  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 finite and infinite
mixture model-based clustering for a CTHMM and achieve inference using Markov
chain Monte Carlo (MCMC). For a finite mixture model with prior on the number
of components, we implement reversible-jump MCMC to facilitate the
trans-dimensional move between different number of clusters. For a Dirichlet
process mixture model, we utilize restricted Gibbs sampling split-merge
proposals to expedite the MCMC algorithm. We employ proposed algorithms to the
simulated data as well as a real data example, and the results demonstrate the
desired performance of the new sampler.
