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

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

2009-06-12

arxiv.org/abs/0906.2341v1

Annals of Applied Probability 2009, Vol. 19, No. 2, 617-640

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP555 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

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.

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