Abstract:
Hierarchical spatio-temporal models have been developed to model complex datasets exhibiting
spatio-temporal (ST) autocorrelation; however, many of these models are purely descriptive
and do not explicitly model the underlying dynamic processes. Animal movement
or general movement behaviors are examples of such dynamic processes; that is, animals, or
agents, move from one place to another over time, and their migration behavior can change
with time and as well as their current (and past) locations. The motivating example for this
thesis aims to model the spatio-temporal movement of the Eurasian collared-dove within
the continental United States from 2001-2010. Existing studies have modeled animal movement
using a reaction-diffusion equation or other systems of differential equation. Recently,
dynamic spatio-temporal models (DSTMs) have incorporated these physical processes into
a Bayesian hierarchical modeling framework. While DSTMs are extremely flexible, they
can be computationally costly to fit and do not scale well to high-dimensional observations.
In this thesis, I propose a computationally-efficient method to fit DSTMs to large spacetime
count-valued datasets. The proposed scalable DSTM utilizes spatial basis functions
to summarize the high-dimensional data as well as a spatial interpolator to assimilate observations
at irregularly-spaced locations.
I demonstrate the approach on simulated examples as well as a real-world dataset that
tracks the prevalence of the Eurasian collared dove. Through a comparative analysis, the
proposed approach is evaluated against a competing method with respect to goodness-of-fit
and uncertainty quantification. In addition, I compare the model-fitting walltimes to assess
the associated computational costs. The thesis concludes with a summary of the main
contributions, discussion of key limitations, and directions for future research.
