the group-level density for all $\theta_i$. Hence, we evaluate the log of the normal density for $\theta_i$ with mean $\mu = 0$ and variance $\tau^2$ (remember that `JAGS` parametrizes the normal distribution in terms of the precision `invTau2` = $1/\tau^2$; in contrast, `R` parametrizes it in terms of the standard deviation) and sum the resulting log density values. The result of this summation is added to the result of the previous summation for the data-level normal distribution. Finally, we need to evaluate the log of the prior density for `invTau2`. This means that we compute the log density of the gamma distribution with parameters $\alpha$ and $\beta$ for the sampled `invTau2` value and add the resulting log density value to the result of summing the data-level and group-level log densities. The unnormalized log posterior for the alternative model can be obtained in a similar fashion. The resulting functions look as follows: ```{r,eval=FALSE} ### functions for evaluating the unnormalized posteriors on log scale ### log_posterior_H0 <- function(samples.row, data) { mu <- 0 invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } log_posterior_H1 <- function(samples.row, data) { mu <- samples.row[[ "mu" ]] invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dnorm(mu, data$mu0, sqrt(data$tau20), log = TRUE) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } ``` ## Specifying the Parameter Bounds The final step before computing the log marginal likelihoods is to specify the parameter bounds. In this example, for both models, all parameters can range from $-\infty$ to $\infty$ except the precision `invTau2` which has a lower bound of zero. These boundary vectors need to be named and the names need to match the order of the parameters. ```{r,eval=FALSE} # specify parameter bounds H0 cn <- colnames(samples_H0$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H0 <- rep(-Inf, length(cn)) ub_H0 <- rep(Inf, length(cn)) names(lb_H0) <- names(ub_H0) <- cn lb_H0[[ "invTau2" ]] <- 0 # specify parameter bounds H1 cn <- colnames(samples_H1$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H1 <- rep(-Inf, length(cn)) ub_H1 <- rep(Inf, length(cn)) names(lb_H1) <- names(ub_H1) <- cn lb_H1[[ "invTau2" ]] <- 0 ``` Note that currently, the lower and upper bound of a parameter cannot be a function of the bounds of another parameter. Furthermore, constraints that depend on multiple parameters of the model are not supported. This excludes, for example, parameters that constitute a covariance matrix or sets of parameters that need to sum to one. ## Computing the (Log) Marginal Likelihoods Now we are ready to compute the log marginal likelihoods using the `bridge_sampler` function. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_example_jags.RData", package = "bridgesampling")) ``` ```{r,eval=FALSE} # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(samples = samples_H0, data = data_H0, log_posterior = log_posterior_H0, lb = lb_H0, ub = ub_H0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(samples = samples_H1, data = data_H1, log_posterior = log_posterior_H1, lb = lb_H1, ub = ub_H1, silent = TRUE) ``` We obtain: ```{r} print(H0.bridge) print(H1.bridge) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Bayesian Model Comparison To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{01}$, that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model: ```{r} # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ``` In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the `post_prob` function: ```{r} # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ``` When the argument `prior_prob` is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the `prior_prob` argument to specify different prior model probabilities: ```{r} # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) ``` bridgesampling/inst/doc/bridgesampling_example_stan.R0000644000176200001440000001014615107052015022633 0ustar liggesusers## ----------------------------------------------------------------------------- library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ## ----eval=FALSE--------------------------------------------------------------- # ### set prior parameters ### # mu0 <- 0 # tau20 <- 1 # alpha <- 1 # beta <- 1 ## ----eval=FALSE--------------------------------------------------------------- # library(rstan) # # # models # stancodeH0 <- 'data { # int n; // number of observations # vector[n] y; // observations # real alpha; # real beta; # real sigma2; # } # parameters { # real tau2; // group-level variance # vector[n] theta; // participant effects # } # model { # target += inv_gamma_lpdf(tau2 | alpha, beta); # target += normal_lpdf(theta | 0, sqrt(tau2)); # target += normal_lpdf(y | theta, sqrt(sigma2)); # } # ' # stancodeH1 <- 'data { # int n; // number of observations # vector[n] y; // observations # real mu0; # real tau20; # real alpha; # real beta; # real sigma2; # } # parameters { # real mu; # real tau2; // group-level variance # vector[n] theta; // participant effects # } # model { # target += normal_lpdf(mu | mu0, sqrt(tau20)); # target += inv_gamma_lpdf(tau2 | alpha, beta); # target += normal_lpdf(theta | mu, sqrt(tau2)); # target += normal_lpdf(y | theta, sqrt(sigma2)); # } # ' # # compile models # stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") # stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") ## ----eval=FALSE--------------------------------------------------------------- # # fit models # stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n, # alpha = alpha, # beta = beta, # sigma2 = sigma2), # iter = 50000, warmup = 1000, chains = 3, cores = 1) # stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, # mu0 = mu0, # tau20 = tau20, # alpha = alpha, # beta = beta, # sigma2 = sigma2), # iter = 50000, warmup = 1000, chains = 3, cores = 1) ## ----echo=FALSE--------------------------------------------------------------- load(system.file("extdata/", "vignette_example_stan.RData", package = "bridgesampling")) ## ----eval=FALSE--------------------------------------------------------------- # # compute log marginal likelihood via bridge sampling for H0 # H0.bridge <- bridge_sampler(stanfitH0, silent = TRUE) # # # compute log marginal likelihood via bridge sampling for H1 # H1.bridge <- bridge_sampler(stanfitH1, silent = TRUE) ## ----------------------------------------------------------------------------- print(H0.bridge) print(H1.bridge) ## ----eval=FALSE--------------------------------------------------------------- # # compute percentage errors # H0.error <- error_measures(H0.bridge)$percentage # H1.error <- error_measures(H1.bridge)$percentage ## ----------------------------------------------------------------------------- print(H0.error) print(H1.error) ## ----------------------------------------------------------------------------- # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ## ----------------------------------------------------------------------------- # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ## ----------------------------------------------------------------------------- # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) bridgesampling/inst/doc/bridgesampling_example_jags.html0000644000176200001440000004104315107052014023354 0ustar liggesusers Hierarchical Normal Example (JAGS)

Hierarchical Normal Example (JAGS)

Quentin F. Gronau

2025-11-18

In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in JAGS. This vignette uses the same models and data as the Stan vignette.

Model and Data

The model that we will use assumes that each of the \(n\) observations \(y_i\) (where \(i\) indexes the observation, \(i = 1,2,...,n\)) is normally distributed with corresponding mean \(\theta_i\) and a common known variance \(\sigma^2\): \(y_i \sim \mathcal{N}(\theta_i, \sigma^2)\). Each \(\theta_i\) is drawn from a normal group-level distribution with mean \(\mu\) and variance \(\tau^2\): \(\theta_i \sim \mathcal{N}(\mu, \tau^2)\). For the group-level mean \(\mu\), we use a normal prior distribution of the form \(\mathcal{N}(\mu_0, \tau^2_0)\). For the group-level variance \(\tau^2\), we use an inverse-gamma prior of the form \(\text{Inv-Gamma}(\alpha, \beta)\). We will use JAGS to fit the model which parametrizes the normal distribution in terms of the precision (i.e., one over the variance). Consequently, we implement this inverse-gamma prior on \(\tau^2\) by placing a gamma prior of the form \(\text{Gamma}(\alpha, \beta)\) on the precision; we call this precision parameter invTau2 in the code.

In this example, we are interested in comparing the null model \(\mathcal{H}_0\), which posits that the group-level mean \(\mu = 0\), to the alternative model \(\mathcal{H}_1\), which allows \(\mu\) to be different from zero. First, we generate some data from the null model:

library(bridgesampling)

### generate data ###
set.seed(12345)

mu <- 0
tau2 <- 0.5
sigma2 <- 1

n <- 20
theta <- rnorm(n, mu, sqrt(tau2))
y <- rnorm(n, theta, sqrt(sigma2))

Next, we specify the prior parameters \(\mu_0\), \(\tau^2_0\), \(\alpha\), and \(\beta\):

### set prior parameters ###
mu0 <- 0
tau20 <- 1
alpha <- 1
beta <- 1

Fitting the Models

Now we can fit the null and the alternative model in JAGS (note that it is necessary to install JAGS for this). One usually requires a larger number of posterior sample for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples (i.e., 50,000 post burn-in samples per chain) for this comparatively simple model.

library(R2jags)

### functions to get posterior samples ###

# H0: mu = 0
getSamplesModelH0 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) {
  
  model <- "
    model {
      for (i in 1:n) {
        theta[i] ~ dnorm(0, invTau2)
          y[i] ~ dnorm(theta[i], 1/sigma2)
      }
      invTau2 ~ dgamma(alpha, beta)
      tau2 <- 1/invTau2
    }"
  
  s <- jags(data, parameters.to.save = c("theta", "invTau2"),
            model.file = textConnection(model),
            n.chains = nchains, n.iter = niter,
            n.burnin = nburnin, n.thin = 1)
  
  return(s)
  
}

# H1: mu != 0
getSamplesModelH1 <- function(data, niter = 52000, nburnin = 2000,
                              nchains = 3) {
  
  model <- "
    model {
      for (i in 1:n) {
        theta[i] ~ dnorm(mu, invTau2)
        y[i] ~ dnorm(theta[i], 1/sigma2)
      }
      mu ~ dnorm(mu0, 1/tau20)
      invTau2 ~ dgamma(alpha, beta)
      tau2 <- 1/invTau2
    }"
  
  s <- jags(data, parameters.to.save = c("theta", "mu", "invTau2"),
            model.file = textConnection(model),
            n.chains = nchains, n.iter = niter,
            n.burnin = nburnin, n.thin = 1)
  
  return(s)
  
}

### get posterior samples ###

# create data lists for JAGS
data_H0 <- list(y = y, n = length(y), alpha = alpha, beta = beta, sigma2 = sigma2)
data_H1 <- list(y = y, n = length(y), mu0 = mu0, tau20 = tau20, alpha = alpha,
                beta = beta, sigma2 = sigma2)

# fit models
samples_H0 <- getSamplesModelH0(data_H0)
samples_H1 <- getSamplesModelH1(data_H1)

Specifying the Unnormalized Log Posterior Function

The next step is to write the corresponding log_posterior (i.e., unnormalized posterior) function for both models. This function takes one draw from the joint posterior and the data object as input and returns the log of the unnormalized joint posterior density. When using MCMC software such as JAGS or Stan, specifying this function is relatively simple. As a rule of thumb, one only needs to look for all places where a “~†sign appears in the model code. The log of the densities on the right-hand side of these “~†symbols needs to be evaluated for the relevant quantities and then these log densities values are summed.

For example, in the null model, there are three “~†signs. Starting at the data-level, we need to evaluate the log of the normal density with mean \(\theta_i\) and variance \(\sigma^2\) for all \(y_i\) and then sum the resulting log density values. Next, we move one step up in the model and evaluate the log of the group-level density for all \(\theta_i\). Hence, we evaluate the log of the normal density for \(\theta_i\) with mean \(\mu = 0\) and variance \(\tau^2\) (remember that JAGS parametrizes the normal distribution in terms of the precision invTau2 = \(1/\tau^2\); in contrast, R parametrizes it in terms of the standard deviation) and sum the resulting log density values. The result of this summation is added to the result of the previous summation for the data-level normal distribution. Finally, we need to evaluate the log of the prior density for invTau2. This means that we compute the log density of the gamma distribution with parameters \(\alpha\) and \(\beta\) for the sampled invTau2 value and add the resulting log density value to the result of summing the data-level and group-level log densities. The unnormalized log posterior for the alternative model can be obtained in a similar fashion. The resulting functions look as follows:

### functions for evaluating the unnormalized posteriors on log scale ###

log_posterior_H0 <- function(samples.row, data) {
  
  mu <- 0
  invTau2 <- samples.row[[ "invTau2" ]]
  theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ]
  
  sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) +
    sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) +
    dgamma(invTau2, data$alpha, data$beta, log = TRUE)
  
}

log_posterior_H1 <- function(samples.row, data) {
  
  mu <- samples.row[[ "mu" ]]
  invTau2 <- samples.row[[ "invTau2" ]]
  theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ]
  
  sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) +
    sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) +
    dnorm(mu, data$mu0, sqrt(data$tau20), log = TRUE) +
    dgamma(invTau2, data$alpha, data$beta, log = TRUE)
  
}

Specifying the Parameter Bounds

The final step before computing the log marginal likelihoods is to specify the parameter bounds. In this example, for both models, all parameters can range from \(-\infty\) to \(\infty\) except the precision invTau2 which has a lower bound of zero. These boundary vectors need to be named and the names need to match the order of the parameters.

# specify parameter bounds H0
cn <- colnames(samples_H0$BUGSoutput$sims.matrix)
cn <- cn[cn != "deviance"]
lb_H0 <- rep(-Inf, length(cn))
ub_H0 <- rep(Inf, length(cn))
names(lb_H0) <- names(ub_H0) <- cn
lb_H0[[ "invTau2" ]] <- 0

# specify parameter bounds H1
cn <- colnames(samples_H1$BUGSoutput$sims.matrix)
cn <- cn[cn != "deviance"]
lb_H1 <- rep(-Inf, length(cn))
ub_H1 <- rep(Inf, length(cn))
names(lb_H1) <- names(ub_H1) <- cn
lb_H1[[ "invTau2" ]] <- 0

Note that currently, the lower and upper bound of a parameter cannot be a function of the bounds of another parameter. Furthermore, constraints that depend on multiple parameters of the model are not supported. This excludes, for example, parameters that constitute a covariance matrix or sets of parameters that need to sum to one.

Computing the (Log) Marginal Likelihoods

Now we are ready to compute the log marginal likelihoods using the bridge_sampler function. We use silent = TRUE to suppress printing the number of iterations to the console:

# compute log marginal likelihood via bridge sampling for H0
H0.bridge <- bridge_sampler(samples = samples_H0, data = data_H0,
                            log_posterior = log_posterior_H0, lb = lb_H0,
                            ub = ub_H0, silent = TRUE)

# compute log marginal likelihood via bridge sampling for H1
H1.bridge <- bridge_sampler(samples = samples_H1, data = data_H1,
                            log_posterior = log_posterior_H1, lb = lb_H1,
                            ub = ub_H1, silent = TRUE)

We obtain:

print(H0.bridge)
## Bridge sampling estimate of the log marginal likelihood: -37.53235
## Estimate obtained in 4 iteration(s) via method "normal".
print(H1.bridge)
## Bridge sampling estimate of the log marginal likelihood: -37.79776
## Estimate obtained in 5 iteration(s) via method "normal".

We can use the error_measures function to compute an approximate percentage error of the estimates:

# compute percentage errors
H0.error <- error_measures(H0.bridge)$percentage
H1.error <- error_measures(H1.bridge)$percentage

We obtain:

print(H0.error)
## [1] "0.144%"
print(H1.error)
## [1] "0.162%"

Bayesian Model Comparison

To compare the null model and the alternative model, we can compute the Bayes factor by using the bf function. In our case, we compute \(\text{BF}_{01}\), that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model:

# compute Bayes factor
BF01 <- bf(H0.bridge, H1.bridge)
print(BF01)
## Estimated Bayes factor in favor of H0.bridge over H1.bridge: 1.30396

In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the post_prob function:

# compute posterior model probabilities (assuming equal prior model probabilities)
post1 <- post_prob(H0.bridge, H1.bridge)
print(post1)
## H0.bridge H1.bridge 
## 0.5659652 0.4340348

When the argument prior_prob is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the prior_prob argument to specify different prior model probabilities:

# compute posterior model probabilities (using user-specified prior model probabilities)
post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4))
print(post2)
## H0.bridge H1.bridge 
## 0.6616986 0.3383014
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bridgesampling/inst/doc/bridgesampling_paper_extended.pdf.asis0000644000176200001440000000020115055304401024440 0ustar liggesusers%\VignetteIndexEntry{bridgesampling: An R Package for Estimating Normalizing Constants (Extended)} %\VignetteEngine{R.rsp::asis} bridgesampling/inst/doc/bridgesampling_stan_ttest.R0000644000176200001440000001137315107052015022346 0ustar liggesusers## ----------------------------------------------------------------------------- library(bridgesampling) set.seed(12345) # Sleep data from t.test example data(sleep) # compute difference scores y <- sleep$extra[sleep$group == 2] - sleep$extra[sleep$group == 1] n <- length(y) ## ----eval=FALSE--------------------------------------------------------------- # library(rstan) # # # models # stancodeH0 <- ' # data { # int n; // number of observations # vector[n] y; // observations # } # parameters { # real sigma2; // variance parameter # } # model { # target += log(1/sigma2); // Jeffreys prior on sigma2 # target += normal_lpdf(y | 0, sqrt(sigma2)); // likelihood # } # ' # stancodeH1 <- ' # data { # int n; // number of observations # vector[n] y; // observations # real r; // Cauchy prior scale # } # parameters { # real delta; # real sigma2;// variance parameter # } # model { # target += cauchy_lpdf(delta | 0, r); // Cauchy prior on delta # target += log(1/sigma2); // Jeffreys prior on sigma2 # target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood # } # ' # # compile models # stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") # stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") ## ----eval=FALSE--------------------------------------------------------------- # # fit models # stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n), # iter = 20000, warmup = 1000, chains = 4, cores = 1, # control = list(adapt_delta = .99)) # stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, r = 1/sqrt(2)), # iter = 20000, warmup = 1000, chains = 4, cores = 1, # control = list(adapt_delta = .99)) ## ----echo=FALSE--------------------------------------------------------------- load(system.file("extdata/", "vignette_stan_ttest.RData", package = "bridgesampling")) ## ----eval=FALSE--------------------------------------------------------------- # H0 <- bridge_sampler(stanfitH0, silent = TRUE) # H1 <- bridge_sampler(stanfitH1, silent = TRUE) ## ----------------------------------------------------------------------------- print(H0) print(H1) ## ----eval=FALSE--------------------------------------------------------------- # # compute percentage errors # H0.error <- error_measures(H0)$percentage # H1.error <- error_measures(H1)$percentage ## ----------------------------------------------------------------------------- print(H0.error) print(H1.error) ## ----------------------------------------------------------------------------- # compute Bayes factor BF10 <- bf(H1, H0) print(BF10) ## ----eval=FALSE--------------------------------------------------------------- # library(BayesFactor) # BF10.BayesFactor <- extractBF(ttestBF(y), onlybf = TRUE) ## ----message=FALSE------------------------------------------------------------ print(BF10.BayesFactor) ## ----eval=FALSE--------------------------------------------------------------- # stancodeHplus <- ' # data { # int n; // number of observations # vector[n] y; // observations # real r; // Cauchy prior scale # } # parameters { # real delta; // constrained to be positive # real sigma2;// variance parameter # } # model { # target += cauchy_lpdf(delta | 0, r) - cauchy_lccdf(0 | 0, r); // Cauchy prior on delta # target += log(1/sigma2); // Jeffreys prior on sigma2 # target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2)); // likelihood # } # ' # # compile and fit model # stanmodelHplus <- stan_model(model_code = stancodeHplus, model_name="stanmodel") # stanfitHplus <- sampling(stanmodelHplus, data = list(y = y, n = n, r = 1/sqrt(2)), # iter = 30000, warmup = 1000, chains = 4, # control = list(adapt_delta = .99)) ## ----eval=FALSE--------------------------------------------------------------- # Hplus <- bridge_sampler(stanfitHplus, silent = TRUE) ## ----------------------------------------------------------------------------- print(Hplus) ## ----eval=FALSE--------------------------------------------------------------- # Hplus.error <- error_measures(Hplus)$percentage ## ----------------------------------------------------------------------------- print(Hplus.error) ## ----------------------------------------------------------------------------- # compute Bayes factor BFplus0 <- bf(Hplus, H0) print(BFplus0) ## ----eval=FALSE--------------------------------------------------------------- # BFplus0.BayesFactor <- extractBF(ttestBF(y, nullInterval = c(0, Inf)), onlybf = TRUE)[1] ## ----------------------------------------------------------------------------- print(BFplus0.BayesFactor) bridgesampling/inst/doc/bridgesampling_paper.pdf.asis0000644000176200001440000000020415055304401022563 0ustar liggesusers%\VignetteIndexEntry{bridgesampling: An R Package for Estimating Normalizing Constants (JSS version)} %\VignetteEngine{R.rsp::asis} bridgesampling/inst/doc/bridgesampling_stan_ttest.html0000644000176200001440000003340415107052015023110 0ustar liggesusers Bayesian One-Sample T-Test (Stan)

Bayesian One-Sample T-Test (Stan)

Quentin F. Gronau

2025-11-18

In this vignette, we explain how we can compute the (log) marginal likelihood and the Bayes factor for models fitted in Stan. This approach has the advantage that the user only needs to pass the fitted stanfit object which contains all information that is necessary to compute the (log) marginal likelihood. Here we show how one can conduct a Bayesian one-sample t-test as implemented in the BayesFactor package (Morey & Rouder, 2015).

Model

The Bayesian one-sample t-test makes the assumption that the observations are normally distributed with mean \(\mu\) and variance \(\sigma^2\). The model is then reparametrized in terms of the standardized effect size \(\delta = \mu/\sigma\). For the standardized effect size, a Cauchy prior with location zero and scale \(r = 1/\sqrt{2}\) is used. For the variance \(\sigma^2\), Jeffreys’s prior is used: \(p(\sigma^2) \propto 1/\sigma^2\).

In this example, we are interested in comparing the null model \(\mathcal{H}_0\), which posits that the effect size \(\delta\) is zero, to the alternative hypothesis \(\mathcal{H}_1\), which assigns \(\delta\) the above described Cauchy prior.

Data

In this example, we will analyze the sleep data set from the t.test example. This data set shows the effect of two soporific drugs (increase in hours of sleep compared to control) on 10 patients. These data can be analyzed via a one-sample t-test by first computing the difference scores and then conducting the t-test using these difference scores as data. The difference scores are calculated as follows:

library(bridgesampling)

set.seed(12345)

# Sleep data from t.test example
data(sleep)

# compute difference scores
y <- sleep$extra[sleep$group == 2] - sleep$extra[sleep$group == 1]
n <- length(y)

Specifying the Models

Next, we implement the models in Stan. Note that to compute the (log) marginal likelihood for a Stan model, we need to specify the model in a certain way. Instad of using "~" signs for specifying distributions, we need to directly use the (log) density functions. The reason for this is that when using the "~" sign, constant terms are dropped which are not needed for sampling from the posterior. However, for computing the marginal likelihood, these constants need to be retained. For instance, instead of writing y ~ normal(mu, sigma) we would need to write target += normal_lpdf(y | mu, sigma). The models can then be specified and compiled as follows (note that it is necessary to install rstan for this):

library(rstan)

# models
stancodeH0 <- '
data {
  int<lower=1> n; // number of observations
  vector[n] y; // observations
}
parameters {
  real<lower=0> sigma2; // variance parameter
}
model {
  target += log(1/sigma2); // Jeffreys prior on sigma2
  target += normal_lpdf(y | 0, sqrt(sigma2)); // likelihood
}
'
stancodeH1 <- '
data {
  int<lower=1> n; // number of observations
  vector[n] y; // observations
  real<lower=0> r; // Cauchy prior scale
}
parameters {
  real delta;
  real<lower=0> sigma2;// variance parameter
}
model {
  target += cauchy_lpdf(delta | 0, r); // Cauchy prior on delta
  target += log(1/sigma2); // Jeffreys prior on sigma2
  target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2));  // likelihood
}
'
# compile models
stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel")
stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel")

Fitting the Models

Now we can fit the null and the alternative model in Stan. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models.

# fit models
stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n),
                      iter = 20000, warmup = 1000, chains = 4, cores = 1,
                      control = list(adapt_delta = .99))
stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, r = 1/sqrt(2)),
                      iter = 20000, warmup = 1000, chains = 4, cores = 1,
                      control = list(adapt_delta = .99))

Computing the (Log) Marginal Likelihoods

Computing the (log) marginal likelihoods via the bridge_sampler function is now easy: we only need to pass the stanfit objects which contain all information necessary. We use silent = TRUE to suppress printing the number of iterations to the console:

H0 <- bridge_sampler(stanfitH0, silent = TRUE)
H1 <- bridge_sampler(stanfitH1, silent = TRUE)

We obtain:

print(H0)
## Bridge sampling estimate of the log marginal likelihood: -20.80934
## Estimate obtained in 4 iteration(s) via method "normal".
print(H1)
## Bridge sampling estimate of the log marginal likelihood: -17.96114
## Estimate obtained in 4 iteration(s) via method "normal".

We can use the error_measures function to compute an approximate percentage error of the estimates:

# compute percentage errors
H0.error <- error_measures(H0)$percentage
H1.error <- error_measures(H1)$percentage

We obtain:

print(H0.error)
## [1] "0.049%"
print(H1.error)
## [1] "0.0655%"

Computing the Bayes Factor

To compare the null model and the alternative model, we can compute the Bayes factor by using the bf function. In our case, we compute \(\text{BF}_{10}\), that is, the Bayes factor which quantifies how much more likely the data are under the alternative versus the null hypothesis:

# compute Bayes factor
BF10 <- bf(H1, H0)
print(BF10)
## Estimated Bayes factor in favor of H1 over H0: 17.25678

We can compare the bridge sampling result to the BayesFactor package result:

library(BayesFactor)
BF10.BayesFactor <- extractBF(ttestBF(y), onlybf = TRUE)

We obtain:

print(BF10.BayesFactor)
## [1] 17.25888

One-sided Test

We can also conduct one-sided tests. For instance, we could test the hypothesis that the effect size is positive versus the null hypothesis. Since we already fitted the null model and computed its marginal likelihood, we only need to slightly adjust the alternative model to reflect the directed hypothesis. To achieve this, we need to truncate the Cauchy prior distribution for \(\delta\) at zero and then renormalize the (log) density. This is easily achieved via the Stan function cauchy_lccdf which corresponds to the log of the complementary cumulative distribution function of the Cauchy distribution. Thus, cauchy_lccdf(0 | 0, r) gives us the log of the area greater than zero which is required for renormalizing the truncated Cauchy prior. The model can then be specified and fitted as follows:

stancodeHplus <- '
data {
  int<lower=1> n; // number of observations
  vector[n] y; // observations
  real<lower=0> r; // Cauchy prior scale
}
parameters {
  real<lower=0> delta; // constrained to be positive
  real<lower=0> sigma2;// variance parameter
}
model {
  target += cauchy_lpdf(delta | 0, r) - cauchy_lccdf(0 | 0, r); // Cauchy prior on delta
  target += log(1/sigma2); // Jeffreys prior on sigma2
  target += normal_lpdf(y | delta*sqrt(sigma2), sqrt(sigma2));  // likelihood
}
'
# compile and fit model
stanmodelHplus <- stan_model(model_code = stancodeHplus, model_name="stanmodel")
stanfitHplus <- sampling(stanmodelHplus, data = list(y = y, n = n, r = 1/sqrt(2)),
                         iter = 30000, warmup = 1000, chains = 4,
                         control = list(adapt_delta = .99))

The (log) marginal likelihood is then computed as follows:

Hplus <- bridge_sampler(stanfitHplus, silent = TRUE)

We obtain:

print(Hplus)
## Bridge sampling estimate of the log marginal likelihood: -17.27045
## Estimate obtained in 4 iteration(s) via method "normal".

We can again use the error_measures function to compute an approximate percentage error of the estimate:

Hplus.error <- error_measures(Hplus)$percentage

We obtain:

print(Hplus.error)
## [1] "0.136%"

The one-sided Bayes factor in favor of a positive effect versus the null hypothesis can be computed as follows:

# compute Bayes factor
BFplus0 <- bf(Hplus, H0)
print(BFplus0)
## Estimated Bayes factor in favor of Hplus over H0: 34.42872

We can compare the bridge sampling result to the BayesFactor package result:

BFplus0.BayesFactor <- extractBF(ttestBF(y, nullInterval = c(0, Inf)), onlybf = TRUE)[1]

We obtain:

print(BFplus0.BayesFactor)
## [1] 34.41694

References

Richard D. Morey and Jeffrey N. Rouder (2015). BayesFactor: Computation of Bayes Factors for Common Designs. R package version 0.9.12-2.

bridgesampling/inst/doc/bridgesampling_example_nimble.html0000644000176200001440000003006015107052015023674 0ustar liggesusers Hierarchical Normal Example (nimble)

Hierarchical Normal Example (nimble)

Quentin F. Gronau, Henrik Singmann & Perry de Valpine

2025-11-18

In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in nimble. The nimble documentation provides a comprehensive overview. This vignette uses the same models and data as the Stan vignette and Jags vignette.

Model and Data

The model that we will use assumes that each of the \(n\) observations \(y_i\) (where \(i\) indexes the observation, \(i = 1,2,...,n\)) is normally distributed with corresponding mean \(\theta_i\) and a common known variance \(\sigma^2\): \(y_i \sim \mathcal{N}(\theta_i, \sigma^2)\). Each \(\theta_i\) is drawn from a normal group-level distribution with mean \(\mu\) and variance \(\tau^2\): \(\theta_i \sim \mathcal{N}(\mu, \tau^2)\). For the group-level mean \(\mu\), we use a normal prior distribution of the form \(\mathcal{N}(\mu_0, \tau^2_0)\). For the group-level variance \(\tau^2\), we use an inverse-gamma prior of the form \(\text{Inv-Gamma}(\alpha, \beta)\).

In this example, we are interested in comparing the null model \(\mathcal{H}_0\), which posits that the group-level mean \(\mu = 0\), to the alternative model \(\mathcal{H}_1\), which allows \(\mu\) to be different from zero. First, we generate some data from the null model:

library(bridgesampling)

### generate data ###
set.seed(12345)

mu <- 0
tau2 <- 0.5
sigma2 <- 1

n <- 20
theta <- rnorm(n, mu, sqrt(tau2))
y <- rnorm(n, theta, sqrt(sigma2))

Next, we specify the prior parameters \(\mu_0\), \(\tau^2_0\), \(\alpha\), and \(\beta\):

### set prior parameters ###
mu0 <- 0
tau20 <- 1
alpha <- 1
beta <- 1

Specifying the Models

Next, we implement the models in nimble. This requires to first transform the code into a nimbleModel, then we need to set the data, and then we can compile the model. Given that nimble is build on BUGS, the similarity between the nimble code and the Jags code is not too surprising.

library("nimble")

# models
codeH0 <- nimbleCode({
  invTau2 ~ dgamma(1, 1)
  tau2 <- 1/invTau2
  for (i in 1:20) {
    theta[i] ~ dnorm(0, sd = sqrt(tau2))
    y[i] ~ dnorm(theta[i], sd = 1)
  }
})
codeH1 <- nimbleCode({
  mu ~ dnorm(0, sd = 1)
  invTau2 ~ dgamma(1, 1)
  tau2 <- 1/invTau2
  for (i in 1:20) {
    theta[i] ~ dnorm(mu, sd = sqrt(tau2))
    y[i] ~ dnorm(theta[i], sd = 1)
  }
})

## steps for H0:
modelH0 <- nimbleModel(codeH0)
modelH0$setData(y = y) # set data
cmodelH0 <- compileNimble(modelH0) # make compiled version from generated C++

## steps for H1:
modelH1 <- nimbleModel(codeH1)
modelH1$setData(y = y) # set data
cmodelH1 <- compileNimble(modelH1) # make compiled version from generated C++

Fitting the Models

Fitting a model with nimble requires one to first create an MCMC function from the (compiled or uncompiled) model. This function then needs to be compiled again. With this object we can then create the samples. Note that nimble uses a reference object semantic so we do not actually need the samples object, as the samples will be saved in the MCMC function objects. But as runMCMC returns them anyway, we nevertheless save them.

One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models.

# build MCMC functions, skipping customization of the configuration.
mcmcH0 <- buildMCMC(modelH0,
                    monitors = modelH0$getNodeNames(stochOnly = TRUE,
                                                    includeData = FALSE))
mcmcH1 <- buildMCMC(modelH1,
                    monitors = modelH1$getNodeNames(stochOnly = TRUE,
                                                    includeData = FALSE))
# compile the MCMC function via generated C++
cmcmcH0 <- compileNimble(mcmcH0, project = modelH0)
cmcmcH1 <- compileNimble(mcmcH1, project = modelH1)

# run the MCMC.  This is a wrapper for cmcmc$run() and extraction of samples.
# the object samplesH1 is actually not needed as the samples are also in cmcmcH1
samplesH0 <- runMCMC(cmcmcH0, niter = 1e5, nburnin = 1000, nchains = 2,
                     progressBar = FALSE)
samplesH1 <- runMCMC(cmcmcH1, niter = 1e5, nburnin = 1000, nchains = 2,
                     progressBar = FALSE)

Computing the (Log) Marginal Likelihoods

Computing the (log) marginal likelihoods via the bridge_sampler function is now easy: we only need to pass the compiled MCMC function objects (of class "MCMC_refClass") which contain all information necessary. We use silent = TRUE to suppress printing the number of iterations to the console:

# compute log marginal likelihood via bridge sampling for H0
H0.bridge <- bridge_sampler(cmcmcH0, silent = TRUE)

# compute log marginal likelihood via bridge sampling for H1
H1.bridge <- bridge_sampler(cmcmcH1, silent = TRUE)

We obtain:

print(H0.bridge)
## Bridge sampling estimate of the log marginal likelihood: -37.52918
## Estimate obtained in 4 iteration(s) via method "normal".
print(H1.bridge)
## Bridge sampling estimate of the log marginal likelihood: -37.80257
## Estimate obtained in 4 iteration(s) via method "normal".

We can use the error_measures function to compute an approximate percentage error of the estimates:

# compute percentage errors
H0.error <- error_measures(H0.bridge)$percentage
H1.error <- error_measures(H1.bridge)$percentage

We obtain:

print(H0.error)
## [1] "0.2%"
print(H1.error)
## [1] "0.22%"

Bayesian Model Comparison

To compare the null model and the alternative model, we can compute the Bayes factor by using the bf function. In our case, we compute \(\text{BF}_{01}\), that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model:

# compute Bayes factor
BF01 <- bf(H0.bridge, H1.bridge)
print(BF01)
## Estimated Bayes factor in favor of H0.bridge over H1.bridge: 1.31441

In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the post_prob function:

# compute posterior model probabilities (assuming equal prior model probabilities)
post1 <- post_prob(H0.bridge, H1.bridge)
print(post1)
## H0.bridge H1.bridge 
## 0.5679244 0.4320756

When the argument prior_prob is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the prior_prob argument to specify different prior model probabilities:

# compute posterior model probabilities (using user-specified prior model probabilities)
post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4))
print(post2)
## H0.bridge H1.bridge 
## 0.6634826 0.3365174
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0 R /Size 332 /ID [<788d9713acb42e50141e4ab157e2489c><962be3b4fc0d2f6e77c06ff3193489de>] >> stream xœí‘Ï+Da†¿{çºB™÷ÎŒŸãÇX™”X( kEù (¥ØX) [j²µ°Ql¦Y`EYHÙ „Hb'¬Ø\÷}üãÞÅÓÛùÎyÏ=çØFŸm‡ŸÆVÀŠXæ Œ7\ µÛ«»¿^Ewÿ Ln¤^ü>]¼|˜üN)Ô‰i]¹óV¬:“[bݹ˜›S}bÓXI¦Õ*Öˆ¶/ÆEg;¤å/Sµ+fJT]à°H|O¬8½F1±!ú¯è7±¡šÚ‚<3Òµ³tì¢Öà¿)¦ópHt'ÄöAܺ™Åe.›œx*Ï–~âgdzÄçé>…óÝ÷y½«äŒ¢Ÿø‡Kùü½6/‰õ_LÇfÒböO¶‘g®ø@—kô73Ž±Ãâ?LÊÿ;TÙm0KdŽ+,ˆñwøÌ~Ømrî+è#ª æ:@? endstream endobj startxref 370113 %%EOF bridgesampling/inst/doc/bridgesampling_example_stan.Rmd0000644000176200001440000001607515055304401023164 0ustar liggesusers--- title: "Hierarchical Normal Example (Stan)" author: "Quentin F. Gronau" date: "`r Sys.Date()`" show_toc: true output: knitr:::html_vignette: toc: yes vignette: > %\VignetteIndexEntry{Hierarchical Normal Example Stan} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- In this vignette, we explain how one can compute marginal likelihoods, Bayes factors, and posterior model probabilities using a simple hierarchical normal model implemented in `Stan`. This vignette uses the same models and data as the [`Jags` vignette](bridgesampling_example_jags.html). ## Model and Data The model that we will use assumes that each of the $n$ observations $y_i$ (where $i$ indexes the observation, $i = 1,2,...,n$) is normally distributed with corresponding mean $\theta_i$ and a common known variance $\sigma^2$: $y_i \sim \mathcal{N}(\theta_i, \sigma^2)$. Each $\theta_i$ is drawn from a normal group-level distribution with mean $\mu$ and variance $\tau^2$: $\theta_i \sim \mathcal{N}(\mu, \tau^2)$. For the group-level mean $\mu$, we use a normal prior distribution of the form $\mathcal{N}(\mu_0, \tau^2_0)$. For the group-level variance $\tau^2$, we use an inverse-gamma prior of the form $\text{Inv-Gamma}(\alpha, \beta)$. In this example, we are interested in comparing the null model $\mathcal{H}_0$, which posits that the group-level mean $\mu = 0$, to the alternative model $\mathcal{H}_1$, which allows $\mu$ to be different from zero. First, we generate some data from the null model: ```{r} library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ``` Next, we specify the prior parameters $\mu_0$, $\tau^2_0$, $\alpha$, and $\beta$: ```{r,eval=FALSE} ### set prior parameters ### mu0 <- 0 tau20 <- 1 alpha <- 1 beta <- 1 ``` ## Specifying the Models Next, we implement the models in `Stan`. Note that to compute the (log) marginal likelihood for a `Stan` model, we need to specify the model in a certain way. Instad of using `"~"` signs for specifying distributions, we need to directly use the (log) density functions. The reason for this is that when using the `"~"` sign, constant terms are dropped which are not needed for sampling from the posterior. However, for computing the marginal likelihood, these constants need to be retained. For instance, instead of writing `y ~ normal(mu, sigma)` we would need to write `target += normal_lpdf(y | mu, sigma)`. The models can then be specified and compiled as follows (note that it is necessary to install `rstan` for this): ```{r, eval=FALSE} library(rstan) # models stancodeH0 <- 'data { int n; // number of observations vector[n] y; // observations real alpha; real beta; real sigma2; } parameters { real tau2; // group-level variance vector[n] theta; // participant effects } model { target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | 0, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' stancodeH1 <- 'data { int n; // number of observations vector[n] y; // observations real mu0; real tau20; real alpha; real beta; real sigma2; } parameters { real mu; real tau2; // group-level variance vector[n] theta; // participant effects } model { target += normal_lpdf(mu | mu0, sqrt(tau20)); target += inv_gamma_lpdf(tau2 | alpha, beta); target += normal_lpdf(theta | mu, sqrt(tau2)); target += normal_lpdf(y | theta, sqrt(sigma2)); } ' # compile models stanmodelH0 <- stan_model(model_code = stancodeH0, model_name="stanmodel") stanmodelH1 <- stan_model(model_code = stancodeH1, model_name="stanmodel") ``` ## Fitting the Models Now we can fit the null and the alternative model in `Stan`. One usually requires a larger number of posterior samples for estimating the marginal likelihood than for simply estimating the model parameters. This is the reason for using a comparatively large number of samples for these simple models. ```{r, eval=FALSE} # fit models stanfitH0 <- sampling(stanmodelH0, data = list(y = y, n = n, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 50000, warmup = 1000, chains = 3, cores = 1) stanfitH1 <- sampling(stanmodelH1, data = list(y = y, n = n, mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2), iter = 50000, warmup = 1000, chains = 3, cores = 1) ``` ## Computing the (Log) Marginal Likelihoods Computing the (log) marginal likelihoods via the `bridge_sampler` function is now easy: we only need to pass the `stanfit` objects which contain all information necessary. We use `silent = TRUE` to suppress printing the number of iterations to the console: ```{r, echo=FALSE} load(system.file("extdata/", "vignette_example_stan.RData", package = "bridgesampling")) ``` ```{r,eval=FALSE} # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(stanfitH0, silent = TRUE) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(stanfitH1, silent = TRUE) ``` We obtain: ```{r} print(H0.bridge) print(H1.bridge) ``` We can use the `error_measures` function to compute an approximate percentage error of the estimates: ```{r,eval=FALSE} # compute percentage errors H0.error <- error_measures(H0.bridge)$percentage H1.error <- error_measures(H1.bridge)$percentage ``` We obtain: ```{r} print(H0.error) print(H1.error) ``` ## Bayesian Model Comparison To compare the null model and the alternative model, we can compute the Bayes factor by using the `bf` function. In our case, we compute $\text{BF}_{01}$, that is, the Bayes factor which quantifies how much more likely the data are under the null versus the alternative model: ```{r} # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ``` In this case, the Bayes factor is close to one, indicating that there is not much evidence for either model. We can also compute posterior model probabilities by using the `post_prob` function: ```{r} # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ``` When the argument `prior_prob` is not specified, as is the case here, the prior model probabilities of all models under consideration are set equal (i.e., in this case with two models to 0.5). However, if we had prior knowledge about how likely both models are, we could use the `prior_prob` argument to specify different prior model probabilities: ```{r} # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) ``` bridgesampling/inst/doc/bridgesampling_example_jags.R0000644000176200001440000001267115107052014022616 0ustar liggesusers## ----------------------------------------------------------------------------- library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ## ----eval=FALSE--------------------------------------------------------------- # ### set prior parameters ### # mu0 <- 0 # tau20 <- 1 # alpha <- 1 # beta <- 1 ## ----eval=FALSE--------------------------------------------------------------- # library(R2jags) # # ### functions to get posterior samples ### # # # H0: mu = 0 # getSamplesModelH0 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { # # model <- " # model { # for (i in 1:n) { # theta[i] ~ dnorm(0, invTau2) # y[i] ~ dnorm(theta[i], 1/sigma2) # } # invTau2 ~ dgamma(alpha, beta) # tau2 <- 1/invTau2 # }" # # s <- jags(data, parameters.to.save = c("theta", "invTau2"), # model.file = textConnection(model), # n.chains = nchains, n.iter = niter, # n.burnin = nburnin, n.thin = 1) # # return(s) # # } # # # H1: mu != 0 # getSamplesModelH1 <- function(data, niter = 52000, nburnin = 2000, # nchains = 3) { # # model <- " # model { # for (i in 1:n) { # theta[i] ~ dnorm(mu, invTau2) # y[i] ~ dnorm(theta[i], 1/sigma2) # } # mu ~ dnorm(mu0, 1/tau20) # invTau2 ~ dgamma(alpha, beta) # tau2 <- 1/invTau2 # }" # # s <- jags(data, parameters.to.save = c("theta", "mu", "invTau2"), # model.file = textConnection(model), # n.chains = nchains, n.iter = niter, # n.burnin = nburnin, n.thin = 1) # # return(s) # # } # # ### get posterior samples ### # # # create data lists for JAGS # data_H0 <- list(y = y, n = length(y), alpha = alpha, beta = beta, sigma2 = sigma2) # data_H1 <- list(y = y, n = length(y), mu0 = mu0, tau20 = tau20, alpha = alpha, # beta = beta, sigma2 = sigma2) # # # fit models # samples_H0 <- getSamplesModelH0(data_H0) # samples_H1 <- getSamplesModelH1(data_H1) # ## ----eval=FALSE--------------------------------------------------------------- # ### functions for evaluating the unnormalized posteriors on log scale ### # # log_posterior_H0 <- function(samples.row, data) { # # mu <- 0 # invTau2 <- samples.row[[ "invTau2" ]] # theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] # # sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + # sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + # dgamma(invTau2, data$alpha, data$beta, log = TRUE) # # } # # log_posterior_H1 <- function(samples.row, data) { # # mu <- samples.row[[ "mu" ]] # invTau2 <- samples.row[[ "invTau2" ]] # theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] # # sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + # sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + # dnorm(mu, data$mu0, sqrt(data$tau20), log = TRUE) + # dgamma(invTau2, data$alpha, data$beta, log = TRUE) # # } # ## ----eval=FALSE--------------------------------------------------------------- # # specify parameter bounds H0 # cn <- colnames(samples_H0$BUGSoutput$sims.matrix) # cn <- cn[cn != "deviance"] # lb_H0 <- rep(-Inf, length(cn)) # ub_H0 <- rep(Inf, length(cn)) # names(lb_H0) <- names(ub_H0) <- cn # lb_H0[[ "invTau2" ]] <- 0 # # # specify parameter bounds H1 # cn <- colnames(samples_H1$BUGSoutput$sims.matrix) # cn <- cn[cn != "deviance"] # lb_H1 <- rep(-Inf, length(cn)) # ub_H1 <- rep(Inf, length(cn)) # names(lb_H1) <- names(ub_H1) <- cn # lb_H1[[ "invTau2" ]] <- 0 ## ----echo=FALSE--------------------------------------------------------------- load(system.file("extdata/", "vignette_example_jags.RData", package = "bridgesampling")) ## ----eval=FALSE--------------------------------------------------------------- # # compute log marginal likelihood via bridge sampling for H0 # H0.bridge <- bridge_sampler(samples = samples_H0, data = data_H0, # log_posterior = log_posterior_H0, lb = lb_H0, # ub = ub_H0, silent = TRUE) # # # compute log marginal likelihood via bridge sampling for H1 # H1.bridge <- bridge_sampler(samples = samples_H1, data = data_H1, # log_posterior = log_posterior_H1, lb = lb_H1, # ub = ub_H1, silent = TRUE) ## ----------------------------------------------------------------------------- print(H0.bridge) print(H1.bridge) ## ----eval=FALSE--------------------------------------------------------------- # # compute percentage errors # H0.error <- error_measures(H0.bridge)$percentage # H1.error <- error_measures(H1.bridge)$percentage ## ----------------------------------------------------------------------------- print(H0.error) print(H1.error) ## ----------------------------------------------------------------------------- # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ## ----------------------------------------------------------------------------- # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ## ----------------------------------------------------------------------------- # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) bridgesampling/inst/doc/bridgesampling_example_nimble.R0000644000176200001440000000753215107052015023141 0ustar liggesusers## ----------------------------------------------------------------------------- library(bridgesampling) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ## ----eval=FALSE--------------------------------------------------------------- # ### set prior parameters ### # mu0 <- 0 # tau20 <- 1 # alpha <- 1 # beta <- 1 ## ----eval=FALSE--------------------------------------------------------------- # library("nimble") # # # models # codeH0 <- nimbleCode({ # invTau2 ~ dgamma(1, 1) # tau2 <- 1/invTau2 # for (i in 1:20) { # theta[i] ~ dnorm(0, sd = sqrt(tau2)) # y[i] ~ dnorm(theta[i], sd = 1) # } # }) # codeH1 <- nimbleCode({ # mu ~ dnorm(0, sd = 1) # invTau2 ~ dgamma(1, 1) # tau2 <- 1/invTau2 # for (i in 1:20) { # theta[i] ~ dnorm(mu, sd = sqrt(tau2)) # y[i] ~ dnorm(theta[i], sd = 1) # } # }) # # ## steps for H0: # modelH0 <- nimbleModel(codeH0) # modelH0$setData(y = y) # set data # cmodelH0 <- compileNimble(modelH0) # make compiled version from generated C++ # # ## steps for H1: # modelH1 <- nimbleModel(codeH1) # modelH1$setData(y = y) # set data # cmodelH1 <- compileNimble(modelH1) # make compiled version from generated C++ # ## ----eval=FALSE--------------------------------------------------------------- # # # build MCMC functions, skipping customization of the configuration. # mcmcH0 <- buildMCMC(modelH0, # monitors = modelH0$getNodeNames(stochOnly = TRUE, # includeData = FALSE)) # mcmcH1 <- buildMCMC(modelH1, # monitors = modelH1$getNodeNames(stochOnly = TRUE, # includeData = FALSE)) # # compile the MCMC function via generated C++ # cmcmcH0 <- compileNimble(mcmcH0, project = modelH0) # cmcmcH1 <- compileNimble(mcmcH1, project = modelH1) # # # run the MCMC. This is a wrapper for cmcmc$run() and extraction of samples. # # the object samplesH1 is actually not needed as the samples are also in cmcmcH1 # samplesH0 <- runMCMC(cmcmcH0, niter = 1e5, nburnin = 1000, nchains = 2, # progressBar = FALSE) # samplesH1 <- runMCMC(cmcmcH1, niter = 1e5, nburnin = 1000, nchains = 2, # progressBar = FALSE) ## ----echo=FALSE--------------------------------------------------------------- load(system.file("extdata/", "vignette_example_nimble.RData", package = "bridgesampling")) ## ----eval=FALSE--------------------------------------------------------------- # # compute log marginal likelihood via bridge sampling for H0 # H0.bridge <- bridge_sampler(cmcmcH0, silent = TRUE) # # # compute log marginal likelihood via bridge sampling for H1 # H1.bridge <- bridge_sampler(cmcmcH1, silent = TRUE) ## ----------------------------------------------------------------------------- print(H0.bridge) print(H1.bridge) ## ----eval=FALSE--------------------------------------------------------------- # # compute percentage errors # H0.error <- error_measures(H0.bridge)$percentage # H1.error <- error_measures(H1.bridge)$percentage ## ----------------------------------------------------------------------------- print(H0.error) print(H1.error) ## ----------------------------------------------------------------------------- # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) ## ----------------------------------------------------------------------------- # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) ## ----------------------------------------------------------------------------- # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) bridgesampling/inst/extdata/0000755000176200001440000000000015055304401015645 5ustar liggesusersbridgesampling/inst/extdata/vignette_stan_ttest.RData0000644000176200001440000000056715055304401022667 0ustar liggesusers‹ r‰0âŠàb```b`f’Ì@& `d`aà‰{000 Yì@Ì’9`rÞPM* Îw`€$lyùE¹‰9PU ¸iûXósS‹¡F±ÃsòÓssà*2KR‹`–䦖dä§@yÌ…††¦œi„52B·09'±f!ÜíIE™)é©@Ö?Œð0ÄÃo¼ºv¹©LÿiÌ0;ûšÕ£ §´Óã®6‰¯®Šcsxè¥å¡ë0Ð30±TÅPmˆU5;Pµ™©)ºrnp¨â2ßÐØ ]‹“›¡4˜à¡nè¸'®y¥;ÍV‹–L°Ä›” `¨â Τ´xXx :77?%5'9ƒ2!å ¤ò#ÙÜ@^Åt»£ÙåA´r;º)ЄŒÏ­ @ÖsJ¬L-vKL.G 4 \i{ïAS/ õV-Ž¦q9;߀¬ѽSAlbridgesampling/inst/extdata/vignette_example_jags.RData0000644000176200001440000000052515055304401023130 0ustar liggesusers‹ r‰0âŠàb```b`f’Ì@& `d`aàÒœzIE™)é© ÌÂ@v æ)8àtD…Û3ØÆw`€$Øòò‹rs ªpÓ(Ö²æ%æ¦Cb‡ æä§çæÀUd–¤Á,ÉM-ÉÈOò˜ L#8Ó!jd„narNb1ÌB¸Ûa>gø‡,†8ƒå™Ì»÷‡žÂƒE„ò`aúOû`†ÙAØóÀ4‘ZT”_„®Ã@ÏÐÄDCµ!NÕfFèªYœÜ ¡aÊ Cû/w9ôjçHÙ\`µ˜!ÃÕÏ””ó0Œpx3)-æ;Û¹sóSRsâ‘fFÀLAÄZ_\ôÈýLöd’e¾©Ûß>nyLx³·“a…ÜŠ§:‹æ¦½H·¿ºl×Q#}Sr­`ø,£bridgesampling/inst/extdata/vignette_example_nimble.RData0000644000176200001440000000052215055304401023447 0ustar liggesusers‹ r‰0âŠàb```b`f’Ì@& `d`aàÒœzIE™)é© ÌÂ@v æ)8àtx«Û ßA€ `ËË/ÊM̪bÀM£XËš—˜›Z 5Š&˜“Ÿž›W‘Y’Z³$7µ$#?Êc.44D0àL#„¨‘º…É9‰Å0 án‡ùœáF°â –g»׶DR3X˜þÓ>$˜avö<0M¤å¡é`1Ð3RÅPkˆU-+P-†b'7Ch€2ÁÐþ+û¥†ð‡€l.°ZÌ`a‚êgJJƒù @8üÅ™”óŠíܹù)©9ñÈ) 3`Æ?Fø°ä—ýÁr?“ý#ü#+ÍgÚß^®P¶vÂ-n'à #¸O­íð«ý´¿ÚÙ`ÿp“1¹V0ü^J&bridgesampling/inst/extdata/vignette_example_stan.RData0000644000176200001440000000052515055304401023151 0ustar liggesusers‹ r‰0âŠàb```b`f’Ì@& `d`aàÒœzIE™)é© ÌÂ@v æ)8àtDè†dëßA„ `ËË/ÊM̪bÀM£XËš—˜›Z 5Š&˜“Ÿž›W‘Y’Z³$7µ$#?Êc.44D0àL#„¨‘º…É9‰Å0 án‡ùœáF°â –§ÿŠ—°ÿ‡‹åÁÂôŸö!Á ³ƒ°ç9€i"µ¨(¿]‡ž¡‰±*†jCœªÍLÐU³8¹BÔ †ö_nÝo[³ Èæ«Å &¨~¦¤4˜×€a„ÃkœIiñ0ß¡ØΛŸ’šœø˜03fÀ"Ö‚üâ ?˜@îg²$=Ég}Œ¢ýí·ÓºŸÄáv2¬0‚[ñTûI¬Ñ\û«+Ì£Îê!× †Wxµ bridgesampling/build/0000755000176200001440000000000015107052015014334 5ustar liggesusersbridgesampling/build/vignette.rds0000644000176200001440000000072215107052015016674 0ustar liggesusers‹­”=OÃ0†Ý6¥€„„Ä‚„À` ?€­Ð*ˆV¤[u4n1$Nd›Ï‰¿ÍB¹¶6$ þ~|w~s—‹yBH™8Õ)WpZYÂnÛ"¶qÈŽë—’ûC¦ Œ.†=ö0ž±Þ5 •{úÛÈÁ/–óì) "­f°ñqOk¦tC̤ûWÚú B·š ŸùYšfh}«#É!øàÒòÐcÎ$ÈþïC@Ï"âÐœ¾‰¶êGžá6‹¸³‰H?±è¡ VÈ}xdŠƒ mÁv½éyw·‹%±vúA{´.è9í@ÿ†Œ"I›Jó4oüi 1} see \code{Details}.} \item{data}{data object which is used in \code{log_posterior}.} \item{lb}{named vector with lower bounds for parameters.} \item{ub}{named vector with upper bounds for parameters.} \item{param_types}{character vector of length \code{ncol(samples)} with \code{"real"}, \code{"simplex"} or \code{"circular"}. For all regular bounded or unbounded continuous parameters, this should just be \code{"real"}. However, if there are parameters which lie on a simplex or on the circle, this should be noted here. Simplex parameters are parameters which are bounded below by zero and collectively sum to one, such as weights in a mixture model. For these, the stick-breaking transformation is performed as described in the Stan reference manual. The circular variables are given a numerical representation to which the normal distribution is most likely a good fit. Only possible to use with \code{bridge_sampler.matrix}.} \item{packages}{character vector with names of packages needed for evaluating \code{log_posterior} in parallel (only relevant if \code{cores > 1} and \code{.Platform$OS.type != "unix"}).} \item{varlist}{character vector with names of variables needed for evaluating \code{log_posterior} (only needed if \code{cores > 1} and \code{.Platform$OS.type != "unix"} as these objects will be exported to the nodes). These objects need to exist in \code{envir}.} \item{envir}{specifies the environment for \code{varlist} (only needed if \code{cores > 1} and \code{.Platform$OS.type != "unix"} as these objects will be exported to the nodes). Default is \code{\link{.GlobalEnv}}.} \item{rcppFile}{in case \code{cores > 1} and \code{log_posterior} is an \code{Rcpp} function, \code{rcppFile} specifies the path to the cpp file (will be compiled on all cores).} } \value{ If \code{repetitions = 1}, returns a list of class \code{"bridge"} with components: \itemize{ \item \code{logml}: estimate of the log marginal likelihood. \item \code{niter}: number of iterations of the iterative updating scheme. \item \code{method}: bridge sampling method that was used to obtain the estimate. \item \code{q11}: log posterior evaluations for posterior samples. \item \code{q12}: log proposal evaluations for posterior samples. \item \code{q21}: log posterior evaluations for samples from the proposal. \item \code{q22}: log proposal evaluations for samples from the proposal. \item \code{mcse_logml}: Monte Carlo standard error of \code{logml} on the log-scale (Micaletto & Vehtari, 2025). } If \code{repetitions > 1}, returns a list of class \code{"bridge_list"} with components: \itemize{ \item \code{logml}: numeric vector of log marginal likelihood estimates. \item \code{niter}: numeric vector with the number of iterations of the iterative updating scheme for each repetition. \item \code{method}: bridge sampling method that was used to obtain the estimates. \item \code{repetitions}: number of repetitions. \item \code{mcse_logml}: numeric vector of Monte Carlo standard errors on the log-scale (Micaletto & Vehtari, 2025), one per repetition. } } \description{ Computes log marginal likelihood via bridge sampling. } \details{ Bridge sampling is implemented as described in Meng and Wong (1996, see equation 4.1) using the "optimal" bridge function. When \code{method = "normal"}, the proposal distribution is a multivariate normal distribution with mean vector equal to the sample mean vector of \code{samples} and covariance matrix equal to the sample covariance matrix of \code{samples}. For a recent tutorial on bridge sampling, see Gronau et al. (in press). When \code{method = "warp3"}, the proposal distribution is a standard multivariate normal distribution and the posterior distribution is "warped" (Meng & Schilling, 2002) so that it has the same mean vector, covariance matrix, and skew as the samples. \code{method = "warp3"} takes approximately twice as long as \code{method = "normal"}. Note that for the \code{matrix} method, the lower and upper bound of a parameter cannot be a function of the bounds of another parameter. Furthermore, constraints that depend on multiple parameters of the model are not supported. This usually excludes, for example, parameters that constitute a covariance matrix or sets of parameters that need to sum to one. However, if the retransformations are part of the model itself and the \code{log_posterior} accepts parameters on the real line and performs the appropriate Jacobian adjustments, such as done for \code{stanfit} and \code{stanreg} objects, such constraints are obviously possible (i.e., we currently do not know of any parameter supported within Stan that does not work with the current implementation through a \code{stanfit} object). \subsection{Parallel Computation}{ On unix-like systems forking is used via \code{\link{mclapply}}. Hence elements needed for evaluation of \code{log_posterior} should be in the \code{\link{.GlobalEnv}}. On other OSes (e.g., Windows), things can get more complicated. For normal parallel computation, the \code{log_posterior} function can be passed as both function and function name. If the latter, it needs to exist in the environment specified in the \code{envir} argument. For parallel computation when using an \code{Rcpp} function, \code{log_posterior} can only be passed as the function name (i.e., character). This function needs to result from calling \code{sourceCpp} on the file specified in \code{rcppFile}. Due to the way \code{rstan} currently works, parallel computations with \code{stanfit} and \code{stanreg} objects only work with forking (i.e., NOT on Windows). } } \note{ To be able to use a \code{stanreg} object for \code{samples}, the user crucially needs to have specified the \code{diagnostic_file} when fitting the model in \pkg{rstanarm}. } \section{Warning}{ Note that the results depend strongly on the parameter priors. Therefore, it is strongly advised to think carefully about the priors before calculating marginal likelihoods. For example, the prior choices implemented in \pkg{rstanarm} or \pkg{brms} might not be optimal from a testing point of view. We recommend to use priors that have been chosen from a testing and not a purely estimation perspective. Also note that for testing, the number of posterior samples usually needs to be substantially larger than for estimation. } \examples{ ## ------------------------------------------------------------------------ ## Example 1: Estimating the Normalizing Constant of a Two-Dimensional ## Standard Normal Distribution ## ------------------------------------------------------------------------ library(bridgesampling) library(mvtnorm) samples <- rmvnorm(1e4, mean = rep(0, 2), sigma = diag(2)) colnames(samples) <- c("x1", "x2") log_density <- function(samples.row, data) { -.5*t(samples.row) \%*\% samples.row } lb <- rep(-Inf, 2) ub <- rep(Inf, 2) names(lb) <- names(ub) <- colnames(samples) bridge_result <- bridge_sampler(samples = samples, log_posterior = log_density, data = NULL, lb = lb, ub = ub, silent = TRUE) # compare to analytical value analytical <- log(2*pi) print(cbind(bridge_result$logml, analytical)) \dontrun{ ## ------------------------------------------------------------------------ ## Example 2: Hierarchical Normal Model ## ------------------------------------------------------------------------ # for a full description of the example, see vignette("bridgesampling_example_jags") library(R2jags) ### generate data ### set.seed(12345) mu <- 0 tau2 <- 0.5 sigma2 <- 1 n <- 20 theta <- rnorm(n, mu, sqrt(tau2)) y <- rnorm(n, theta, sqrt(sigma2)) ### set prior parameters alpha <- 1 beta <- 1 mu0 <- 0 tau20 <- 1 ### functions to get posterior samples ### ### H0: mu = 0 getSamplesModelH0 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(0, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1) return(s) } ### H1: mu != 0 getSamplesModelH1 <- function(data, niter = 52000, nburnin = 2000, nchains = 3) { model <- " model { for (i in 1:n) { theta[i] ~ dnorm(mu, invTau2) y[i] ~ dnorm(theta[i], 1/sigma2) } mu ~ dnorm(mu0, 1/tau20) invTau2 ~ dgamma(alpha, beta) tau2 <- 1/invTau2 }" s <- jags(data, parameters.to.save = c("theta", "mu", "invTau2"), model.file = textConnection(model), n.chains = nchains, n.iter = niter, n.burnin = nburnin, n.thin = 1) return(s) } ### get posterior samples ### # create data lists for Jags data_H0 <- list(y = y, n = length(y), alpha = alpha, beta = beta, sigma2 = sigma2) data_H1 <- list(y = y, n = length(y), mu0 = mu0, tau20 = tau20, alpha = alpha, beta = beta, sigma2 = sigma2) # fit models samples_H0 <- getSamplesModelH0(data_H0) samples_H1 <- getSamplesModelH1(data_H1) ### functions for evaluating the unnormalized posteriors on log scale ### log_posterior_H0 <- function(samples.row, data) { mu <- 0 invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } log_posterior_H1 <- function(samples.row, data) { mu <- samples.row[[ "mu" ]] invTau2 <- samples.row[[ "invTau2" ]] theta <- samples.row[ paste0("theta[", seq_along(data$y), "]") ] sum(dnorm(data$y, theta, data$sigma2, log = TRUE)) + sum(dnorm(theta, mu, 1/sqrt(invTau2), log = TRUE)) + dnorm(mu, data$mu0, sqrt(data$tau20), log = TRUE) + dgamma(invTau2, data$alpha, data$beta, log = TRUE) } # specify parameter bounds H0 cn <- colnames(samples_H0$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H0 <- rep(-Inf, length(cn)) ub_H0 <- rep(Inf, length(cn)) names(lb_H0) <- names(ub_H0) <- cn lb_H0[[ "invTau2" ]] <- 0 # specify parameter bounds H1 cn <- colnames(samples_H1$BUGSoutput$sims.matrix) cn <- cn[cn != "deviance"] lb_H1 <- rep(-Inf, length(cn)) ub_H1 <- rep(Inf, length(cn)) names(lb_H1) <- names(ub_H1) <- cn lb_H1[[ "invTau2" ]] <- 0 # compute log marginal likelihood via bridge sampling for H0 H0.bridge <- bridge_sampler(samples = samples_H0, data = data_H0, log_posterior = log_posterior_H0, lb = lb_H0, ub = ub_H0, silent = TRUE) print(H0.bridge) # compute log marginal likelihood via bridge sampling for H1 H1.bridge <- bridge_sampler(samples = samples_H1, data = data_H1, log_posterior = log_posterior_H1, lb = lb_H1, ub = ub_H1, silent = TRUE) print(H1.bridge) # compute percentage error print(error_measures(H0.bridge)$percentage) print(error_measures(H1.bridge)$percentage) # compute Bayes factor BF01 <- bf(H0.bridge, H1.bridge) print(BF01) # compute posterior model probabilities (assuming equal prior model probabilities) post1 <- post_prob(H0.bridge, H1.bridge) print(post1) # compute posterior model probabilities (using user-specified prior model probabilities) post2 <- post_prob(H0.bridge, H1.bridge, prior_prob = c(.6, .4)) print(post2) } \dontrun{ ## ------------------------------------------------------------------------ ## Example 3: rstanarm ## ------------------------------------------------------------------------ library(rstanarm) # N.B.: remember to specify the diagnostic_file fit_1 <- stan_glm(mpg ~ wt + qsec + am, data = mtcars, chains = 2, cores = 2, iter = 5000, diagnostic_file = file.path(tempdir(), "df.csv")) bridge_1 <- bridge_sampler(fit_1) fit_2 <- update(fit_1, formula = . ~ . + cyl) bridge_2 <- bridge_sampler(fit_2, method = "warp3") bf(bridge_1, bridge_2) } } \references{ Gronau, Q. F., Singmann, H., & Wagenmakers, E.-J. (2020). bridgesampling: An R Package for Estimating Normalizing Constants. \emph{Journal of Statistical Software, 92}. \doi{10.18637/jss.v092.i10} Gronau, Q. F., Sarafoglou, A., Matzke, D., Ly, A., Boehm, U., Marsman, M., Leslie, D. S., Forster, J. J., Wagenmakers, E.-J., & Steingroever, H. (in press). A tutorial on bridge sampling. \emph{Journal of Mathematical Psychology}. \url{https://arxiv.org/abs/1703.05984} \cr \code{vignette("bridgesampling_tutorial")} Gronau, Q. F., Wagenmakers, E.-J., Heck, D. W., & Matzke, D. (2019). A Simple Method for Comparing Complex Models: Bayesian Model Comparison for Hierarchical Multinomial Processing Tree Models Using Warp-III Bridge Sampling. \emph{Psychometrika}, 84(1), 261–284. \doi{10.1007/s11336-018-9648-3} Meng, X.-L., & Wong, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. \emph{Statistica Sinica, 6}, 831-860. \url{https://www3.stat.sinica.edu.tw/statistica/j6n4/j6n43/j6n43.htm} Meng, X.-L., & Schilling, S. (2002). Warp bridge sampling. \emph{Journal of Computational and Graphical Statistics, 11(3)}, 552-586. \doi{10.1198/106186002457} Micaletto, G., & Vehtari, A. (2025). Monte Carlo standard errors for bridge sampling marginal likelihood estimation. \emph{arXiv preprint}, arXiv:2508.14487. \url{https://arxiv.org/abs/2508.14487} Overstall, A. M., & Forster, J. J. (2010). Default Bayesian model determination methods for generalised linear mixed models. \emph{Computational Statistics & Data Analysis, 54}, 3269-3288. \doi{10.1016/j.csda.2010.03.008} } \seealso{ \code{\link{bf}} allows the user to calculate Bayes factors and \code{\link{post_prob}} allows the user to calculate posterior model probabilities from bridge sampling estimates. \code{\link{bridge-methods}} lists some additional methods that automatically invoke the \code{\link{error_measures}} function. } \author{ Quentin F. Gronau and Henrik Singmann. Parallel computing (i.e., \code{cores > 1}) and the \code{stanfit} method use code from \code{rstan} by Jiaqing Guo, Jonah Gabry, and Ben Goodrich. Ben Goodrich added the \code{stanreg} method. Kees Mulder added methods for simplex and circular variables. Giorgio Micaletto and Aki Vehtari added the \code{CmdStanMCMC} method (for \code{cmdstanr}) and calculation of the Monte Carlo Standard Error (MCSE). } bridgesampling/man/bridge-methods.Rd0000644000176200001440000000241415055304401017176 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/bridge_methods.R \name{bridge-methods} \alias{bridge-methods} \alias{summary.bridge} \alias{summary.bridge_list} \alias{print.summary.bridge} \alias{print.summary.bridge_list} \alias{print.bridge} \alias{print.bridge_list} \title{Methods for bridge and bridge_list objects} \usage{ \method{summary}{bridge}(object, na.rm = TRUE, ...) \method{summary}{bridge_list}(object, na.rm = TRUE, ...) \method{print}{summary.bridge}(x, ...) \method{print}{summary.bridge_list}(x, ...) \method{print}{bridge}(x, ...) \method{print}{bridge_list}(x, na.rm = TRUE, ...) } \arguments{ \item{object, x}{object of class \code{bridge} or \code{bridge_list} as returned from \code{\link{bridge_sampler}}.} \item{na.rm}{logical. Should NA estimates in \code{bridge_list} objects be removed? Passed to \code{\link{error_measures}}.} \item{...}{further arguments, currently ignored.} } \value{ The \code{summary} methods return a \code{data.frame} which contains the log marginal likelihood plus the result returned from invoking \code{\link{error_measures}}. The \code{print} methods simply print and return nothing. } \description{ Methods defined for objects returned from the generic \code{\link{bridge_sampler}} function. } bridgesampling/man/error_measures.Rd0000644000176200001440000000540315055304401017337 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/error_measures.R \name{error_measures} \alias{error_measures} \alias{error_measures.bridge} \alias{error_measures.bridge_list} \title{Error Measures for Estimated Marginal Likelihood} \usage{ error_measures(bridge_object, ...) \method{error_measures}{bridge}(bridge_object, ...) \method{error_measures}{bridge_list}(bridge_object, na.rm = TRUE, ...) } \arguments{ \item{bridge_object}{an object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}.} \item{...}{additional arguments (currently ignored).} \item{na.rm}{a logical indicating whether missing values in logml estimates should be removed. Ignored for the \code{bridge} method.} } \value{ If \code{bridge_object} is of class \code{"bridge"} and has been obtained with \code{method = "normal"} and \code{repetitions = 1}, returns a list with components: \itemize{ \item \code{re2}: approximate relative mean-squared error for marginal likelihood estimate. \item \code{cv}: approximate coefficient of variation for marginal likelihood estimate (assumes that bridge estimate is unbiased). \item \code{percentage}: approximate percentage error of marginal likelihood estimate. } If \code{bridge_object} is of class \code{"bridge_list"}, returns a list with components: \itemize{ \item \code{min}: minimum of the log marginal likelihood estimates. \item \code{max}: maximum of the log marginal likelihood estimates. \item \code{IQR}: interquartile range of the log marginal likelihood estimates. } } \description{ Computes error measures for estimated marginal likelihood. } \details{ Computes error measures for marginal likelihood bridge sampling estimates. The approximate errors for a \code{bridge_object} of class \code{"bridge"} that has been obtained with \code{method = "normal"} and \code{repetitions = 1} are based on Fruehwirth-Schnatter (2004). Not applicable in case the object of class \code{"bridge"} has been obtained with \code{method = "warp3"} and \code{repetitions = 1}. To assess the uncertainty of the estimate in this case, it is recommended to run the \code{"warp3"} procedure multiple times. } \note{ For examples, see \code{\link{bridge_sampler}} and the accompanying vignettes: \cr \code{vignette("bridgesampling_example_jags")} \cr \code{vignette("bridgesampling_example_stan")} } \references{ Fruehwirth-Schnatter, S. (2004). Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques. \emph{The Econometrics Journal, 7}, 143-167. \doi{10.1111/j.1368-423X.2004.00125.x} } \seealso{ The \code{summary} methods for \code{bridge} and \code{bridge_list} objects automatically invoke this function, see \code{\link{bridge-methods}}. } \author{ Quentin F. Gronau } bridgesampling/man/bf.Rd0000644000176200001440000000674315055304401014701 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/bf.R \name{bf} \alias{bf} \alias{bayes_factor} \alias{bayes_factor.default} \alias{bf.bridge} \alias{bf.bridge_list} \alias{bf.default} \title{Bayes Factor(s) from Marginal Likelihoods} \usage{ bf(x1, x2, log = FALSE, ...) bayes_factor(x1, x2, log = FALSE, ...) \method{bayes_factor}{default}(x1, x2, log = FALSE, ...) \method{bf}{bridge}(x1, x2, log = FALSE, ...) \method{bf}{bridge_list}(x1, x2, log = FALSE, ...) \method{bf}{default}(x1, x2, log = FALSE, ...) } \arguments{ \item{x1}{Object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. Additionally, the default method assumes that \code{x1} is a single numeric log marginal likelihood (e.g., from \code{\link{logml}}) and will throw an error otherwise.} \item{x2}{Object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. Additionally, the default method assumes that \code{x2} is a single numeric log marginal likelihood (e.g., from \code{\link{logml}}) and will throw an error otherwise.} \item{log}{Boolean. If \code{TRUE}, the function returns the log of the Bayes factor. Default is \code{FALSE}.} \item{...}{currently not used here, but can be used by other methods.} } \value{ For the default method returns a list of class \code{"bf_default"} with components: \itemize{ \item \code{bf}: (scalar) value of the Bayes factor in favor of the model associated with \code{x1} over the model associated with \code{x2}. \item \code{log}: Boolean which indicates whether \code{bf} corresponds to the log Bayes factor. } For the method for \code{"bridge"} objects returns a list of class \code{"bf_bridge"} with components: \itemize{ \item \code{bf}: (scalar) value of the Bayes factor in favor of the model associated with \code{x1} over the model associated with \code{x2}. \item \code{log}: Boolean which indicates whether \code{bf} corresponds to the log Bayes factor. } For the method for \code{"bridge_list"} objects returns a list of class \code{"bf_bridge_list"} with components: \itemize{ \item \code{bf}: a numeric vector consisting of Bayes factors where each element gives the Bayes factor for one set of logmls in favor of the model associated with \code{x1} over the model associated with \code{x2}. The length of this vector is given by the \code{"bridge_list"} element with the most \code{repetitions}. Elements with fewer repetitions will be recycled (with warning). \item \code{bf_median_based}: (scalar) value of the Bayes factor in favor of the model associated with \code{x1} over the model associated with \code{x2} that is based on the median values of the logml estimates. \item \code{log}: Boolean which indicates whether \code{bf} corresponds to the log Bayes factor. } } \description{ Generic function that computes Bayes factor(s) from marginal likelihoods. \code{bayes_factor()} is simply an (S3 generic) alias for \code{bf()}. } \details{ Computes the Bayes factor (Kass & Raftery, 1995) in favor of the model associated with \code{x1} over the model associated with \code{x2}. } \note{ For examples, see \code{\link{bridge_sampler}} and the accompanying vignettes: \cr \code{vignette("bridgesampling_example_jags")} \cr \code{vignette("bridgesampling_example_stan")} } \references{ Kass, R. E., & Raftery, A. E. (1995). Bayes factors. \emph{Journal of the American Statistical Association, 90(430)}, 773-795. \doi{10.1080/01621459.1995.10476572} } \author{ Quentin F. Gronau } bridgesampling/man/ier.Rd0000644000176200001440000001304715055304401015064 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/ier-data.R \docType{data} \encoding{UTF-8} \name{ier} \alias{ier} \title{Standardized International Exchange Rate Changes from 1975 to 1986} \format{ A matrix with 143 rows and 6 columns. } \source{ West, M., Harrison, J. (1997). \emph{Bayesian forecasting and dynamic models} (2nd ed.). Springer-Verlag, New York. Lopes, H. F., West, M. (2004). Bayesian model assessment in factor analysis. \emph{Statistica Sinica, 14}, 41-67. } \usage{ ier } \description{ This data set contains the changes in monthly international exchange rates for pounds sterling from January 1975 to December 1986 obtained from West and Harrison (1997, pp. 612-615). Currencies tracked are US Dollar (column \code{us_dollar}), Canadian Dollar (column \code{canadian_dollar}), Japanese Yen (column \code{yen}), French Franc (column \code{franc}), Italian Lira (column \code{lira}), and the (West) German Mark (column \code{mark}). Each series has been standardized with respect to its sample mean and standard deviation. } \examples{ \dontrun{ ################################################################################ # BAYESIAN FACTOR ANALYSIS (AS PROPOSED BY LOPES & WEST, 2004) ################################################################################ library(bridgesampling) library(rstan) cores <- 4 options(mc.cores = cores) data("ier") #------------------------------------------------------------------------------- # plot data #------------------------------------------------------------------------------- currency <- colnames(ier) label <- c("US Dollar", "Canadian Dollar", "Yen", "Franc", "Lira", "Mark") op <- par(mfrow = c(3, 2), mar = c(6, 6, 3, 3)) for (i in seq_along(currency)) { plot(ier[,currency[i]], type = "l", col = "darkblue", axes = FALSE, ylim = c(-4, 4), ylab = "", xlab = "", lwd = 2) axis(1, at = 0:12*12, labels = 1975:1987, cex.axis = 1.7) axis(2, at = pretty(c(-4, 4)), las = 1, cex.axis = 1.7) mtext("Year", 1, cex = 1.5, line = 3.2) mtext("Exchange Rate Changes", 2, cex = 1.4, line = 3.2) mtext(label[i], 3, cex = 1.6, line = .1) } par(op) #------------------------------------------------------------------------------- # stan model #------------------------------------------------------------------------------- model_code <- "data { int T; // number of observations int m; // number of variables int k; // number of factors matrix[T,m] Y; // data matrix } transformed data { int r; vector[m] zeros; r = m * k - k * (k - 1) / 2; // number of non-zero factor loadings zeros = rep_vector(0.0, m); } parameters { real beta_lower[r - k]; // lower-diagonal elements of beta real beta_diag [k]; // diagonal elements of beta vector[m] sigma2; // residual variances } transformed parameters { matrix[m,k] beta; cov_matrix[m] Omega; // construct lower-triangular factor loadings matrix { int index_lower = 1; for (j in 1:k) { for (i in 1:m) { if (i == j) { beta[j,j] = beta_diag[j]; } else if (i >= j) { beta[i,j] = beta_lower[index_lower]; index_lower = index_lower + 1; } else { beta[i,j] = 0.0; } } } } Omega = beta * beta' + diag_matrix(sigma2); } model { // priors target += normal_lpdf(beta_diag | 0, 1) - k * normal_lccdf(0 | 0, 1); target += normal_lpdf(beta_lower | 0, 1); target += inv_gamma_lpdf(sigma2 | 2.2 / 2.0, 0.1 / 2.0); // likelihood for(t in 1:T) { target += multi_normal_lpdf(Y[t] | zeros, Omega); } }" # compile model model <- stan_model(model_code = model_code) #------------------------------------------------------------------------------- # fit models and compute log marginal likelihoods #------------------------------------------------------------------------------- # function for generating starting values init_fun <- function(nchains, k, m) { r <- m * k - k * (k - 1) / 2 out <- vector("list", nchains) for (i in seq_len(nchains)) { beta_lower <- array(runif(r - k, 0.05, 1), dim = r - k) beta_diag <- array(runif(k, .05, 1), dim = k) sigma2 <- array(runif(m, .05, 1.5), dim = m) out[[i]] <- list(beta_lower = beta_lower, beta_diag = beta_diag, sigma2 = sigma2) } return(out) } set.seed(1) stanfit <- bridge <- vector("list", 3) for (k in 1:3) { stanfit[[k]] <- sampling(model, data = list(Y = ier, T = nrow(ier), m = ncol(ier), k = k), iter = 11000, warmup = 1000, chains = 4, init = init_fun(nchains = 4, k = k, m = ncol(ier)), cores = cores, seed = 1) bridge[[k]] <- bridge_sampler(stanfit[[k]], method = "warp3", repetitions = 10, cores = cores) } # example output summary(bridge[[2]]) #------------------------------------------------------------------------------- # compute posterior model probabilities #------------------------------------------------------------------------------- pp <- post_prob(bridge[[1]], bridge[[2]], bridge[[3]], model_names = c("k = 1", "k = 2", "k = 3")) pp op <- par(mar = c(6, 6, 3, 3)) boxplot(pp, axes = FALSE, ylim = c(0, 1), ylab = "", xlab = "") axis(1, at = 1:3, labels = colnames(pp), cex.axis = 1.7) axis(2, cex.axis = 1.1) mtext("Posterior Model Probability", 2, cex = 1.5, line = 3.2) mtext("Number of Factors", 1, cex = 1.4, line = 3.2) par(op) } } \keyword{dataset} bridgesampling/man/turtles.Rd0000644000176200001440000001154415055304401016007 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/turtles-data.R \docType{data} \encoding{UTF-8} \name{turtles} \alias{turtles} \title{Turtles Data from Janzen, Tucker, and Paukstis (2000)} \format{ A data.frame with 244 rows and 3 variables. } \source{ Janzen, F. J., Tucker, J. K., & Paukstis, G. L. (2000). Experimental analysis of an early life-history stage: Selection on size of hatchling turtles. \emph{Ecology, 81(8)}, 2290-2304. \doi{10.2307/177115} Overstall, A. M., & Forster, J. J. (2010). Default Bayesian model determination methods for generalised linear mixed models. \emph{Computational Statistics & Data Analysis, 54}, 3269-3288. \doi{10.1016/j.csda.2010.03.008} Sinharay, S., & Stern, H. S. (2005). An empirical comparison of methods for computing Bayes factors in generalized linear mixed models. \emph{Journal of Computational and Graphical Statistics, 14(2)}, 415-435. \doi{10.1198/106186005X47471} } \usage{ turtles } \description{ This data set contains information about 244 newborn turtles from 31 different clutches. For each turtle, the data set includes information about survival status (column \code{y}; 0 = died, 1 = survived), birth weight in grams (column \code{x}), and clutch (family) membership (column \code{clutch}; an integer between one and 31). The clutches have been ordered according to mean birth weight. } \examples{ \dontrun{ ################################################################################ # BAYESIAN GENERALIZED LINEAR MIXED MODEL (PROBIT REGRESSION) ################################################################################ library(bridgesampling) library(rstan) data("turtles") #------------------------------------------------------------------------------- # plot data #------------------------------------------------------------------------------- # reproduce Figure 1 from Sinharay & Stern (2005) xticks <- pretty(turtles$clutch) yticks <- pretty(turtles$x) plot(1, type = "n", axes = FALSE, ylab = "", xlab = "", xlim = range(xticks), ylim = range(yticks)) points(turtles$clutch, turtles$x, pch = ifelse(turtles$y, 21, 4), cex = 1.3, col = ifelse(turtles$y, "black", "darkred"), bg = "grey", lwd = 1.3) axis(1, cex.axis = 1.4) mtext("Clutch Identifier", side = 1, line = 2.9, cex = 1.8) axis(2, las = 1, cex.axis = 1.4) mtext("Birth Weight (Grams)", side = 2, line = 2.6, cex = 1.8) #------------------------------------------------------------------------------- # Analysis: Natural Selection Study (compute same BF as Sinharay & Stern, 2005) #------------------------------------------------------------------------------- ### H0 (model without random intercepts) ### H0_code <- "data { int N; int y[N]; real x[N]; } parameters { real alpha0_raw; real alpha1_raw; } transformed parameters { real alpha0 = sqrt(10.0) * alpha0_raw; real alpha1 = sqrt(10.0) * alpha1_raw; } model { // priors target += normal_lpdf(alpha0_raw | 0, 1); target += normal_lpdf(alpha1_raw | 0, 1); // likelihood for (i in 1:N) { target += bernoulli_lpmf(y[i] | Phi(alpha0 + alpha1 * x[i])); } }" ### H1 (model with random intercepts) ### H1_code <- "data { int N; int y[N]; real x[N]; int C; int clutch[N]; } parameters { real alpha0_raw; real alpha1_raw; vector[C] b_raw; real sigma2; } transformed parameters { vector[C] b; real sigma = sqrt(sigma2); real alpha0 = sqrt(10.0) * alpha0_raw; real alpha1 = sqrt(10.0) * alpha1_raw; b = sigma * b_raw; } model { // priors target += - 2 * log(1 + sigma2); // p(sigma2) = 1 / (1 + sigma2) ^ 2 target += normal_lpdf(alpha0_raw | 0, 1); target += normal_lpdf(alpha1_raw | 0, 1); // random effects target += normal_lpdf(b_raw | 0, 1); // likelihood for (i in 1:N) { target += bernoulli_lpmf(y[i] | Phi(alpha0 + alpha1 * x[i] + b[clutch[i]])); } }" set.seed(1) ### fit models ### stanfit_H0 <- stan(model_code = H0_code, data = list(y = turtles$y, x = turtles$x, N = nrow(turtles)), iter = 15500, warmup = 500, chains = 4, seed = 1) stanfit_H1 <- stan(model_code = H1_code, data = list(y = turtles$y, x = turtles$x, N = nrow(turtles), C = max(turtles$clutch), clutch = turtles$clutch), iter = 15500, warmup = 500, chains = 4, seed = 1) set.seed(1) ### compute (log) marginal likelihoods ### bridge_H0 <- bridge_sampler(stanfit_H0) bridge_H1 <- bridge_sampler(stanfit_H1) ### compute approximate percentage errors ### error_measures(bridge_H0)$percentage error_measures(bridge_H1)$percentage ### summary ### summary(bridge_H0) summary(bridge_H1) ### compute Bayes factor ("true" value: BF01 = 1.273) ### bf(bridge_H0, bridge_H1) } } \keyword{dataset} bridgesampling/man/post_prob.Rd0000644000176200001440000000763615055304401016323 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/post_prob.R \name{post_prob} \alias{post_prob} \alias{post_prob.bridge} \alias{post_prob.bridge_list} \alias{post_prob.default} \title{Posterior Model Probabilities from Marginal Likelihoods} \usage{ post_prob(x, ..., prior_prob = NULL, model_names = NULL) \method{post_prob}{bridge}(x, ..., prior_prob = NULL, model_names = NULL) \method{post_prob}{bridge_list}(x, ..., prior_prob = NULL, model_names = NULL) \method{post_prob}{default}(x, ..., prior_prob = NULL, model_names = NULL) } \arguments{ \item{x}{Object of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. Additionally, the default method assumes that all passed objects are numeric log marginal likelihoods (e.g., from \code{\link{logml}}) and will throw an error otherwise.} \item{...}{further objects of class \code{"bridge"} or \code{"bridge_list"} as returned from \code{\link{bridge_sampler}}. Or numeric values for the default method.} \item{prior_prob}{numeric vector with prior model probabilities. If omitted, a uniform prior is used (i.e., all models are equally likely a priori). The default \code{NULL} corresponds to equal prior model weights.} \item{model_names}{If \code{NULL} (the default) will use model names derived from deparsing the call. Otherwise will use the passed values as model names.} } \value{ For the default method and the method for \code{"bridge"} objects, a named numeric vector with posterior model probabilities (i.e., which sum to one). For the method for \code{"bridge_list"} objects, a matrix consisting of posterior model probabilities where each row sums to one and gives the model probabilities for one set of logmls. The (named) columns correspond to the models and the number of rows is given by the \code{"bridge_list"} element with the most \code{repetitions}. Elements with fewer repetitions will be recycled (with warning). } \description{ Generic function that computes posterior model probabilities from marginal likelihoods. } \note{ For realistic examples, see \code{\link{bridge_sampler}} and the accompanying vignettes: \cr \code{vignette("bridgesampling_example_jags")} \cr \code{vignette("bridgesampling_example_stan")} } \examples{ H0 <- structure(list(logml = -20.8084543022433, niter = 4, method = "normal"), .Names = c("logml", "niter", "method"), class = "bridge") H1 <- structure(list(logml = -17.9623077558729, niter = 4, method = "normal"), .Names = c("logml", "niter", "method"), class = "bridge") H2 <- structure(list(logml = -19, niter = 4, method = "normal"), .Names = c("logml", "niter", "method"), class = "bridge") post_prob(H0, H1, H2) post_prob(H1, H0) ## all produce the same (only names differ): post_prob(H0, H1, H2) post_prob(H0$logml, H1$logml, H2$logml) post_prob(c(H0$logml, H1$logml, H2$logml)) post_prob(H0$logml, c(H1$logml, H2$logml)) post_prob(H0$logml, c(H1$logml, H2$logml), model_names = c("H0", "H1", "H2")) ### with bridge list elements: H0L <- structure(list(logml = c(-20.8088381186739, -20.8072772698116, -20.808454454621, -20.8083419072281, -20.8087870541247, -20.8084887398113, -20.8086023582344, -20.8079083169745, -20.8083048489095, -20.8090050811436 ), niter = c(4, 4, 4, 4, 4, 4, 4, 4, 4, 4), method = "normal", repetitions = 10), .Names = c("logml", "niter", "method", "repetitions"), class = "bridge_list") H1L <- structure(list(logml = c(-17.961665507006, -17.9611290723151, -17.9607509604499, -17.9608629535992, -17.9602093576442, -17.9600223300432, -17.9610157118017, -17.9615557696561, -17.9608437034849, -17.9606743200309 ), niter = c(4, 4, 4, 4, 4, 4, 4, 4, 3, 4), method = "normal", repetitions = 10), .Names = c("logml", "niter", "method", "repetitions"), class = "bridge_list") post_prob(H1L, H0L) post_prob(H1L, H0L, H0) # last element recycled with warning. } \author{ Quentin F. Gronau and Henrik Singmann } bridgesampling/DESCRIPTION0000644000176200001440000000472415107257542014766 0ustar liggesusersPackage: bridgesampling Type: Package Title: Bridge Sampling for Marginal Likelihoods and Bayes Factors Version: 1.2-1 Authors@R: c(person(given="Quentin F.", family="Gronau", role=c("aut", "cre"), email="Quentin.F.Gronau@gmail.com", comment=c(ORCID="0000-0001-5510-6943")), person(given="Henrik", family="Singmann", role="aut", comment=c(ORCID="0000-0002-4842-3657")), person(given="Jonathan J.", family="Forster", role="ctb"), person(given="Eric-Jan", family="Wagenmakers", role="ths"), person(family="The JASP Team", role="ctb"), person("Jiqiang", "Guo", role = "ctb"), person("Jonah", "Gabry", role = "ctb"), person("Ben", "Goodrich", role = c("ctb")), person("Kees", "Mulder", role = c("ctb")), person("Perry", "de Valpine", role = c("ctb")), person(given="Aki", family="Vehtari", role = c("ctb")), person(given="Giorgio", family="Micaletto", role = c("ctb")) ) Depends: R (>= 3.0.0) Imports: mvtnorm, Matrix, Brobdingnag, stringr, coda, parallel, scales, utils, methods Suggests: testthat, Rcpp, RcppEigen, R2jags, rjags, runjags, knitr, rmarkdown, R.rsp, BayesFactor, rstan, rstanarm, nimble, MCMCpack, cmdstanr (>= 0.6.0) Description: Provides functions for estimating marginal likelihoods, Bayes factors, posterior model probabilities, and normalizing constants in general, via different versions of bridge sampling (Meng & Wong, 1996, ). Gronau, Singmann, & Wagenmakers (2020) . Additional_repositories: https://stan-dev.r-universe.dev/ License: GPL (>= 2) LazyData: true RoxygenNote: 7.3.3 Encoding: UTF-8 VignetteBuilder: knitr, R.rsp URL: https://github.com/quentingronau/bridgesampling NeedsCompilation: no Packaged: 2025-11-18 11:10:07 UTC; singmann Author: Quentin F. Gronau [aut, cre] (ORCID: ), Henrik Singmann [aut] (ORCID: ), Jonathan J. Forster [ctb], Eric-Jan Wagenmakers [ths], The JASP Team [ctb], Jiqiang Guo [ctb], Jonah Gabry [ctb], Ben Goodrich [ctb], Kees Mulder [ctb], Perry de Valpine [ctb], Aki Vehtari [ctb], Giorgio Micaletto [ctb] Maintainer: Quentin F. Gronau Repository: CRAN Date/Publication: 2025-11-19 06:10:42 UTC