Efficient Exploration of Multi-Modal Posterior Distributions

TL;DR

This paper introduces a novel mixed MCMC algorithm designed to efficiently explore multi-modal posterior distributions by enabling transitions between different modes, overcoming limitations of traditional MCMC methods.

Contribution

The paper proposes a new mixed MCMC variant with a specially designed proposal density that allows efficient exploration of multi-modal posteriors, maintaining Markovian properties.

Findings

Demonstrated effectiveness on a toy inference problem

Efficiently explores multiple modes without getting stuck

Maintains Markovian properties in the sampling process

Abstract

The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become stuck in one local mode, become non-Markovian or require an excessively long time to explore the global properties of the distribution. We propose a novel variant of MCMC, mixed MCMC, which exploits a specially designed proposal density to allow the generation candidate points from any of a number of different modes. This new method is efficient by design, and is strictly Markovian. We present our method and apply it to a toy model inference problem to demonstrate its validity.