Associations Between Gaussian Markov Random Fields and Gaussian Geostatistical Models with an Application to Model the Impact of Air Pollution on Human Health

Abstract

Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GMRFs) are two distinct approaches commonly used in modeling point referenced and areal data, respectively. In this dissertation, the relations between GMRFs and GGMs are explored based on approximations of GMRFs by GGMs, and vice versa. The proposed framework for the comparison of GGMS and GMRFs is based on minimizing the distance between the corresponding spectral density functions. In particular, the Kullback-Leibler discrepancy of spectral densities and the chi-squared distance between spectral densities are used as the metrics for the approximation. The proposed methodology is illustrated using empirical studies.

As a part of application, we model associations between speciated fine particulate matter (PM) and mortality. Mortality counts and PM are obtained at county and point levels, respectively. To combine the variables with different spatial resolutions, we aggregate PM to the county level. The aggregated PM are modeled using GMRFs, and associations between PM and mortality are investigated based on Bayesian hierarchical spatio-temporal framework. This model is applied to speciated PM[subscript 2.5] and monthly mortality counts over the entire U.S. region for 1999-2000. We obtain high relative risks of mortality associated to PM[subscript 2.5] in the Eastern and Southern California area. Particularly, NO₃ and crustal materials have greater health effects in the Western U.S., while SO₄ and NH₄ have more of an impact in the Eastern U.S. We show that the average risk associated with PM[subscript 2.5] is approximately twice what we obtained for PM₁₀.