Statistics Ph.D. Dissertation Defense - Shuying Wang

The 2024 Dissertation Defenses begins on Friday April 12, from 11:00 a.m. to 1:00 p.m. with Shuying Wang. This event will be hybrid. If you need the Zoom link, please email stat.admin@austin.utexas.edu.

Title: Bayesian Inference for Stochastic Compartmental Models and Marginal Cox Process

Advisor: Stephen Walker

Abstract: This dissertation addresses the computational challenges posed by Bayesian Markov Chain Monte Carlo (MCMC) data augmentation methods in the stochastic compartmental models with partially observed data. We present a novel algorithm for estimating the stochastic SIR/SEIR epidemic model within a Bayesian framework, which can be readily extended to more complex stochastic compartmental models. Specifically, based on the infinitesimal conditional independence properties of the model, we are able to find a proposal distribution for a Metropolis-Hastings algorithm which is very close to the correct posterior distribution. In particular, it acts as a very good proposal for the unknown number of events, such as the number of infected individuals, as well as the times of occurrences. Therefore, rather than perform a Metropolis step updating one missing data point at a time, we are able to have a single proposal for the entire set of missing observations. Moreover, the dissertation explores the theoretical framework of continuous-time count processes, leading to the development of a marginalized Poisson-driven Cox process aimed at addressing overdispersion in count data. This innovation facilitates a more efficient and precise analysis by enabling the direct calculation of the marginal likelihood function, thus bypassing the complexities of sampling the unobserved stochastic intensity process.