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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