Faculty Publications

Bayesian Modeling And Inference For Geometrically Anisotropic Spatial Data

Document Type

Article

Keywords

Contour plot, Correlation functions, Importance sampling, Second-order stationary, Semivariogram, Wishart distribution

Journal/Book/Conference Title

Mathematical Geology

Volume

31

Issue

1

First Page

67

Last Page

83

Abstract

A geometrically anisotropic spatial process can be viewed as being a linear transformation of an isotropic spatial process. Customary semivariogram estimation techniques often involve ed hoc selection of the linear transformation to reduce the region to isotropy and then fitting a valid parametric semivariogram to the data under the transformed coordinates. We propose a Bayesian methodology which simultaneously estimates the linear transformation and the other semivariogram parameters. In addition, the Bayesian paradigm allows full inference for any characteristic of the geometrically anisotropic model rather than merely providing a point estimate. Our work is motivated by a dataset of scallop catches in the Atlantic Ocean in 1990 and also in 1993. The 1990 data provide useful prior information about the nature of the anisotropy of the process. Exploratory data analysis (EDA) techniques such as directional empirical semivariograms and the rose diagram are widely used by practitioners. We recommend a suitable contour plot to detect departures from isotropy. We then present a fully Bayesian analysis of the 1993 scallop data, demonstrating the range of inferential possibilities.

Department

Department of Mathematics

Original Publication Date

1-1-1999

DOI of published version

10.1023/A:1007593314277

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