Open Access
Translator Disclaimer
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


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.


Download Citation

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.


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

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

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


Vol.19 • No. 2 • April 2009
Back to Top