Bayesian analysis for reversible Markov chains

• 成果类型: Article
• 署名作者: Diaconis, Persi; Rolles, Silke W. W.
• 署名单位: Stanford University; Eindhoven University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000290
• 发表日期: 2006
• 页码: 1270-1292
• 关键词: reinforced random-walk; mixtures; THEOREMS; trees

摘要

We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Polya's urn. We give closed form normalizing constants, a simple method of simulation from the posterior and a characterization along the lines of W. E. Johnson's characterization of the Dirichlet prior.