Population-Based Reversible Jump Markov Chain Monte Carlo

TL;DR

This paper extends population-based MCMC methods to trans-dimensional problems, proving their uniform ergodicity and demonstrating superior convergence and performance over traditional reversible jump samplers in Bayesian variable selection and mixture modeling.

Contribution

It introduces a population-based trans-dimensional MCMC algorithm, proves its uniform ergodicity, and shows its improved convergence and efficiency over existing methods.

Findings

Population algorithms outperform reversible jump samplers in convergence rate.

The proposed method effectively handles high and trans-dimensional target measures.

Application to gene expression data demonstrates superior performance in real-world scenarios.

Abstract

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of these population algorithms, under mild assumptions. This result is used to demonstrate the superiority, in terms of convergence rate, of a population transition kernel over a reversible jump sampler for a Bayesian variable selection problem. We also give an example of a population algorithm for a Bayesian multivariate mixture model with an unknown number of components. This is applied to gene expression data of 1000 data points in six dimensions and it is demonstrated that our algorithm out performs some competing Markov chain samplers.