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

• 成果类型: Article
• 署名作者: Woodard, Dawn B.; Schmidler, Scott C.; Huber, Mark
• 署名单位: Duke University; Duke University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP555
• 发表日期: 2009
• 页码: 617-640
• 关键词: markov-chains; monte-carlo; CONVERGENCE

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.