Parallel and interacting Markov chains Monte Carlo method

TL;DR

This paper introduces an interacting parallel MCMC method that improves convergence and handles multi-modal distributions by allowing chains to propose candidates for each other, providing a novel approach to sampling multiple independent realizations.

Contribution

The paper proposes a new interacting parallel MCMC strategy where chains propose candidates for each other, enhancing convergence and multi-modality handling compared to independent chains.

Findings

Method can speed up convergence to the target law.

Method effectively handles multi-modal distributions.

Interacting chains form a valid MCMC for the product measure.

Abstract

In many situations it is important to be able to propose $N$ independent realizations of a given distribution law. We propose a strategy for making $N$ parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of an independent $N$-sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of $N$ target measures. Compared to independent parallel chains this method is more time consuming, but we show through concrete examples that it possesses many advantages: it can speed up convergence toward the target law as well as handle the multi-modal case.