Spatio-temporal methods for applications in biological and environmental studies

Abstract

With advances in technology over the past few decades, the availability and resolution of spatial and spatio-temporal data have increased dramatically. As a result, many research fields now face new analytical and computational challenges in effectively utilizing such complex data. This thesis develops spatio-temporal models within the Bayesian framework to address practical problems in epidemiology, engineering, and environmental science.

In Chapter 2, we develop a Bayesian hierarchical model to investigate the temporal and spatial evolution of spike protein sequences of SARS-CoV-2, which serve as critical targets for vaccines and neutralizing antibodies. To reduce dimensionality and facilitate interpretation, the sequences are grouped into representative clusters based on their similarity. The robustness of the model is demonstrated through simulation studies. We then apply the model to real-world sequence data and the results uncover clear geographical differences in the spread of SARS-CoV-2 variants.

In Chapter 3, we propose a Bayesian hierarchical model to address the challenge of spatial misalignment in spatio-temporal data using the INLA-SPDE approach. The research is motivated by the study of harmful algal bloom (HAB) events in environmental science, where the convention is to conduct separate analyses based on either in situ samples or satellite images. Our methodology combines the different data sources in a “fusion” model via the construction of projection matrices in both spatial and temporal domains. Simulation studies demonstrate that the proposed fusion model generally outperforms standalone models in both parameter estimation and predictive accuracy. This fusion framework thus represents an important step toward a unified characterization of bloom dynamics.

In Chapter 4, we investigate the effects of the spatial arrangement of knots on the flexural properties of lumber crossarms using Bayesian methods. The proposed frameworks integrate a deterministic analysis of induced mechanical stress with a Bayesian modeling approach that captures uncertainties in the failure mechanisms. To further enhance model flexibility, we extend the framework to a Bayesian mixture model, which enables the identification and quantification of multiple underlying failure mechanisms observed in lumber testing.