OPTIMAL SCALINGS FOR LOCAL METROPOLIS-HASTINGS CHAINS ON NONPRODUCT TARGETS IN HIGH DIMENSIONS

• 成果类型: Article
• 署名作者: Beskos, Alexandros; Roberts, Gareth; Stuart, Andrew
• 署名单位: University of Warwick; University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP563
• 发表日期: 2009
• 页码: 863-898
• 关键词: WEAK-CONVERGENCE; algorithms; diffusion

摘要

We investigate local MCMC algorithms, namely the random-walk Metropolis and the Langevin algorithms, and identify the optimal choice of the local step-size as a function of the dimension n of the state space, asymptotically as n -> infinity. We consider target distributions defined as a change of measure from a product law. Such structures arise, for instance, in inverse problems or Bayesian contexts when a product prior is combined with the likelihood. We state analytical results on the asymptotic behavior of the algorithms under general conditions on the change of measure. Our theory is motivated by applications on conditioned diffusion processes and inverse problems related to the 2D Navier-Stokes equation.