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GEOSTATS: gaussian and spherical variograms

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  • Donald Myers
    A further comment appropro Gregoire s comment of 22 Sept in repsonse to Oliveira s comment of 19 September. It is well-known (although perhaps not written
    Message 1 of 1 , Sep 24, 1997
      A further comment appropro Gregoire's comment of 22 Sept in
      repsonse to Oliveira's comment of 19 September.

      It is well-known (although perhaps not written down anywhere)
      that it is best to use at least a small nugget with a Gaussian
      model otherwise the kriging coefficient matrix is likely to
      be ill-conditioned, making the results very unstable (numerically).
      As for MLE estimation of variogram parameters this always
      requires distributional assumptions that may not be valid or
      at least very reasonable.

      Any valid model (conditionally negative definite for a variogram)
      will result in a unique solution for the kriging equations, i.e.
      the coefficient matrix is invertible. It doesn't matter
      whether the model "appears" to fit the sample variogram or
      not. Obviously that doesn't mean that the kriging results
      will be "good", fitting variograms is partly science and
      partly an art. The good and the bad part of kriging is that
      the weights in the kriging estimator do not directly depend on
      the data and do not depend on any distributional assumptions,
      I say directly since few if any would apply kriging without
      making some effort to match the variogram model to the data.
      Note that some software does exactly that however, SURFER
      uses a linear variogram model and the slope of the model has no
      effect on the kriging weights (only on the kriging variances).
      Some other software that supposedly incorporates kriging but
      does not allow the user to input a model does the same thing.

      The question of whether the results (from kriging) are "good" is
      not a statistical nor a mathematical question.

      Donald E. Myers
      Department of Mathematics
      University of Arizona
      Tucson, AZ 85721
      http://www.u.arizona.edu/~donaldm
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