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1276GEOSTATS: Linear Model of Coregionalization -- Devil's Advocate

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  • Todd Mowrer
    Jun 4, 1999
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      Let me precede my comment with a clear statement that I would never
      ignore the linear model of coregionalization (LMC) in my analyses.
      However, there are citable instances in the non-theoretical
      subject-matter literature of people apparently ignoring it, and it is
      conceivable that one might be asked to peer review such an article.
      Now for argument's sake, from a "devil's advocate" position, my
      question is: What is the consequence of negative cokriging variances?
      Does one no longer have a best linear unbiased estimator? It would seem
      to me that one would still obtain a minimum variance (from the
      semi-variogram) weighted combination of measured values to estimate
      unknown locations. If you don't use cokriging variances for anything,
      e.g., co-conditional simulation, (or even look at them, much less
      mention them ), why care?
      Now if you can't invert a matrix, you'll know it. And if you get a
      "spikey" response surface for your primary response variable, that's
      obviously not good for predictive purposes. But if you get a
      "reasonable" response surface (particularly one with a lower
      cross-validation score than from a conservative coregionalized model),
      then it would seem one has gotten off free, perhaps by stumbling into a
      set of (cross) variograms that work (conform to the LMC). Thank you for
      your comments to help me understand the LMC better.
      Best regards...
      Todd Mowrer, Research Scientist
      Rocky Mountain Research Station
      USDA Forest Service
      Fort Collins, Colorado 80526 USA
      tel: +970 498-1255
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