Bayesian analysis of variable-order, reversible Markov chains

摘要

We define a conjugate prior for the reversible Markov chain of order $r$. Theprior arises from a partially exchangeable reinforced random walk, in the sameway that the Beta distribution arises from the exchangeable Poly\'{a} urn. Anextension to variable-order Markov chains is also derived. We show the utilityof this prior in testing the order and estimating the parameters of areversible Markov model.