Congratulations to Our Newest PhD Graduate, Dr. Tsering Dolkar!

The Department of Statistics at Virginia Tech is proud to announce and celebrate the successful completion of Dr. Tsering Dolkar's doctoral degree requirements.

Dr. Tsering Dolkar successfully defended her dissertation titled "Bayesian Dynamic Clustering Factor Models" on April 28, 2026, a significant milestone representing years of rigorous work, dedication, and impactful research. 

Title: Bayesian Dynamic Clustering Factor Models.

Abstract: Bayesian Dynamic Clustering Factor Models (BDCFM) and Bayesian Dynamic Clustering Factor Models with regressors (BDCFM-R) aim to analyze multivariate longitudinal data. They combine factor models (FA) with hidden Markov models (HMM) to concomitantly perform dimension reduction, clustering, and estimation of the dynamic transitions of subjects through clusters. FA is a dimensionality reduction technique helpful in analyzing big data with many variables to consider. HMM is based on augmenting the Markov chain. A Markov chain is a model for a sequence of states, where each state can take one of several possible values. It describes the probabilities of moving from one state to another. The key idea is simple: to predict what happens next, you only need to know the current state. What happened earlier in the sequence does not matter, except through its effect on the current state. A hidden Markov model (HMM) allows us to talk about both observed events and hidden events that we think of as causal factors in our probabilistic model. We develop efficient Gibbs samplers for exploration of the posterior distributions for BDCFM and BDCFM-R. BDCFM-R is an extension of BDCFM that allows regressors to affect the transition of subjects among the clusters over time. We use BDCFM-R to capture the impact of changes in latent factors and changes in regressors at the previous time points on the probability of transitioning clusters at future time points. Analyses of simulated datasets show that our estimation approaches work well both at parameter estimation and clustering of subjects. Finally, we illustrate the utility of our BDCFM and BDCFM-R with analyses of a dataset on opioid use disorder.