MINIMISING MCMC VARIANCE VIA DIFFUSION LIMITS, WITH AN APPLICATION TO SIMULATED TEMPERING

• 成果类型: Article
• 署名作者: Roberts, Gareth O.; Rosenthal, Jeffrey
• 署名单位: University of Warwick; University of Toronto
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP918
• 发表日期: 2014
• 页码: 131-149
• 关键词: time markov-chains; monte-carlo; metropolis algorithms; target distributions; CONVERGENCE; discrete

摘要

We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth death chains which themselves satisfy Peskun orderings. We then apply our results to simulated tempering algorithms to establish which choice of inverse temperatures minimises the asymptotic variance of all functionals and thus leads to the most efficient MCMC algorithm.