Robust Markov Chain Monte Carlo Methods • rmcmc

rmcmc is an R package for simulating Markov chains using the Barker proposal to compute Markov chain Monte Carlo (MCMC) estimates of expectations with respect to a target distribution on a real-valued vector space. The Barker proposal, described in Livingstone and Zanella (2022) https://doi.org/10.1111/rssb.12482, is a gradient-based MCMC algorithm inspired by the Barker accept-reject rule. It combines the robustness of simpler MCMC schemes such as random-walk Metropolis with the efficiency of gradient-based algorithms such as Metropolis adjusted Langevin algorithm.

Installation

You can install the development version of rmcmc like so:

# install.packages("devtools")
devtools::install_github("UCL/rmcmc")

Example

This is a basic example which shows you how to generate samples from a normal target distribution with random scales. Adapters are used to tune the proposal scale to achieve a target average acceptance probability; to tune the proposal shape with per-dimension scale factors based on online estimates of the target distribution variances.

library(rmcmc)

set.seed(876287L)
dimension <- 3
scales <- exp(2 * rnorm(dimension))
target_distribution <- list(
  log_density = function(x) -sum((x / scales)^2) / 2,
  gradient_log_density = function(x) -x / scales^2
)
proposal <- barker_proposal(target_distribution)
adapters <- list(
  scale_adapter(proposal, initial_scale = 1., target_accept_prob = 0.4),
  variance_adapter(proposal)
)
n_warm_up_iteration <- 1000
n_main_iteration <- 1000
initial_state <- chain_state(rnorm(dimension))
results <- sample_chain(
  target_distribution = target_distribution,
  proposal = proposal,
  initial_state = initial_state,
  n_warm_up_iteration = n_warm_up_iteration,
  n_main_iteration = n_main_iteration,
  adapters = adapters
)
mean_accept_prob <- mean(results$statistics$accept_prob)
adapted_shape <- proposal$parameters()$shape
cat(
  sprintf("Average acceptance probability is %.2f", mean_accept_prob),
  sprintf("True target scales: %s", toString(scales)),
  sprintf("Adapter scale est.: %s", toString(adapted_shape)),
  sep = "\n"
)
#> Average acceptance probability is 0.46
#> True target scales: 2.26617033226883, 1.89818769776724, 0.0767505506297473
#> Adapter scale est.: 1.77277384748788, 1.71554065105575, 0.0804144979270686

rmcmc: Robust Markov chain Monte Carlo methods

Installation

Example