Reversible Genetically Modified Mode Jumping MCMC

TL;DR

This paper presents a reversible GMJMCMC algorithm that efficiently estimates posterior model probabilities in large, complex model spaces, improving upon previous methods by ensuring proper MCMC properties.

Contribution

The paper introduces a reversible version of GMJMCMC that guarantees proper MCMC convergence and accurate posterior probability estimation in high-dimensional model spaces.

Findings

The reversible GMJMCMC converges to the true posterior model probabilities.

The new algorithm outperforms previous GMJMCMC in complex model spaces.

It provides reliable inference where classical MCMC struggles.

Abstract

In this paper, we introduce a reversible version of a genetically modified mode jumping Markov chain Monte Carlo algorithm (GMJMCMC) for inference on posterior model probabilities in complex model spaces, where the number of explanatory variables is prohibitively large for classical Markov Chain Monte Carlo methods. Unlike the earlier proposed GMJMCMC algorithm, the introduced algorithm is a proper MCMC and its limiting distribution corresponds to the posterior marginal model probabilities in the explored model space under reasonable regularity conditions.