Importance sampling for families of distributions

• 成果类型: Article
• 署名作者: Madras, N; Piccioni, M
• 署名单位: York University - Canada; University of L'Aquila
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 1202-1225
• 关键词: monte-carlo technique; bayesian computation; phase-transitions; markov-chains; GIBBS SAMPLER; statistics

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.