In the thesis, we focused on cluster analysis with longitudinal data. In the Study of Women's Health Across the Nation (SWAN), we are interested in identifying trending groups based on repeated hormone observations, and in the association between hormone trends and women's health during menopause. we proposed a Bayesian semi-parametric model with a Dirichlet Process (DP) that allows for irregular data and model-based clustering of women based on their hormone profiles. We identified distinct developmental trajectories for both E2 and FSH hormones, and discussed relationships between profiles and other factors. Urinary Incontinence (UI) is considered as a specific measure of women's health, and we extended our approach to jointly model UI and hormone outcomes in order to explore the association between UI status and the pattern of hormone changes over the menopausal transition.
In the study of Johne's disease in cattle, we developed a particular finite mixture model for diagnosis based on bivariate longitudinal outcomes. The subjects were clustered into three disease phases: uninfected and two categories of disease.
In addition, we discussed Label Switching issues in Bayesian finite and infinite mixture models, and proposed an ad-hoc method to address them to obtain inferences for the parameters on the component level.