2006/05/31 by Persi Diaconis, Silke W. W. Rolles · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Markov Chains and Monte Carlo Methods #math.ST #msc:62C10 #msc:62M02 #stat.TH
paper · pdf · doi:10.1214/009053606000000290
published as Annals of Statistics 2006, Vol. 34, No. 3, 1270-1292 · Published at http://dx.doi.org/10.1214/009053606000000290 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2006/06/01 · arxiv created 2006/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 Pólya’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.