Stability of sequential Markov Chain Monte Carlo methods

Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany

Abstract

Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling schemes. We develop a stability analysis by funtional inequalities for a nonlinear flow of probability measures describing the limit behavior of the methods as the number of particles tends to infinity. Stability results are derived both under global and local assumptions on the generator of the underlying Metropolis dynamics. This allows us to prove that the combined methods sometimes have good asymptotic stability properties in multimodal setups where traditional MCMC methods mix extremely slowly. For example, this holds for the mean field Ising model at all temperatures.