Abstract:

Isotropic covariance functions are routinely adopted in specifying models for point-referenced spatial data. Implicit in such modeling is the assumption that spatial dependence is not directional. Geometric anisotropic models offer a class of specifications which incorporate directional dependence. They have received little attention in the literature because their associated parameters increase and become difficult to identify as we increase richness of the function. This paper aims to illuminate when and how much such models for random effects in geostatistical settings improve predictive performance, and to explore a Bayesian framework to facilitate fitting such models. We show that geometric anisotropy yields better predictive performance when the data significantly departs from isotropy (anisotropy ratio is much greater than one), and the improvement is more prominent when spatial variance is greater than pure error. The improvement in predictive performance is illustrated through modeling scallop catches data. We perform full Bayesian inference on all model parameters using Metropolis algorithm.

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Advisor: Dr. Alan Gelfand