Bayesian mixtures of discretely observed multi-state models

In this paper we propose a clustering technique for discretely observed 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 inferences for relevant process features. To model individual heterogeneity we consider both finite mixtures and Dirichlet process mixture (DPM) of di↵erent 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 inference for Markov, semi-Markov and in-homogeneous Markov models with an application to a real dataset.