FAST LANGEVIN BASED ALGORITHM FOR MCMC IN HIGH DIMENSIONS

• 成果类型: Article
• 署名作者: Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.
• 署名单位: University of Warwick; University of Geneva; University of Edinburgh
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1257
• 发表日期: 2017
• 页码: 2195-2237
• 关键词: transient phase; hastings; CONVERGENCE; approximations

摘要

We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension d. The improved complexity is O(d(1/5)) compared to the complexity O(d(1/3)) of the standard approach. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate (with asymptotical value 0.704), independently of the target distribution. Numerical experiments confirm our theoretical findings.