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Bayesian modeling and inference for geometrically anisotropic spatial data

Publication ,  Journal Article
Ecker, MD; Gelfand, AE
Published in: Mathematical Geology
January 1, 1999

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.

Duke Scholars

Published In

Mathematical Geology

DOI

ISSN

0882-8121

Publication Date

January 1, 1999

Volume

31

Issue

1

Start / End Page

67 / 83

Related Subject Headings

  • Geochemistry & Geophysics
  • 0914 Resources Engineering and Extractive Metallurgy
  • 0403 Geology
  • 0102 Applied Mathematics
 

Citation

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Ecker, M. D., & Gelfand, A. E. (1999). Bayesian modeling and inference for geometrically anisotropic spatial data. Mathematical Geology, 31(1), 67–83. https://doi.org/10.1023/A:1007593314277
Ecker, M. D., and A. E. Gelfand. “Bayesian modeling and inference for geometrically anisotropic spatial data.” Mathematical Geology 31, no. 1 (January 1, 1999): 67–83. https://doi.org/10.1023/A:1007593314277.
Ecker MD, Gelfand AE. Bayesian modeling and inference for geometrically anisotropic spatial data. Mathematical Geology. 1999 Jan 1;31(1):67–83.
Ecker, M. D., and A. E. Gelfand. “Bayesian modeling and inference for geometrically anisotropic spatial data.” Mathematical Geology, vol. 31, no. 1, Jan. 1999, pp. 67–83. Scopus, doi:10.1023/A:1007593314277.
Ecker MD, Gelfand AE. Bayesian modeling and inference for geometrically anisotropic spatial data. Mathematical Geology. 1999 Jan 1;31(1):67–83.

Published In

Mathematical Geology

DOI

ISSN

0882-8121

Publication Date

January 1, 1999

Volume

31

Issue

1

Start / End Page

67 / 83

Related Subject Headings

  • Geochemistry & Geophysics
  • 0914 Resources Engineering and Extractive Metallurgy
  • 0403 Geology
  • 0102 Applied Mathematics