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.
Publié le : 2009-04-15
Classification:
Markov chain Monte Carlo,
tempering,
rapidly mixing Markov chains,
spectral gap,
Metropolis algorithm,
65C40,
65C05
@article{1241702244,
author = {Woodard, Dawn B. and Schmidler, Scott C. and Huber, Mark},
title = {Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions},
journal = {Ann. Appl. Probab.},
volume = {19},
number = {1},
year = {2009},
pages = { 617-640},
language = {en},
url = {http://dml.mathdoc.fr/item/1241702244}
}
Woodard, Dawn B.; Schmidler, Scott C.; Huber, Mark. Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions. Ann. Appl. Probab., Tome 19 (2009) no. 1, pp. 617-640. http://gdmltest.u-ga.fr/item/1241702244/