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Continuous spatial process models for spatial extreme values

Publication ,  Journal Article
Sang, H; Gelfand, AE
Published in: Journal of Agricultural, Biological, and Environmental Statistics
January 28, 2010

We propose a hierarchical modeling approach for explaining a collection of point-referenced extreme values. In particular, annual maxima over space and time are assumed to follow generalized extreme value (GEV) distributions, with parameters μ, σ, and ξ specified in the latent stage to reflect underlying spatio-temporal structure. The novelty here is that we relax the conditionally independence assumption in the first stage of the hierarchial model, an assumption which has been adopted in previous work. This assumption implies that realizations of the the surface of spatial maxima will be everywhere discontinuous. For many phenomena including, e. g., temperature and precipitation, this behavior is inappropriate. Instead, we offer a spatial process model for extreme values that provides mean square continuous realizations, where the behavior of the surface is driven by the spatial dependence which is unexplained under the latent spatio-temporal specification for the GEV parameters. In this sense, the first stage smoothing is viewed as fine scale or short range smoothing while the larger scale smoothing will be captured in the second stage of the modeling. In addition, as would be desired, we are able to implement spatial interpolation for extreme values based on this model. A simulation study and a study on actual annual maximum rainfall for a region in South Africa are used to illustrate the performance of the model. © 2009 International Biometric Society.

Duke Scholars

Published In

Journal of Agricultural, Biological, and Environmental Statistics

DOI

EISSN

1537-2693

ISSN

1085-7117

Publication Date

January 28, 2010

Volume

15

Issue

1

Start / End Page

49 / 65

Related Subject Headings

  • Statistics & Probability
  • 49 Mathematical sciences
  • 41 Environmental sciences
  • 31 Biological sciences
  • 06 Biological Sciences
  • 05 Environmental Sciences
  • 01 Mathematical Sciences
 

Citation

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Sang, H., & Gelfand, A. E. (2010). Continuous spatial process models for spatial extreme values. Journal of Agricultural, Biological, and Environmental Statistics, 15(1), 49–65. https://doi.org/10.1007/s13253-009-0010-1
Sang, H., and A. E. Gelfand. “Continuous spatial process models for spatial extreme values.” Journal of Agricultural, Biological, and Environmental Statistics 15, no. 1 (January 28, 2010): 49–65. https://doi.org/10.1007/s13253-009-0010-1.
Sang H, Gelfand AE. Continuous spatial process models for spatial extreme values. Journal of Agricultural, Biological, and Environmental Statistics. 2010 Jan 28;15(1):49–65.
Sang, H., and A. E. Gelfand. “Continuous spatial process models for spatial extreme values.” Journal of Agricultural, Biological, and Environmental Statistics, vol. 15, no. 1, Jan. 2010, pp. 49–65. Scopus, doi:10.1007/s13253-009-0010-1.
Sang H, Gelfand AE. Continuous spatial process models for spatial extreme values. Journal of Agricultural, Biological, and Environmental Statistics. 2010 Jan 28;15(1):49–65.
Journal cover image

Published In

Journal of Agricultural, Biological, and Environmental Statistics

DOI

EISSN

1537-2693

ISSN

1085-7117

Publication Date

January 28, 2010

Volume

15

Issue

1

Start / End Page

49 / 65

Related Subject Headings

  • Statistics & Probability
  • 49 Mathematical sciences
  • 41 Environmental sciences
  • 31 Biological sciences
  • 06 Biological Sciences
  • 05 Environmental Sciences
  • 01 Mathematical Sciences