Clustering for Continuous-Time Hidden Markov Models

We develop clustering procedures for longitudinal trajectories based on a continuous-time hidden Markov model (CTHMM) and a generalized linear observation model. Specifically in this paper, we carry out infinite mixture model-based clustering for CTHMM and achieve inference using Markov chain Monte Carlo (MCMC). Specifically, for Bayesian nonparametric inference using a Dirichlet process mixture model, we utilize restricted Gibbs sampling split-merge proposals to expedite the MCMC algorithm. We employ the proposed algorithm to the simulated data as well as a large real data example, and the results demonstrate the desired performance of the new sampler.