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

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

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

Source: Ann. Appl. Probab. Volume 19, Number 2 (2009), 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.

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Primary Subjects: 65C40

Secondary Subjects: 65C05

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

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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1241702244
Digital Object Identifier: doi:10.1214/08-AAP555
Zentralblatt MATH identifier: 05566094
Mathematical Reviews number (MathSciNet): MR2521882

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