Monte Carlo Methods for Multi-Modal Distributions

This paper explores auxiliary variable strategies for designing Monte Carlo algorithms to sample from multi-modal distributions. Naive importance sampling and Markov chain Monte Carlo methods perform poorly in such situations, motivating the development of alternative methods-in particular, those based on a multi-scale representation of the target distribution. Here we present a novel multi-scale algorithm for sampling from products of Gaussian mixtures, a canonical example in which multi-modality arises frequently in practice. This algorithm is based on a fusion of importance sampling and Markov chain Monte Carlo steps through the recently proposed framework of sequential Monte Carlo samplers. Simulation results indicate that in comparison to either form of sampling technique alone, the resulting algorithm performs more robustly in multi-modal cases than those previously reported in the literature.