Dirichlet process multi-state mixture models

A Bayesian nonparametric framework is introduced for modeling discretely observed trajectories of continuous-time multi-state processes. By employing Dirichlet Process Mixtures with Markov, inhomogeneous Markov, and semi-Markov kernels, the approach flexibly captures unobserved heterogeneity in the process dynamics. Crucially, the mixture structure induces a generalized form of non-Markovianity, as future state predictions depend on the entire observed history through component-specific weighting. This allows the model to capture complex temporal dependencies and memory effects beyond the scope of traditional multi-state models. The effectiveness of the methodology is demonstrated through simulation studies and an application to a real data set.