Bayesian analysis for reversible Markov chains
Open Access
- 1 June 2006
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 34 (3)
- https://doi.org/10.1214/009053606000000290
Abstract
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.Comment: 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.orgKeywords
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