## ----include = FALSE---------------------------------------------------------- knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) ## ----echo = TRUE-------------------------------------------------------------- library(stors) modes_bi <- c(0.00134865, 3.99865) f_bi <- function(x) { 0.5 * (sqrt(2 * pi))^(-1) * exp(-(x^2) / 2) + 0.5 * (sqrt(2 * pi))^(-1) * exp(-((x - 4)^2) / 2) } h_bi <- function(x) log(f_bi(x)) h_prime_bi <- function(x) { (-(exp(-1 / 2 * (-4 + x)^2) * 0.5 * (-4 + x)) / sqrt(2 * pi) - (exp(-x^2 / 2) * 0.5 * x) / sqrt(2 * pi)) / ((exp(-x^2 / 2) * 0.5) / sqrt(2 * pi) + (exp(-1 / 2 * (-4 + x)^2) * 0.5) / sqrt(2 * pi)) } bi_proposal <- build_proposal(lower = -Inf, upper = Inf, modes = modes_bi, f = f_bi, h = h_bi, h_prime = h_prime_bi) plot(bi_proposal) ## ----echo = TRUE-------------------------------------------------------------- # Printing the properties of the custom proposal print(bi_proposal) # Visualizing the custom proposal plot(bi_proposal) ## ----echo = TRUE-------------------------------------------------------------- # Creating a sampler function using the custom proposal bi_sampler <- build_sampler(bi_proposal) plot(bi_proposal) # Generating samples from the target distribution sample <- bi_sampler(10^3) hist(sample, main = "Sample Generated From Multi-modal Distribution ", xlab = "Value", col = "lightblue", border = "white") ## ----echo = TRUE-------------------------------------------------------------- # Define modes for the multi-modal distribution modes_bi <- c(0.00134865, 3.99865) # Build a truncated proposal for the multi-modal distribution bi_trunc_proposal <- build_proposal( lower = -1, upper = 6, modes = modes_bi, f = f_bi, h = h_bi, h_prime = h_prime_bi, steps = 2040 ) # Visualize the truncated proposal plot(bi_trunc_proposal, main = "Truncated Multi-Modal Proposal (-1, 6)", xlab = "Value", col = "skyblue") # Create a sampler for the truncated distribution bi_sampler_trunc_sampler <- build_sampler(bi_trunc_proposal) # Generate 10^3 samples from the truncated distribution sample <- bi_sampler_trunc_sampler(10^3) # Generate 10^3 samples from the truncated distribution sample <- bi_sampler_trunc_sampler(10^3) # Visualize the generated samples hist( sample, main = "Histogram of Samples from Truncated Multi-Modal Distribution", xlab = "Value", col = "lightgreen", border = "white" ) ## ----echo = TRUE-------------------------------------------------------------- save_proposal(bi_proposal, "bimodal_proposal") ## ----include = FALSE---------------------------------------------------------- for (i in 1:3) { save_proposal(bi_proposal, paste0("bimodal_proposal_", i)) } ## ----echo = TRUE-------------------------------------------------------------- bi_proposal <- load_proposal("bimodal_proposal") ## ----echo = TRUE-------------------------------------------------------------- print_proposals() ## ----echo = TRUE-------------------------------------------------------------- delete_proposal("bimodal_proposal") print_proposals() ## ----include = FALSE---------------------------------------------------------- for (i in 1:3) { delete_proposal(paste0("bimodal_proposal_", i)) }