Bayesian mixtures of semi-Markov models

In this paper we propose a clustering technique for continuous-time semi- Markov models in order to take account of groups of individuals having similar process realizations. In fact fitting standard parametric models in presence of het- erogeneity between population groups may produce biased inferences for relevant process feautres. To model individual heterogeneity we consider a Dirichlet process mixture (DPM) of semi-Markov continuous-time models. We also consider the case of discretely observed trajectories of continuous time processes, providing an algo- rithm which clusterize the observations after having reconstructed the continuous- time paths between the observed points. Full MCMC inference is performed with an application to a real dataset.