CONDITIONS FOR RAPID MIXING OF PARALLEL AND SIMULATED TEMPERING ON MULTIMODAL DISTRIBUTIONS

被引：51

作者：

Woodard, Dawn B. ^{[1
]}

Schmidler, Scott C. ^{[1
]}

Huber, Mark ^{[2
]}

机构：

[1] Duke Univ, Dept Stat Sci, Durham, NC 27708 USA

[2] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2009年 / 19卷 / 02期

关键词：

Markov chain Monte Carlo; tempering; rapidly mixing Markov chains; spectral gap; Metropolis algorithm; MARKOV-CHAINS; MONTE-CARLO; CONVERGENCE;

D O I：

10.1214/08-AAP555

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：617 / 640

页数：24

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