Anisotropic Matérn correlation and spatial prediction using REML

  • Kathryn A. Haskard
  • Brian R. Cullis
  • Arūnas P. Verbyla


The Matérn correlation function provides great flexibility for modeling spatially correlated random processes in two dimensions, in particular via a smoothness parameter, whose estimation allows data to determine the degree of smoothness of a spatial process. The extension to include anisotropy provides a very general and flexible class of spatial covariance functions that can be used in a model-based approach to geostatistics, in which parameter estimation is achieved via REML and prediction is within the E-BLUP framework. In this article we develop a general class of linear mixed models using an anisotropic Matérn class with an extended metric. The approach is illustrated by application to soil salinity data in a rice-growing field in Australia, and to fine-scale soil pH data. It is found that anisotropy is an important aspect of both datasets, emphasizing the value of a straightforward and accessible approach to modeling anisotropy.

Key Words

Geometric anisotropy Kriging Model-based geostatistics Residual maximum likelihood Spatial correlation 


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Copyright information

© International Biometric Society 2007

Authors and Affiliations

  • Kathryn A. Haskard
    • 1
  • Brian R. Cullis
    • 2
  • Arūnas P. Verbyla
    • 3
  1. 1.BiometricsSASARDIAdelaideAustralia
  2. 2.New South Wales Department of Primary IndustriesWagga WaggaAustralia
  3. 3.School of Agriculture, Food and WineThe University of AdelaideGlen OsmondAustralia

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