Conditions for Rapid Mixing of Parallel and Simulated Tempering on Multimodal Distributions

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2009

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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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Woodard,Dawn B.;Schmidler,Scott C.;Huber,Mark. 2009. Conditions for Rapid Mixing of Parallel and Simulated Tempering on Multimodal Distributions. Annals of Applied Probability 19(2): 617-640.

Published Version (Please cite this version)

10.1214/08-AAP555

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Schmidler

Scott C. Schmidler

Associate Professor of Statistical Science

Research Interests:

  • Monte Carlo methods; high-dimensional sampling algorithms; Mixing times of Markov chains; MCMC; Sequential Monte Carlo; probabilistic graphical models; Bayesian computation; Computational complexity of statistical inference.

  • Computational biology; Protein structure and folding; computational immunology; computational biophysics; statistical physics; computational statistical mechanics; molecular evolution.

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