Bayesian analysis of phase-type distributions

By developing methods for simulation of absorbing Markov processes conditionally on the absorption time, a Markov chain Monte Carlo (MCMC) has earlier been constructed which can be exploited to simulate from the posterior distribution of the parameters of a phase-type distribution given a sample of apsorption times. Such distributions occur typically in risk theory and in queuing theory as distribution of service times in complicated networks. The method is extended to cover the case with an unknown number of phases, using reversible jump MCMC. Cooperation with Mogens Bladt, National University of Mexico, Mexico.