The Annals of Applied Probability

Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions

Dawn B. Woodard, Scott C. Schmidler, and Mark Huber

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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.

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Ann. Appl. Probab. Volume 19, Number 2 (2009), 617-640.

First available in Project Euclid: 7 May 2009

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Zentralblatt MATH identifier

Primary: 65C40: Computational Markov chains
Secondary: 65C05: Monte Carlo methods

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


Woodard, Dawn B.; Schmidler, Scott C.; Huber, Mark. Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions. Ann. Appl. Probab. 19 (2009), no. 2, 617--640. doi:10.1214/08-AAP555.

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