Tang, M. (STAT) – Bayesian Modeling and Scalable Inference for Count Time Series in Infectious Disease Surveillance

Real-time monitoring of infectious disease outbreaks calls for statistical models that recover interpretable quantities such as the time-varying reproduction number from noisy count data, track posterior uncertainty, and run on time scales compatible with daily updates. Existing methods address these aims through separate model classes. Discretized Hawkes processes, Poisson autoregressions, and distributed lag models each capture self-exciting transmission through alternative parameterizations of the same conditional mean structure, but they have been developed across separate software packages with model-specific inference routines, which makes structural model comparison cumbersome in practice. This dissertation develops a unified Bayesian framework for count time series in disease surveillance, organized around three threads. First, a class of dynamic generalized transfer function models places the three modeling families inside a common modular state-space class built from six independent components. A hybrid variational algorithm combines sequential Monte Carlo on the latent trajectory with stochastic gradient ascent on the static parameters. Second, a multivariate extension to spatially connected regions, a Bayesian network Hawkes model, jointly estimates time-varying source-specific reproduction numbers and a sparse transmission network learned from data through a regularized horseshoe prior. The observed reproduction number at each
location is decomposed into a local component and an imported component. Posterior inference proceeds through a blocked Markov chain Monte Carlo sampler, with a particle Laplace variational counterpart developed for routine refits at larger spatial scales. Third, an R package implements the unified univariate framework through a compositional specification interface aligned with the six modular components, with the two inference engines available behind a single entry point. The methods are illustrated through simulation studies and applications to daily COVID-19 case counts from Santa Cruz County and from ten California counties.

Event Host: Meini Tang, Ph.D. Candidate, Statistical Science 

Advisor: Raquel Prado

Zoom: https://ucsc.zoom.us/j/97990210796?pwd=e59WbsNrYgYSITmMw0OIT5f1SQThEN.1

Passcode:  479460