Dirichlet process multi-state mixture models

Barone, Rosario

doi:10.1016/j.csda.2026.108359

Dirichlet process multi-state mixture models

2026-02-01

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PRE

AI

DOI：10.1016/j.csda.2026.108359

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Abstract

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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.

Keywords:

Bayesian nonparametrics

Clustering

Inhomogeneous Markov

Semi-Markov

Uniformization

Dirichlet process multi-state mixture models

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