rmcmc: Robust Markov chain Monte Carlo methods

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 sample from a standard normal distribution, and compute average acceptance probability over chain.

library(rmcmc)

target_distribution <- list(
  log_density = function(x) sum(x^2) / 2,
  grad_log_density = function(x) x
)
proposal <- barker_proposal(target_distribution, step_size = 2.)
n_sample <- 1000
dimension <- 2
state <- chain_state(rnorm(dimension))
sum_accept_prob <- 0
for (s in 2:n_sample) {
  state_and_statistics <- sample_metropolis_hastings(
    state, target_distribution, proposal
  )
  state <- state_and_statistics$state
  accept_prob <- state_and_statistics$statistics$accept_prob
  sum_accept_prob <- sum_accept_prob + accept_prob
}
mean_accept_prob <- sum_accept_prob / n_sample
message(sprintf("Average acceptance probability is %.2f", mean_accept_prob))
#> Average acceptance probability is 0.21