Scalable Methods for Modeling Dynamic Spatio-Temporal Data
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Hsu, Yu-Lin
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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.
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Keywords
Spatio-temporal models, Spatial interpolator, Basis expansion, Computationally efficient, Bayesian hierarchical modeling