Bayesian analysis for finite Markov chains
The paper provides Bayesian estimation of the transition probabilities of a Markov chain. Some other estimation methods are complicated enough since they involve the distribution function of the observed transition matrix, which is quite cumbersome. On the contrary, Bayesian estimation is easier, since the Dirichlet family is conjugate for the transition probabilities, and hence fully Bayesian inference is easily available. The paper discusses hypothesis testing based on posterior densities. In particular, the two-state Markov chain is discussed. Several different kinds of testing hypotheses are considered using different parametric functions of the transition probabilities. Illustrative examples are provided for many cases. Bayes factors, highest density regions and central credible sets, as well as other measures are described for both a uniform and umbrella-pattern prior distributions.
scientific article; zbMATH DE number 1375309