Parallel Tempering Markov Chain Monte Carlo

ptmc: Parallel Tempering Markov Chain Monte Carlo for Discrete Spaces

ptmc is an R package designed to perform Bayesian inference using a Parallel Tempering Markov Chain Monte Carlo (PT-MCMC) algorithm. This implementation allows efficient exploration of discrete parameter spaces, making it especially useful for models where standard MCMC techniques struggle with multimodal posteriors or slow convergence. This implementation is a generalised version of the algorithm outlined by Miasojedow et al. 2012.

Features

  • Implements a Metropolis-Hastings algorithm with parallel tempering for enhanced sampling efficiency.
  • Supports arbitrary user-defined likelihood and prior functions , enabling application to a wide range of models.
  • Designed to effectively sample from complex posterior distributions with multiple modes.
  • Parallelized execution across chains for improved performance.

Why Use Parallel Tempering?

Standard MCMC techniques can become inefficient when dealing with posterior distributions that:

  • Have multiple modes (e.g., distinct peaks in probability).
  • Feature complex discrete spaces where local exploration struggles to reach distant areas of high probability.

Parallel tempering mitigates these challenges by running multiple chains at different “temperatures.” High-temperature chains explore the parameter space more broadly, while low-temperature chains focus on precise posterior estimation. Occasional exchanges between chains help the algorithm escape local optima and improve convergence.

Installation

To install the ptmc package, follow these steps:

Step 1: Install R

Make sure you have R installed on your system. You can download R from https://cran.r-project.org/.

Step 2: Install ptmc from GitHub

You can install the development version of ptmc from GitHub using the devtools package. If you don’t already have devtools installed, you can install it with:


install.packages("devtools")
devtools::install_github("dchodge/ptmc")

Step 3: Load ptmc from GitHub

After installation, you can load the serojump package into your R session with:


library(ptmc)

See background/ptmc.pdf.

Getting Started

We offer several examples of how to implement this package.

  • Case 1: A simple implementation with a continuous space of parameters
  • Case 2: Negronis all round: simulation recovery of a discrete model 🍹

Contributing

We welcome contributions and suggestions! If you’d like to contribute to the ptmc package or report issues, please feel free to:

  • Submit a pull request on GitHub.
  • Open an issue on the repository.

If you have any questions or feedback, or would like more informative vignettes, you can contact the package maintainer at:

David Hodgson Email: david.hodgson@lshtm.ac.uk

Project Status

This package is actively maintained and in a stable, usable state. New features and improvements are continually being developed.