UC Santa Cruz

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. Discrete-time Hawkes-type models, 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 intrinsic 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 block Markov chain Monte Carlo sampler, with a particle Laplace variational counterpart developed for routine updates 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.