A note on Metropolis-Hastings kernels for general state spaces

• 成果类型: Article
• 署名作者: Tierney, L
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 1-9
• 关键词: bayesian computation; markov-chains

摘要

The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a specified invariant distribution. This note describes necessary and sufficient conditions on the candidate generation kernel and the acceptance probability function for the resulting transition kernel and invariant distribution to satisfy the detailed balance conditions. A simple general formulation is used that covers a range of special cases treated separately in the literature. In addition, results on a useful partial ordering of finite state space reversible transition kernels are extended to general state spaces and used to compare the performance of two approaches to using mixtures in Metropolis-Hastings kernels.