GEOMETRIC ERGODICITY OF THE BOUNCY PARTICLE SAMPLER

• 成果类型: Article
• 署名作者: Durmus, Alain; Guillin, Arnaud; Monmarche, Pierre
• 署名单位: Universite Paris Saclay; Universite Clermont Auvergne (UCA); Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1552
• 发表日期: 2020
• 页码: 2069-2098
• 关键词: monte-carlo; large deviations; LIMIT-THEOREMS; state; simulation; rates; times; mcmc

摘要

The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic piecewise deterministic Markov process for which the target measure is invariant. This paper deals with theoretical properties of BPS. First, we establish geometric ergodicity of the associated semi-group under weaker conditions than in (Ann. Statist. 47 (2019) 1268-1287) both on the target distribution and the velocity probability distribution. This result is based on a new coupling of the process which gives a quantitative minorization condition and yields more insights on the convergence. In addition, we study on a toy model the dependency of the convergence rates on the dimension of the state space. Finally, we apply our results to the analysis of simulated annealing algorithms based on BPS.