Bayesian analysis for reversible Markov chains

Persi Diaconis, Silke W. W. Rolles
2006 Annals of Statistics  
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 P\'{o}lya'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.
doi:10.1214/009053606000000290 fatcat:r2scqcldxvdplockl4j6nybs3u