  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.
