From 838022094d9562e60fc476f5fbd20c3cf2b4b77f Mon Sep 17 00:00:00 2001 From: markean Date: Fri, 19 Jan 2024 20:33:33 -0500 Subject: [PATCH] kl retel_r code and results added --- DESCRIPTION | 2 +- retel-paper/code/simulations/kl/retel_r/n10.R | 201 ++++++++++++++++++ retel-paper/code/simulations/kl/retel_r/n2.R | 201 ++++++++++++++++++ retel-paper/code/simulations/kl/retel_r/n4.R | 201 ++++++++++++++++++ retel-paper/code/simulations/kl/retel_r/n6.R | 201 ++++++++++++++++++ retel-paper/code/simulations/kl/retel_r/n8.R | 201 ++++++++++++++++++ retel-paper/simulations/kl/retel_r/n10.rds | Bin 0 -> 36913 bytes retel-paper/simulations/kl/retel_r/n10.txt | 9 + retel-paper/simulations/kl/retel_r/n2.rds | Bin 0 -> 36421 bytes retel-paper/simulations/kl/retel_r/n2.txt | 9 + retel-paper/simulations/kl/retel_r/n4.rds | Bin 0 -> 36510 bytes retel-paper/simulations/kl/retel_r/n4.txt | 9 + retel-paper/simulations/kl/retel_r/n6.rds | Bin 0 -> 36717 bytes retel-paper/simulations/kl/retel_r/n6.txt | 9 + retel-paper/simulations/kl/retel_r/n8.rds | Bin 0 -> 36777 bytes retel-paper/simulations/kl/retel_r/n8.txt | 9 + 16 files changed, 1051 insertions(+), 1 deletion(-) create mode 100644 retel-paper/code/simulations/kl/retel_r/n10.R create mode 100644 retel-paper/code/simulations/kl/retel_r/n2.R create mode 100644 retel-paper/code/simulations/kl/retel_r/n4.R create mode 100644 retel-paper/code/simulations/kl/retel_r/n6.R create mode 100644 retel-paper/code/simulations/kl/retel_r/n8.R create mode 100644 retel-paper/simulations/kl/retel_r/n10.rds create mode 100644 retel-paper/simulations/kl/retel_r/n10.txt create mode 100644 retel-paper/simulations/kl/retel_r/n2.rds create mode 100644 retel-paper/simulations/kl/retel_r/n2.txt create mode 100644 retel-paper/simulations/kl/retel_r/n4.rds create mode 100644 retel-paper/simulations/kl/retel_r/n4.txt create mode 100644 retel-paper/simulations/kl/retel_r/n6.rds create mode 100644 retel-paper/simulations/kl/retel_r/n6.txt create mode 100644 retel-paper/simulations/kl/retel_r/n8.rds create mode 100644 retel-paper/simulations/kl/retel_r/n8.txt diff --git a/DESCRIPTION b/DESCRIPTION index 6d4efa9..b7971cd 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Package: retel Type: Package Title: Regularized Exponentially Tilted Empirical Likelihood -Version: 0.0.0.9604 +Version: 0.0.0.9605 Authors@R: c( person("Eunseop", "Kim", email = "markean@pm.me", role = c("aut", "cre")), diff --git a/retel-paper/code/simulations/kl/retel_r/n10.R b/retel-paper/code/simulations/kl/retel_r/n10.R new file mode 100644 index 0000000..d7f2c43 --- /dev/null +++ b/retel-paper/code/simulations/kl/retel_r/n10.R @@ -0,0 +1,201 @@ +## 1. Load packages +options(warn = -1) +options(scipen = 999) +library(coda) +suppressMessages(library(doParallel)) # parallel backend +suppressMessages(library(doRNG)) # reproducible parallel loop +library(mvtnorm) +library(retel) + + +## 2. Parameters +# Sample size for each group +n <- 10L + + +## 3. Constants +# Tau +tau <- log(n) +# Standard deviation of prior +sd_mu <- 10 +# Simulation replications +S <- 1e+03L +# MCMC parameters +B <- 5000L + + +## 4. Functions +f <- function(x, par) { + x - par +} +# Prior and posterior computation +log_prior <- function(mu, theta) { + dnorm(mu, mean = 0, sd = sd_mu, log = TRUE) - + sum(log(pi * (1 + (theta - mu)^2L))) +} +loglr <- function(theta, x1, x2) { + retel(f, x1, theta[1L], mean(x1) - theta[1L], 1, tau, "reduced") + + retel(f, x2, theta[2L], mean(x2) - theta[2L], 1, tau, "reduced") +} +log_posterior_unnormalized <- function(mu_p, theta, x1, x2) { + log_prior(mu_p, theta) + loglr(theta, x1, x2) +} + + +## 5. Simulations +cat("< Method = RETEL_r>\n") +cat("< Simulation replications =", S, ">\n") +cat("< MCMC runs =", 2L * B, ">\n") +cat("< n =", n, ">\n") +set.seed(12542) +cl <- makeCluster(24L) +registerDoParallel(cl) +result <- foreach( + i = icount(S), .combine = "rbind", .inorder = FALSE, + .packages = c("coda", "mvtnorm", "retel") +) %dorng% { + # Generate data + x1 <- rnorm(n, mean = -3, sd = 1) + x2 <- rnorm(n, mean = 3, sd = 1) + + # MCMC chain 1 + mu_sample1 <- vector("numeric", length = B) + mu_sample1[1L] <- rnorm(1L) + theta_sample1 <- matrix(nrow = B, ncol = 2L) + theta_sample1[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace1 <- vector("logical", length = B) + acceptace1[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample1[i - 1L], theta_sample1[i - 1L, ]), + sigma = c(1, 0.3, 0.3) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample1[i - 1L], theta_sample1[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample1[i] <- mu_p + theta_sample1[i, ] <- theta_p + acceptace1[i] <- TRUE + } else { + mu_sample1[i] <- mu_sample1[i - 1L] + theta_sample1[i, ] <- theta_sample1[i - 1L, ] + acceptace1[i] <- FALSE + } + } + + # MCMC chain 2 + mu_sample2 <- vector("numeric", length = B) + mu_sample2[1L] <- rnorm(1L) + theta_sample2 <- matrix(nrow = B, ncol = 2L) + theta_sample2[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace2 <- vector("logical", length = B) + acceptace2[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample2[i - 1L], theta_sample2[i - 1L, ]), + sigma = c(1, 0.3, 0.3) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample2[i - 1L], theta_sample2[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample2[i] <- mu_p + theta_sample2[i, ] <- theta_p + acceptace2[i] <- TRUE + } else { + mu_sample2[i] <- mu_sample2[i - 1L] + theta_sample2[i, ] <- theta_sample2[i - 1L, ] + acceptace2[i] <- FALSE + } + } + + # KL divergence + df <- data.frame( + index = seq_len(2L * B), mu = c(mu_sample1, mu_sample2), + theta1 = c(theta_sample1[, 1L], theta_sample2[, 1L]), + theta2 = c(theta_sample1[, 2L], theta_sample2[, 2L]), + acceptace = c(acceptace1, acceptace2), + chain = rep(c(1L, 2L), each = B) + ) + pd <- density(df$mu) + pd_estimate <- approxfun(pd$x, pd$y, + yleft = .Machine$double.eps, + yright = .Machine$double.eps + ) + integrand <- function(x) { + pd_estimate(x) * { + log(pd_estimate(x)) - dnorm(x, mean = 0, sd = sd_mu, log = TRUE) + } + } + kl <- tryCatch(integrate(integrand, lower = -Inf, upper = Inf)$value, + warning = \(x) NA, error = \(x) NA + ) + # Compute KL by taking the average when integration does not work + if (is.na(kl)) { + kl <- mean( + log(pd_estimate(df$mu)) - dnorm(df$mu, mean = 0, sd = sd_mu, log = TRUE) + ) + } + # Potential scale reduction factors + mu_c1 <- mcmc(df$mu[seq_len(B)]) + mu_c2 <- mcmc(df$mu[seq(B + 1L, 2L * B)]) + theta1_c1 <- mcmc(df$theta1[seq_len(B)]) + theta1_c2 <- mcmc(df$theta1[seq(B + 1L, 2L * B)]) + theta2_c1 <- mcmc(df$theta2[seq_len(B)]) + theta2_c2 <- mcmc(df$theta2[seq(B + 1L, 2L * B)]) + theta1_psrf <- gelman.diag(mcmc.list(theta1_c1, theta1_c2))$psrf[1L] + mu_psrf <- gelman.diag(mcmc.list(mu_c1, mu_c2))$psrf[1L] + theta2_psrf <- gelman.diag(mcmc.list(theta2_c1, theta2_c2))$psrf[1L] + + c(kl, mu_psrf, theta1_psrf, theta2_psrf, mean(df$acceptace)) +} +stopCluster(cl) + + +## 6. Results +colnames(result) <- + c("kl", "mu_psrf", "theta1_psrf", "theta2_psrf", "acceptace") +# Remove invalid values +result <- result[is.finite(result[, "mu_psrf"]), ] +cat("Expected KL: ", + mean(result[, "kl"], na.rm = TRUE), " (", + round(sd(result[, "kl"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("mu psrf: ", + mean(result[, "mu_psrf"], na.rm = TRUE), " (", + round(sd(result[, "mu_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta1 psrf: ", + mean(result[, "theta1_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta1_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta2 psrf: ", + mean(result[, "theta2_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta2_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("Acceptance rate: ", + mean(result[, "acceptace"], na.rm = TRUE), " (", + round(sd(result[, "acceptace"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) diff --git a/retel-paper/code/simulations/kl/retel_r/n2.R b/retel-paper/code/simulations/kl/retel_r/n2.R new file mode 100644 index 0000000..33118d8 --- /dev/null +++ b/retel-paper/code/simulations/kl/retel_r/n2.R @@ -0,0 +1,201 @@ +## 1. Load packages +options(warn = -1) +options(scipen = 999) +library(coda) +suppressMessages(library(doParallel)) # parallel backend +suppressMessages(library(doRNG)) # reproducible parallel loop +library(mvtnorm) +library(retel) + + +## 2. Parameters +# Sample size for each group +n <- 2L + + +## 3. Constants +# Tau +tau <- 1 +# Standard deviation of prior +sd_mu <- 10 +# Simulation replications +S <- 1e+03L +# MCMC parameters +B <- 5000L + + +## 4. Functions +f <- function(x, par) { + x - par +} +# Prior and posterior computation +log_prior <- function(mu, theta) { + dnorm(mu, mean = 0, sd = sd_mu, log = TRUE) - + sum(log(pi * (1 + (theta - mu)^2L))) +} +loglr <- function(theta, x1, x2) { + retel(f, x1, theta[1L], mean(x1) - theta[1L], 1, tau, "reduced") + + retel(f, x2, theta[2L], mean(x2) - theta[2L], 1, tau, "reduced") +} +log_posterior_unnormalized <- function(mu_p, theta, x1, x2) { + log_prior(mu_p, theta) + loglr(theta, x1, x2) +} + + +## 5. Simulations +cat("< Method = RETEL_r>\n") +cat("< Simulation replications =", S, ">\n") +cat("< MCMC runs =", 2L * B, ">\n") +cat("< n =", n, ">\n") +set.seed(12542) +cl <- makeCluster(24L) +registerDoParallel(cl) +result <- foreach( + i = icount(S), .combine = "rbind", .inorder = FALSE, + .packages = c("coda", "mvtnorm", "retel") +) %dorng% { + # Generate data + x1 <- rnorm(n, mean = -3, sd = 1) + x2 <- rnorm(n, mean = 3, sd = 1) + + # MCMC chain 1 + mu_sample1 <- vector("numeric", length = B) + mu_sample1[1L] <- rnorm(1L) + theta_sample1 <- matrix(nrow = B, ncol = 2L) + theta_sample1[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace1 <- vector("logical", length = B) + acceptace1[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample1[i - 1L], theta_sample1[i - 1L, ]), + sigma = c(10, 1, 1) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample1[i - 1L], theta_sample1[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample1[i] <- mu_p + theta_sample1[i, ] <- theta_p + acceptace1[i] <- TRUE + } else { + mu_sample1[i] <- mu_sample1[i - 1L] + theta_sample1[i, ] <- theta_sample1[i - 1L, ] + acceptace1[i] <- FALSE + } + } + + # MCMC chain 2 + mu_sample2 <- vector("numeric", length = B) + mu_sample2[1L] <- rnorm(1L) + theta_sample2 <- matrix(nrow = B, ncol = 2L) + theta_sample2[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace2 <- vector("logical", length = B) + acceptace2[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample2[i - 1L], theta_sample2[i - 1L, ]), + sigma = c(10, 1, 1) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample2[i - 1L], theta_sample2[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample2[i] <- mu_p + theta_sample2[i, ] <- theta_p + acceptace2[i] <- TRUE + } else { + mu_sample2[i] <- mu_sample2[i - 1L] + theta_sample2[i, ] <- theta_sample2[i - 1L, ] + acceptace2[i] <- FALSE + } + } + + # KL divergence + df <- data.frame( + index = seq_len(2L * B), mu = c(mu_sample1, mu_sample2), + theta1 = c(theta_sample1[, 1L], theta_sample2[, 1L]), + theta2 = c(theta_sample1[, 2L], theta_sample2[, 2L]), + acceptace = c(acceptace1, acceptace2), + chain = rep(c(1L, 2L), each = B) + ) + pd <- density(df$mu) + pd_estimate <- approxfun(pd$x, pd$y, + yleft = .Machine$double.eps, + yright = .Machine$double.eps + ) + integrand <- function(x) { + pd_estimate(x) * { + log(pd_estimate(x)) - dnorm(x, mean = 0, sd = sd_mu, log = TRUE) + } + } + kl <- tryCatch(integrate(integrand, lower = -Inf, upper = Inf)$value, + warning = \(x) NA, error = \(x) NA + ) + # Compute KL by taking the average when integration does not work + if (is.na(kl)) { + kl <- mean( + log(pd_estimate(df$mu)) - dnorm(df$mu, mean = 0, sd = sd_mu, log = TRUE) + ) + } + # Potential scale reduction factors + mu_c1 <- mcmc(df$mu[seq_len(B)]) + mu_c2 <- mcmc(df$mu[seq(B + 1L, 2L * B)]) + theta1_c1 <- mcmc(df$theta1[seq_len(B)]) + theta1_c2 <- mcmc(df$theta1[seq(B + 1L, 2L * B)]) + theta2_c1 <- mcmc(df$theta2[seq_len(B)]) + theta2_c2 <- mcmc(df$theta2[seq(B + 1L, 2L * B)]) + theta1_psrf <- gelman.diag(mcmc.list(theta1_c1, theta1_c2))$psrf[1L] + mu_psrf <- gelman.diag(mcmc.list(mu_c1, mu_c2))$psrf[1L] + theta2_psrf <- gelman.diag(mcmc.list(theta2_c1, theta2_c2))$psrf[1L] + + c(kl, mu_psrf, theta1_psrf, theta2_psrf, mean(df$acceptace)) +} +stopCluster(cl) + + +## 6. Results +colnames(result) <- + c("kl", "mu_psrf", "theta1_psrf", "theta2_psrf", "acceptace") +# Remove invalid values +result <- result[is.finite(result[, "mu_psrf"]), ] +cat("Expected KL: ", + mean(result[, "kl"], na.rm = TRUE), " (", + round(sd(result[, "kl"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("mu psrf: ", + mean(result[, "mu_psrf"], na.rm = TRUE), " (", + round(sd(result[, "mu_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta1 psrf: ", + mean(result[, "theta1_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta1_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta2 psrf: ", + mean(result[, "theta2_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta2_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("Acceptance rate: ", + mean(result[, "acceptace"], na.rm = TRUE), " (", + round(sd(result[, "acceptace"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) diff --git a/retel-paper/code/simulations/kl/retel_r/n4.R b/retel-paper/code/simulations/kl/retel_r/n4.R new file mode 100644 index 0000000..4c4cafd --- /dev/null +++ b/retel-paper/code/simulations/kl/retel_r/n4.R @@ -0,0 +1,201 @@ +## 1. Load packages +options(warn = -1) +options(scipen = 999) +library(coda) +suppressMessages(library(doParallel)) # parallel backend +suppressMessages(library(doRNG)) # reproducible parallel loop +library(mvtnorm) +library(retel) + + +## 2. Parameters +# Sample size for each group +n <- 4L + + +## 3. Constants +# Tau +tau <- log(n) +# Standard deviation of prior +sd_mu <- 10 +# Simulation replications +S <- 1e+03L +# MCMC parameters +B <- 5000L + + +## 4. Functions +f <- function(x, par) { + x - par +} +# Prior and posterior computation +log_prior <- function(mu, theta) { + dnorm(mu, mean = 0, sd = sd_mu, log = TRUE) - + sum(log(pi * (1 + (theta - mu)^2L))) +} +loglr <- function(theta, x1, x2) { + retel(f, x1, theta[1L], mean(x1) - theta[1L], 1, tau, "reduced") + + retel(f, x2, theta[2L], mean(x2) - theta[2L], 1, tau, "reduced") +} +log_posterior_unnormalized <- function(mu_p, theta, x1, x2) { + log_prior(mu_p, theta) + loglr(theta, x1, x2) +} + + +## 5. Simulations +cat("< Method = RETEL_r>\n") +cat("< Simulation replications =", S, ">\n") +cat("< MCMC runs =", 2L * B, ">\n") +cat("< n =", n, ">\n") +set.seed(12542) +cl <- makeCluster(24L) +registerDoParallel(cl) +result <- foreach( + i = icount(S), .combine = "rbind", .inorder = FALSE, + .packages = c("coda", "mvtnorm", "retel") +) %dorng% { + # Generate data + x1 <- rnorm(n, mean = -3, sd = 1) + x2 <- rnorm(n, mean = 3, sd = 1) + + # MCMC chain 1 + mu_sample1 <- vector("numeric", length = B) + mu_sample1[1L] <- rnorm(1L) + theta_sample1 <- matrix(nrow = B, ncol = 2L) + theta_sample1[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace1 <- vector("logical", length = B) + acceptace1[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample1[i - 1L], theta_sample1[i - 1L, ]), + sigma = c(4, 1, 1) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample1[i - 1L], theta_sample1[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample1[i] <- mu_p + theta_sample1[i, ] <- theta_p + acceptace1[i] <- TRUE + } else { + mu_sample1[i] <- mu_sample1[i - 1L] + theta_sample1[i, ] <- theta_sample1[i - 1L, ] + acceptace1[i] <- FALSE + } + } + + # MCMC chain 2 + mu_sample2 <- vector("numeric", length = B) + mu_sample2[1L] <- rnorm(1L) + theta_sample2 <- matrix(nrow = B, ncol = 2L) + theta_sample2[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace2 <- vector("logical", length = B) + acceptace2[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample2[i - 1L], theta_sample2[i - 1L, ]), + sigma = c(4, 1, 1) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample2[i - 1L], theta_sample2[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample2[i] <- mu_p + theta_sample2[i, ] <- theta_p + acceptace2[i] <- TRUE + } else { + mu_sample2[i] <- mu_sample2[i - 1L] + theta_sample2[i, ] <- theta_sample2[i - 1L, ] + acceptace2[i] <- FALSE + } + } + + # KL divergence + df <- data.frame( + index = seq_len(2L * B), mu = c(mu_sample1, mu_sample2), + theta1 = c(theta_sample1[, 1L], theta_sample2[, 1L]), + theta2 = c(theta_sample1[, 2L], theta_sample2[, 2L]), + acceptace = c(acceptace1, acceptace2), + chain = rep(c(1L, 2L), each = B) + ) + pd <- density(df$mu) + pd_estimate <- approxfun(pd$x, pd$y, + yleft = .Machine$double.eps, + yright = .Machine$double.eps + ) + integrand <- function(x) { + pd_estimate(x) * { + log(pd_estimate(x)) - dnorm(x, mean = 0, sd = sd_mu, log = TRUE) + } + } + kl <- tryCatch(integrate(integrand, lower = -Inf, upper = Inf)$value, + warning = \(x) NA, error = \(x) NA + ) + # Compute KL by taking the average when integration does not work + if (is.na(kl)) { + kl <- mean( + log(pd_estimate(df$mu)) - dnorm(df$mu, mean = 0, sd = sd_mu, log = TRUE) + ) + } + # Potential scale reduction factors + mu_c1 <- mcmc(df$mu[seq_len(B)]) + mu_c2 <- mcmc(df$mu[seq(B + 1L, 2L * B)]) + theta1_c1 <- mcmc(df$theta1[seq_len(B)]) + theta1_c2 <- mcmc(df$theta1[seq(B + 1L, 2L * B)]) + theta2_c1 <- mcmc(df$theta2[seq_len(B)]) + theta2_c2 <- mcmc(df$theta2[seq(B + 1L, 2L * B)]) + theta1_psrf <- gelman.diag(mcmc.list(theta1_c1, theta1_c2))$psrf[1L] + mu_psrf <- gelman.diag(mcmc.list(mu_c1, mu_c2))$psrf[1L] + theta2_psrf <- gelman.diag(mcmc.list(theta2_c1, theta2_c2))$psrf[1L] + + c(kl, mu_psrf, theta1_psrf, theta2_psrf, mean(df$acceptace)) +} +stopCluster(cl) + + +## 6. Results +colnames(result) <- + c("kl", "mu_psrf", "theta1_psrf", "theta2_psrf", "acceptace") +# Remove invalid values +result <- result[is.finite(result[, "mu_psrf"]), ] +cat("Expected KL: ", + mean(result[, "kl"], na.rm = TRUE), " (", + round(sd(result[, "kl"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("mu psrf: ", + mean(result[, "mu_psrf"], na.rm = TRUE), " (", + round(sd(result[, "mu_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta1 psrf: ", + mean(result[, "theta1_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta1_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta2 psrf: ", + mean(result[, "theta2_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta2_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("Acceptance rate: ", + mean(result[, "acceptace"], na.rm = TRUE), " (", + round(sd(result[, "acceptace"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) diff --git a/retel-paper/code/simulations/kl/retel_r/n6.R b/retel-paper/code/simulations/kl/retel_r/n6.R new file mode 100644 index 0000000..72d4f86 --- /dev/null +++ b/retel-paper/code/simulations/kl/retel_r/n6.R @@ -0,0 +1,201 @@ +## 1. Load packages +options(warn = -1) +options(scipen = 999) +library(coda) +suppressMessages(library(doParallel)) # parallel backend +suppressMessages(library(doRNG)) # reproducible parallel loop +library(mvtnorm) +library(retel) + + +## 2. Parameters +# Sample size for each group +n <- 6L + + +## 3. Constants +# Tau +tau <- log(n) +# Standard deviation of prior +sd_mu <- 10 +# Simulation replications +S <- 1e+03L +# MCMC parameters +B <- 5000L + + +## 4. Functions +f <- function(x, par) { + x - par +} +# Prior and posterior computation +log_prior <- function(mu, theta) { + dnorm(mu, mean = 0, sd = sd_mu, log = TRUE) - + sum(log(pi * (1 + (theta - mu)^2L))) +} +loglr <- function(theta, x1, x2) { + retel(f, x1, theta[1L], mean(x1) - theta[1L], 1, tau, "reduced") + + retel(f, x2, theta[2L], mean(x2) - theta[2L], 1, tau, "reduced") +} +log_posterior_unnormalized <- function(mu_p, theta, x1, x2) { + log_prior(mu_p, theta) + loglr(theta, x1, x2) +} + + +## 5. Simulations +cat("< Method = RETEL_r>\n") +cat("< Simulation replications =", S, ">\n") +cat("< MCMC runs =", 2L * B, ">\n") +cat("< n =", n, ">\n") +set.seed(12542) +cl <- makeCluster(24L) +registerDoParallel(cl) +result <- foreach( + i = icount(S), .combine = "rbind", .inorder = FALSE, + .packages = c("coda", "mvtnorm", "retel") +) %dorng% { + # Generate data + x1 <- rnorm(n, mean = -3, sd = 1) + x2 <- rnorm(n, mean = 3, sd = 1) + + # MCMC chain 1 + mu_sample1 <- vector("numeric", length = B) + mu_sample1[1L] <- rnorm(1L) + theta_sample1 <- matrix(nrow = B, ncol = 2L) + theta_sample1[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace1 <- vector("logical", length = B) + acceptace1[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample1[i - 1L], theta_sample1[i - 1L, ]), + sigma = c(2, 0.5, 0.5) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample1[i - 1L], theta_sample1[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample1[i] <- mu_p + theta_sample1[i, ] <- theta_p + acceptace1[i] <- TRUE + } else { + mu_sample1[i] <- mu_sample1[i - 1L] + theta_sample1[i, ] <- theta_sample1[i - 1L, ] + acceptace1[i] <- FALSE + } + } + + # MCMC chain 2 + mu_sample2 <- vector("numeric", length = B) + mu_sample2[1L] <- rnorm(1L) + theta_sample2 <- matrix(nrow = B, ncol = 2L) + theta_sample2[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace2 <- vector("logical", length = B) + acceptace2[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample2[i - 1L], theta_sample2[i - 1L, ]), + sigma = c(2, 0.5, 0.5) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample2[i - 1L], theta_sample2[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample2[i] <- mu_p + theta_sample2[i, ] <- theta_p + acceptace2[i] <- TRUE + } else { + mu_sample2[i] <- mu_sample2[i - 1L] + theta_sample2[i, ] <- theta_sample2[i - 1L, ] + acceptace2[i] <- FALSE + } + } + + # KL divergence + df <- data.frame( + index = seq_len(2L * B), mu = c(mu_sample1, mu_sample2), + theta1 = c(theta_sample1[, 1L], theta_sample2[, 1L]), + theta2 = c(theta_sample1[, 2L], theta_sample2[, 2L]), + acceptace = c(acceptace1, acceptace2), + chain = rep(c(1L, 2L), each = B) + ) + pd <- density(df$mu) + pd_estimate <- approxfun(pd$x, pd$y, + yleft = .Machine$double.eps, + yright = .Machine$double.eps + ) + integrand <- function(x) { + pd_estimate(x) * { + log(pd_estimate(x)) - dnorm(x, mean = 0, sd = sd_mu, log = TRUE) + } + } + kl <- tryCatch(integrate(integrand, lower = -Inf, upper = Inf)$value, + warning = \(x) NA, error = \(x) NA + ) + # Compute KL by taking the average when integration does not work + if (is.na(kl)) { + kl <- mean( + log(pd_estimate(df$mu)) - dnorm(df$mu, mean = 0, sd = sd_mu, log = TRUE) + ) + } + # Potential scale reduction factors + mu_c1 <- mcmc(df$mu[seq_len(B)]) + mu_c2 <- mcmc(df$mu[seq(B + 1L, 2L * B)]) + theta1_c1 <- mcmc(df$theta1[seq_len(B)]) + theta1_c2 <- mcmc(df$theta1[seq(B + 1L, 2L * B)]) + theta2_c1 <- mcmc(df$theta2[seq_len(B)]) + theta2_c2 <- mcmc(df$theta2[seq(B + 1L, 2L * B)]) + theta1_psrf <- gelman.diag(mcmc.list(theta1_c1, theta1_c2))$psrf[1L] + mu_psrf <- gelman.diag(mcmc.list(mu_c1, mu_c2))$psrf[1L] + theta2_psrf <- gelman.diag(mcmc.list(theta2_c1, theta2_c2))$psrf[1L] + + c(kl, mu_psrf, theta1_psrf, theta2_psrf, mean(df$acceptace)) +} +stopCluster(cl) + + +## 6. Results +colnames(result) <- + c("kl", "mu_psrf", "theta1_psrf", "theta2_psrf", "acceptace") +# Remove invalid values +result <- result[is.finite(result[, "mu_psrf"]), ] +cat("Expected KL: ", + mean(result[, "kl"], na.rm = TRUE), " (", + round(sd(result[, "kl"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("mu psrf: ", + mean(result[, "mu_psrf"], na.rm = TRUE), " (", + round(sd(result[, "mu_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta1 psrf: ", + mean(result[, "theta1_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta1_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta2 psrf: ", + mean(result[, "theta2_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta2_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("Acceptance rate: ", + mean(result[, "acceptace"], na.rm = TRUE), " (", + round(sd(result[, "acceptace"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) diff --git a/retel-paper/code/simulations/kl/retel_r/n8.R b/retel-paper/code/simulations/kl/retel_r/n8.R new file mode 100644 index 0000000..a4f80bf --- /dev/null +++ b/retel-paper/code/simulations/kl/retel_r/n8.R @@ -0,0 +1,201 @@ +## 1. Load packages +options(warn = -1) +options(scipen = 999) +library(coda) +suppressMessages(library(doParallel)) # parallel backend +suppressMessages(library(doRNG)) # reproducible parallel loop +library(mvtnorm) +library(retel) + + +## 2. Parameters +# Sample size for each group +n <- 8L + + +## 3. Constants +# Tau +tau <- log(n) +# Standard deviation of prior +sd_mu <- 10 +# Simulation replications +S <- 1e+03L +# MCMC parameters +B <- 5000L + + +## 4. Functions +f <- function(x, par) { + x - par +} +# Prior and posterior computation +log_prior <- function(mu, theta) { + dnorm(mu, mean = 0, sd = sd_mu, log = TRUE) - + sum(log(pi * (1 + (theta - mu)^2L))) +} +loglr <- function(theta, x1, x2) { + retel(f, x1, theta[1L], mean(x1) - theta[1L], 1, tau, "reduced") + + retel(f, x2, theta[2L], mean(x2) - theta[2L], 1, tau, "reduced") +} +log_posterior_unnormalized <- function(mu_p, theta, x1, x2) { + log_prior(mu_p, theta) + loglr(theta, x1, x2) +} + + +## 5. Simulations +cat("< Method = RETEL_r>\n") +cat("< Simulation replications =", S, ">\n") +cat("< MCMC runs =", 2L * B, ">\n") +cat("< n =", n, ">\n") +set.seed(12542) +cl <- makeCluster(24L) +registerDoParallel(cl) +result <- foreach( + i = icount(S), .combine = "rbind", .inorder = FALSE, + .packages = c("coda", "mvtnorm", "retel") +) %dorng% { + # Generate data + x1 <- rnorm(n, mean = -3, sd = 1) + x2 <- rnorm(n, mean = 3, sd = 1) + + # MCMC chain 1 + mu_sample1 <- vector("numeric", length = B) + mu_sample1[1L] <- rnorm(1L) + theta_sample1 <- matrix(nrow = B, ncol = 2L) + theta_sample1[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace1 <- vector("logical", length = B) + acceptace1[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample1[i - 1L], theta_sample1[i - 1L, ]), + sigma = c(2, 0.5, 0.5) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample1[i - 1L], theta_sample1[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample1[i] <- mu_p + theta_sample1[i, ] <- theta_p + acceptace1[i] <- TRUE + } else { + mu_sample1[i] <- mu_sample1[i - 1L] + theta_sample1[i, ] <- theta_sample1[i - 1L, ] + acceptace1[i] <- FALSE + } + } + + # MCMC chain 2 + mu_sample2 <- vector("numeric", length = B) + mu_sample2[1L] <- rnorm(1L) + theta_sample2 <- matrix(nrow = B, ncol = 2L) + theta_sample2[1L, ] <- c(rnorm(1L, mean = -2), rnorm(1L, mean = 2)) + acceptace2 <- vector("logical", length = B) + acceptace2[1L] <- FALSE + for (i in seq_len(B)[-1L]) { + # Sample proposal value + prop <- rmvnorm(1L, + mean = c(mu_sample2[i - 1L], theta_sample2[i - 1L, ]), + sigma = c(2, 0.5, 0.5) * diag(3L) + ) + mu_p <- prop[1L] + theta_p <- prop[2L:3L] + # Compute log ratio of unnormailzed posterior densities + logr <- log_posterior_unnormalized(mu_p, theta_p, x1, x2) - + log_posterior_unnormalized( + mu_sample2[i - 1L], theta_sample2[i - 1L, ], x1, x2 + ) + # Sample uniform random variable + u <- runif(1L) + # Accept or reject + if (isTRUE(log(u) < logr)) { + mu_sample2[i] <- mu_p + theta_sample2[i, ] <- theta_p + acceptace2[i] <- TRUE + } else { + mu_sample2[i] <- mu_sample2[i - 1L] + theta_sample2[i, ] <- theta_sample2[i - 1L, ] + acceptace2[i] <- FALSE + } + } + + # KL divergence + df <- data.frame( + index = seq_len(2L * B), mu = c(mu_sample1, mu_sample2), + theta1 = c(theta_sample1[, 1L], theta_sample2[, 1L]), + theta2 = c(theta_sample1[, 2L], theta_sample2[, 2L]), + acceptace = c(acceptace1, acceptace2), + chain = rep(c(1L, 2L), each = B) + ) + pd <- density(df$mu) + pd_estimate <- approxfun(pd$x, pd$y, + yleft = .Machine$double.eps, + yright = .Machine$double.eps + ) + integrand <- function(x) { + pd_estimate(x) * { + log(pd_estimate(x)) - dnorm(x, mean = 0, sd = sd_mu, log = TRUE) + } + } + kl <- tryCatch(integrate(integrand, lower = -Inf, upper = Inf)$value, + warning = \(x) NA, error = \(x) NA + ) + # Compute KL by taking the average when integration does not work + if (is.na(kl)) { + kl <- mean( + log(pd_estimate(df$mu)) - dnorm(df$mu, mean = 0, sd = sd_mu, log = TRUE) + ) + } + # Potential scale reduction factors + mu_c1 <- mcmc(df$mu[seq_len(B)]) + mu_c2 <- mcmc(df$mu[seq(B + 1L, 2L * B)]) + theta1_c1 <- mcmc(df$theta1[seq_len(B)]) + theta1_c2 <- mcmc(df$theta1[seq(B + 1L, 2L * B)]) + theta2_c1 <- mcmc(df$theta2[seq_len(B)]) + theta2_c2 <- mcmc(df$theta2[seq(B + 1L, 2L * B)]) + theta1_psrf <- gelman.diag(mcmc.list(theta1_c1, theta1_c2))$psrf[1L] + mu_psrf <- gelman.diag(mcmc.list(mu_c1, mu_c2))$psrf[1L] + theta2_psrf <- gelman.diag(mcmc.list(theta2_c1, theta2_c2))$psrf[1L] + + c(kl, mu_psrf, theta1_psrf, theta2_psrf, mean(df$acceptace)) +} +stopCluster(cl) + + +## 6. Results +colnames(result) <- + c("kl", "mu_psrf", "theta1_psrf", "theta2_psrf", "acceptace") +# Remove invalid values +result <- result[is.finite(result[, "mu_psrf"]), ] +cat("Expected KL: ", + mean(result[, "kl"], na.rm = TRUE), " (", + round(sd(result[, "kl"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("mu psrf: ", + mean(result[, "mu_psrf"], na.rm = TRUE), " (", + round(sd(result[, "mu_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta1 psrf: ", + mean(result[, "theta1_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta1_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("theta2 psrf: ", + mean(result[, "theta2_psrf"], na.rm = TRUE), " (", + round(sd(result[, "theta2_psrf"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) +cat("Acceptance rate: ", + mean(result[, "acceptace"], na.rm = TRUE), " (", + round(sd(result[, "acceptace"], na.rm = TRUE) / sqrt(S), 4L), ")", "\n", + sep = "" +) diff --git 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b/retel-paper/simulations/kl/retel_r/n8.txt new file mode 100644 index 0000000..4140ee7 --- /dev/null +++ b/retel-paper/simulations/kl/retel_r/n8.txt @@ -0,0 +1,9 @@ +< Method = RETEL_r> +< Simulation replications = 1000 > +< MCMC runs = 10000 > +< n = 8 > +Expected KL: 0.8969079 (0.0021) +mu psrf: 1.041503 (0.0019) +theta1 psrf: 1.004814 (0.0002) +theta2 psrf: 1.004373 (0.0001) +Acceptance rate: 0.2233309 (0.001)