WEAK CONVERGENCE AND OPTIMAL SCALING OF RANDOM WALK METROPOLIS ALGORITHMS

作     者：Roberts, G. O. Gelman, A. Gilks, W. R. 

作者机构：Univ Cambridge Stat Lab Cambridge CB2 1SB England Columbia Univ Dept Stat New York NY 10027 USA Inst Publ Hlth MRC Biostat Unit Cambridge CB2 2SR England 

出 版 物：《ANNALS OF APPLIED PROBABILITY》 (应用概率纪事)

年 卷 期：1997年第7卷第1期

页      面：110-120页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：NSF [SBR-92-23637  DMS-94-04305  DMS-94-57824] 

主　　题：Metropolis algorithm weak convergence optimal scaling Markov chain Monte Carlo 

摘      要：This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges to infinity. When the proposal variance is appropriately scaled according to n, the sequence of stochastic processes formed by the first component of each Markov chain converges to the appropriate limiting Langevin diffusion process. The limiting diffusion approximation admits a straightforward efficiency maximization problem, and the resulting asymptotically optimal policy is related to the asymptotic acceptance rate of proposed moves for the algorithm. The asymptotically optimal acceptance rate is 0.234 under quite general conditions. The main result is proved in the case where the target density has a symmetric product form. Extensions of the result are discussed.