Augmented Ensemble MCMC sampling in Factorial Hidden Markov Models

TL;DR

This paper introduces an augmented ensemble MCMC method combining parallel tempering, auxiliary variables, and genetic algorithms to improve Bayesian inference in factorial hidden Markov models, addressing challenges of exploring complex posterior landscapes.

Contribution

The paper presents a novel ensemble MCMC algorithm that enhances sampling efficiency for factorial HMMs by integrating multiple advanced techniques.

Findings

Improved mixing and exploration of the posterior landscape.

Enhanced sampling efficiency demonstrated in simulations.

Better performance in a cancer genomics application.

Abstract

Bayesian inference for factorial hidden Markov models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often restricted to exploration around localised regions that depend on initialisation. We introduce a general purpose ensemble Markov Chain Monte Carlo (MCMC) technique to improve on existing poorly mixing samplers. This is achieved by combining parallel tempering and an auxiliary variable scheme to exchange information between the chains in an efficient way. The latter exploits a genetic algorithm within an augmented Gibbs sampler. We compare our technique with various existing samplers in a simulation study as well as in a cancer genomics application, demonstrating the improvements obtained by our augmented ensemble approach.