Bayesian analysis of variable-order, reversible markov chains1

Abstract

We define a conjugate prior for the reversible Markov chain of order r. The prior rises from a partially exchangeable reinforced random walk, in the same way that the Beta distribution arises from the exchangeable Polyáurn. An extension to variable-order Markov chains is also derived. We show the utility of this prior in testing the order and estimating the parameters of areversible Markov model. © Institute of Mathematical Statistics, 2011.