A PIECEWISE DETERMINISTIC SCALING LIMIT OF LIFTED METROPOLIS-HASTINGS IN THE CURIE WEISS MODEL

• 成果类型: Article
• 署名作者: Bierkens, Joris; Roberts, Gareth
• 署名单位: Delft University of Technology; University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1217
• 发表日期: 2017
• 页码: 846-882
• 关键词: long-time behavior; variance reduction; steins method

摘要

In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis Hastings (LMH). A scaling limit of the magnetization process in the Curie Weiss model is derived for LMH, as well as for Metropolis Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n(1/2) for LMH, which should be compared to n for MH. At the critical temperature, the required jump rate equals n(3/4) for LMH and n(3/2) for MH, in agreement with experimental results of Turitsyn, Chertkov and Vucelja (2011). The scaling limit of LMH turns out to be a nonreversible piecewise deterministic exponentially ergodic zig-zag Markov process.