Mark Huber Publications

Conditions for Rapid Mixing of Parallel and Simulated Tempering on Multimodal Distributions
D. B. Woodard, S. C. Schmidler and M. Huber, Annals of Applied Probability, vol. 19, no. 2 (2009), pp. 617—640.

Abstract: We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.

Keywords: Markov chain Monte Carlo; tempering; rapidly mixing Markov chains; spectral gap; Metropolis algorithm

2000 Mathematics Subject Classification: Primary 65C40, Secondary 65C05