Bayesian mixtures of discretely observed multi-state models

In this paper we propose a clustering technique for discretely ob- served continuous-time models in order to take account of groups of individuals having similar process realizations. In fact, fitting standard parametric models in presence of heterogeneity between population groups may produce biased infer- ences for relevant process features. To model individual heterogeneity we consider both finite mixtures and Dirichlet process mixture (DPM) of different multi-state models. We base our algorithms on the whole reconstructed trajectories with the reconstruction step conducted by the uniformization technique usually employed for the generation of Markovian multi-state processes. We present MCMC in- ference for Markov, semi-Markov and in-homogeneous Markov models with an application to a real dataset.