Associate ProfessorDuquesne University
Bayesian Process-Convolution Approaches to Specifying Spatial Dependence Structure
This dissertation considers the Bayesian treatment of Gaussian random field models which incorporate uncertainty in the correlation structure of the field. This uncertainty is expressed in the context of a process convolution model for isotropic spatial processes, where the convolution kernel choice governs the structure of the spatial dependence. Nonparametric representation of the convolution kernels is shown to provide great latitude in describing spatial dependence. Specifically, we construct a unimodal, radially symmetric kernel with two dimensional domain by stacking cylinders of varying height and decreasing radii on top of one another in concentric fashion. Adjusting the radii and heights of the kernel-composing cylinders corresponds to an adjustment in the dependence structure of the Gaussian random field. We employ Bayesian methods to identify appropriate heights and radii in the context of: i) simulated data, so that model fit can be better understood while providing a means to compare nonparametric kernel specification with more traditional modeling approaches; and ii) wheat yield data, in an effort to determine the effects of different wheat varieties on wheat yield. Special consideration of edge effects in spatial analyses is given through two geostatistical applications: Chesapeake Bay pollution data and water surface temperature data about the coast of Florida. The Chesapeake Bay application introduces convolution kernel adjustment as a way to account for edges in the domain of a spatial process; standard spatial models make no accommodations for such edges. Kernel adjustment is shown to provide more realistic estimates of prediction uncertainty. The Florida application reveals how sensitive Gaussian random field predictions can be to distance metric choice. We propose a distance metric for use in select situations which can provide more realistic predictions.