Multi-Scale MCMC Methods for Sampling from Products of Gaussian Mixtures

This paper addresses the important and ubiquitous problem of sampling from a product of Gaussian mixtures. An exact solution is often computationally infeasible, thus motivating the development of efficient sampling schemes. However, naive Markov chain Monte Carlo algorithms perform poorly in cases where the product mixture is highly multi-modal. In this paper we follow the trend of recent work utilizing multi-scale sampling methods, and propose two new multi-scale Markov chain Monte Carlo algorithms based on simulated and parallel tempering. Empirical results indicate that for the same computational budget, this class of methods can improve performance in cases with widely separated modes.