Small-world mcmc and convergence to multi-modal distributions: From slow mixing to fast mixing

• 成果类型: Article
• 署名作者: Guan, Yongtao; Krone, Stephen M.
• 署名单位: University of Chicago; University of Idaho
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000772
• 发表日期: 2007
• 页码: 284-304
• 关键词: chain monte-carlo; markov-chains; INEQUALITY; SPACES; bounds

摘要

We compare convergence rates of Metropolis-Hastings chains to multimodal target distributions when the proposal distributions can be of local and small world type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is slowly mixing (in the complexity of the problem) into a chain that is rapidly mixing. To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for logconcave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes.