  The literature on Bayesian methods for the analysis of discrete-time
semi-Markov processes is sparse. In this paper, we introduce the semi-Markov
beta-Stacy process, a stochastic process useful for the Bayesian non-parametric
analysis of semi-Markov processes. The semi-Markov beta-Stacy process is
conjugate with respect to data generated by a semi-Markov process, a property
which makes it easy to obtain probabilistic forecasts. Its predictive
distributions are characterized by a reinforced random walk on a system of
urns.
