Non-reversible parallel tempering: A scalable highly parallel MCMC scheme

• 成果类型: Article
• 署名作者: Syed, Saifuddin; Bouchard-Cote, Alexandre; Deligiannidis, George; Doucet, Arnaud
• 署名单位: University of British Columbia; University of Oxford
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12464
• 发表日期: 2022
• 页码: 321-350
• 关键词: monte-carlo method; exchange; MODEL; simulation; number

摘要

Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution pi with a density L with respect to a reference distribution pi 0 and compute the normalizing constant integral Ld pi 0. A typical use case is when pi 0 is a prior distribution, L a likelihood function and pi the corresponding posterior distribution.