CONVERGENCE OF SEQUENTIAL MARKOV CHAIN MONTE CARLO METHODS: I. NONLINEAR FLOW OF PROBABILITY MEASURES

Sequential Monte Carlo Samplers are a class of sto- chastic algorithms for Monte Carlo integral estimation w.r.t. proba- bility 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 nonlin- ear ∞ow of probability measures describing the limit behavior of the methods as the number of particles tends to inflnity. 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 asymp- totic stability properties in multimodal setups where traditional MCMC methods mix extremely slowly. For example, this holds for the mean fleld Ising model at all temperatures.

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