Mark Huber Publications
Conditions for Rapid Mixing of Parallel and Simulated Tempering on
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
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