Abstract:

Statistical inference for nonlinear and non-Gaussian dynamic models of moderate and high dimensions is an open research area. Such models may require simulation-based methodology when linearization and Gaussian approximations are not appropriate. The particle filter has allowed likelihood-based inference for such problems when the dimension of the problem is small, but degrades in performance as the dimension of the model increases. This is due to the exponential growth in the volumes to be represented by Monte Carlo simulations as dimension grows. In epidemiology, this curse of dimensionality problem occurs when we jointly model the epidemiological dynamics in a group of neighboring towns that are coupled via immigration or travel. In this dissertation, I present two innovations that make methodological and practical progress in data analysis for nonlinear and non-Gaussian dynamic models with coupled disease models as the primary problem of interest. All work was done jointly with my co-advisers Dr. Ionides and Dr. King as well as Dr. Joonha Park and Allister Ho.

The first innovation is a group of simulation-based methods that take advantage of localization - the idea that dependence between far enough spatial units in a spatially coupled model is negligible - to make approximations enabling scalable likelihood estimation. I show theoretical results for the methods and examples of its use on three different models, including a coupled measles model in England.

The second innovation is the open-source R package spatPomp. This package builds on the strengths of the pomp package for model development and testing while adding new components that allow the implementation of new methods that are tailored for moderate- and high-dimensional problems. Various algorithms and utility functions are implemented and the package is available on the Comprehensive R Archive Network (CRAN) repository of packages.