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April 2009 Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
Dawn B. Woodard, Scott C. Schmidler, Mark Huber
Ann. Appl. Probab. 19(2): 617-640 (April 2009). DOI: 10.1214/08-AAP555

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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Dawn B. Woodard. Scott C. Schmidler. Mark Huber. "Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions." Ann. Appl. Probab. 19 (2) 617 - 640, April 2009. https://doi.org/10.1214/08-AAP555

Information

Published: April 2009
First available in Project Euclid: 7 May 2009

zbMATH: 1171.65008
MathSciNet: MR2521882
Digital Object Identifier: 10.1214/08-AAP555

Subjects:
Primary: 65C40
Secondary: 65C05

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

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 2 • April 2009
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