1276GEOSTATS: Linear Model of Coregionalization -- Devil's Advocate
- Jun 4, 1999Let 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.
Todd Mowrer, Research Scientist
Rocky Mountain Research Station
USDA Forest Service
Fort Collins, Colorado 80526 USA
tel: +970 498-1255
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