Date of Award

Fall 2016

Project Type

Dissertation

Program or Major

Statistics

Degree Name

Doctor of Philosophy

First Advisor

Ernst Linder

Second Advisor

Linyuan Li

Third Advisor

Haiying Wang

Abstract

In this dissertation, the flexibility of Bayesian hierarchical models specified using a latent Gaussian Markov Random Field (GMRF) are evaluated for use in analyzing large complex spatial and spatio-temporal data with the goal of contributing to an interdisciplinary effort of developing an eco-epidemiological model that quantifies the relationship between remotely sensed water quality and the incidence of ALS (Amyotrophic Lateral Sclerosis or Lou Gehrig’s Disease) over large areas such as Northern New England (NNE).

In particular, a Log-Gaussian Cox Process (LGCP) specified by the logarithm of a GMRF on a regular lattice is shown to allow for simultaneous estimation of the spatial distribution of ALS risk and its relationship to remotely sensed water quality metrics. This approach improves on previous analyses of the dataset considered by explicitly accounting for the spatial uncertainty in determining locations of ALS “hotspots” needed in the estimation of the hotspots’ relationship to the water quality of lakes in NNE.

Finally, since warming lake temperatures have been associated with more frequent cyanobacteria blooms (blue-green algae), which is a possible risk factor of ALS, a spatially varying coefficient model specified with an Extended Autoregression (EAR) latent process is used in an analysis of remotely sensed surface water temperatures of Lake Champlain. New interpretations of the EAR model are suggested and issues relating to its parameter’s identifiability are investigated.

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