# [S] Gaussian Kriging

Steven I . Pousty (sip94001@uconnvm.uconn.edu)
Thu, 15 Oct 1998 11:06:39 -0400

Thanks everyone for the quick and accurate responses.
My original question

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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