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

2009/04/01 by Dawn B. Woodard, Scott C. Schmidler, Mark Huber · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics

paper · pdf · doi:10.1214/08-aap555

openalex publication_date 2009/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Logarithmic Sobolev inequalities for finite Markov chains

Cited by

• On the Infinite Swapping Limit for Parallel Tempering
• Adaptive Path Sampling in Metastable Posterior Distributions

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