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GEOSTATS: Gaussian Kriging

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  • Steven I . Pousty
    Thanks everyone for the quick and accurate responses. My original question Can you please help me decipher the following message from S+ spatial module... ...
    Message 1 of 1 , Oct 15, 1998
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      Thanks everyone for the quick and accurate responses.
      My original question

      Can you please help me decipher the following message from S+ spatial
      module...
      > elev.krige.gaus <- krige(Z~loc(X,Y), data = elev, covfun=gauss.cov,
      + range = 90, sill = 115)
      Error in .Fortran("ssukrige",: Covariance matrix is not positive
      definite
      Dumped
      Warning messages:
      Covariance matrix is not positive definite in: .Fortran("ssukrige",
      .
      I can get krige to work for a spherical model, but not for the
      gaussian. Is this a problem with a large matrix (over 900 elements in
      the elev data set) in S+?


      The solution (2 parts) provided by Stephen Kaluzny, J. Kern, K.
      Malakhanow, D. Allard, B. Ripley, A. Riding, D. Myers, and C.D. Lloyd:

      The first is that since many of my values are close together S+ is
      treating them as in the same area. Therefore I needed to increase the
      number of values used in the covariance function interpolation. It turns
      out that the "nc = " parameter controls this. I increased from the
      default (1000) to 500000 (the most allowed by the default memory
      settings).

      Concurrent with this I also added a nugget value of 3 to my model. As
      Donalsd Myers puts it:

      "However the problem with the Gaussian is a further complication. If you

      examine the graph of a Gaussian you see that it has values that are
      almost
      zero (assuming no nugget) for a considerable distance (relative to the
      range) hence when one uses the usual kind of a search neighborhood,
      i.e.,
      only the nearest data locations, this can result in lot of variogram
      values
      in the kriging matrix that are nearly zero. This likely results in an
      ill-conditionned matrix and depending on how they attempt to solve the
      system of equations it may not have a unique solution."

      But just increasing my nugget to 3 was not sufficient, therefore I
      increased the nugget AND the nc value. Hope this helps ppl in the
      future.

      Thanks again...
      Steven Pousty

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