The semi-Markov beta-Stacy process: a Bayesian non-parametric prior for semi-Markov processes

The literature on Bayesian methods for the analysis of discrete-time semi-Markov processes is sparse. In this paper, we introduce the \emph{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 uniquely characterized by a reinforced random walk on a system of urns.