Parallel Metropolis–Hastings Coupler

Abstract

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. In this letter, we present a novel interacting parallel MCMC scheme, called parallel Metropolis–Hastings coupler (PMHC), where the information provided by different parallel MCMC chains is properly combined by the use of another advanced MCMC method, called normal kernel coupler (NKC). The NKC employs a mixture of densities as proposal density, which is updated according to a population of states. The PMHC is particularly efficient in multimodal scenarios, since it obtains a faster exploration of the state space with respect to other benchmark techniques. Several numerical simulations are provided showing the efficiency and robustness of the proposed method.