BAYESIAN NONPARAMETRIC ANALYSIS OF REVERSIBLE MARKOV CHAINS

• 成果类型: Article
• 署名作者: Bacallado, Sergio; Favaro, Stefano; Trippa, Lorenzo
• 署名单位: Stanford University; University of Turin; Collegio Carlo Alberto; Harvard University; Harvard T.H. Chan School of Public Health; Harvard University; Harvard University Medical Affiliates; Dana-Farber Cancer Institute
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1102
• 发表日期: 2013
• 页码: 870-896
• 关键词: reinforced random-walk

摘要

We introduce a three-parameter random walk with reinforcement, called the (theta, alpha, beta) scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter beta smoothly tunes the (theta, alpha, beta) scheme between this edge reinforced random walk and the classical exchangeable two-parameter Hoppe urn scheme, while the parameters a and theta modulate how many states are typically visited. Resorting to de Finetti's theorem for Markov chains, we use the (theta, alpha, beta) scheme to define a nonparametric prior for Bayesian analysis of reversible Markov chains. The prior is applied in Bayesian nonparametric inference for species sampling problems with data generated from a reversible Markov chain with an unknown transition kernel. As a real example, we analyze data from molecular dynamics simulations of protein folding.