Importance sampling for families of distributions

作     者：Madras, N Piccioni, M 

作者机构：York Univ Dept Math & Stat N York ON M3J 1P3 Canada Univ Aquila Dipartimento Matemat Pura & Applicata I-67100 Laquila Italy 

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

年 卷 期：1999年第9卷第4期

页      面：1202-1225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] 

主　　题：Markov chain Monte Carlo importance sampling simulated tempering Metropolis algorithm spectral gap Ising model 

摘      要：This paper analyzes the performance of importance sampling distributions for computing expectations with respect to a whole family of probability laws in the context of Markov chain Monte Carlo simulation methods. Motivations for such a study arise in statistics as well as in statistical physics. Two choices of importance sampling distributions are considered in detail: mixtures of the distributions of interest and distributions that are uniform over energy levels (motivated by physical applications). We analyze two examples, a witch s hat distribution and the mean field Ising model, to illustrate the advantages that such simulation procedures are expected to offer in a greater generality. The connection with the recently proposed simulated tempering method is also examined.