Rejection-free Ensemble MCMC with applications to Factorial Hidden Markov Models

Bayesian inference for complex models is challenging due to the need to explore high-dimensional spaces and multimodality and standard Monte Carlo samplers can have difficulties effectively exploring the posterior. We introduce a general purpose rejection-free 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 move to exchange information between the chains. We demonstrate this ensemble MCMC scheme on Bayesian inference in Factorial Hidden Markov Models. This high-dimensional inference problem is difficult due to the exponentially sized latent variable space. Existing sampling approaches mix slowly and can get trapped in local modes. We show that the performance of these samplers is improved by our rejection-free ensemble technique and that the method is attractive and easy-to-use since no parameter tuning is required.