Bayesian analysis for reversible markov chains

Persi Diaconis, Silke W.W. Rolles

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


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.

Original languageEnglish
Pages (from-to)1270-1292
Number of pages23
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 2006
Externally publishedYes


  • Bayesian analysis
  • Conjugate priors
  • Hypothesis testing
  • Reversible Markov chains


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