Conditions for Rapid Mixing of Parallel and Simulated Tempering on Multimodal Distributions
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.
Type
Other articleSubject
markov chain monte carlotempering
rapidly mixing markov chains
spectral gap
metropolis algorithm
markov-chains
monte-carlo
convergence
statistics & probability
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https://hdl.handle.net/10161/4407Published Version (Please cite this version)
10.1214/08-AAP555Citation
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.
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Scott C. Schmidler
Associate Professor of Statistical Science

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