# Bayesian Clustering for Continuous-Time Hidden Markov Models

## TL;DR

This paper introduces novel Bayesian clustering methods for continuous-time hidden Markov models, utilizing advanced MCMC techniques for improved inference in both finite and infinite mixture models.

## Contribution

It develops new Bayesian clustering algorithms for CTHMMs using reversible-jump and split-merge MCMC methods, enhancing inference for mixture models.

## Key findings

- Algorithms perform well on simulated data
- Effective inference for finite and infinite mixtures
- Demonstrated applicability on real data

## Abstract

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.