[R-sig-Geo] Gaussian Variogram Positive Definite?

[Paulo Justiniano Ribeiro Jr]

Brian

Gaussian variograms are known to generate numeric problems
in case you have the nugget parameter equals to zero.
This occours because the almost flat
and with points very close to each other the covariance matrix will be
nearly-singular -- numerically singular.

Soma alternatives are:
1. choose another covariance model:
   for instance a Matern model with smoothness parameter  to ensure a
behaviour which is similar to the gaussian (e.g. kappa = 4 in the
parametrisation used in geoR

2. add a small nugget to the model to make the covariance matrix
diagonally dominant

hope this helps

best
P.J.




Paulo Justiniano Ribeiro Jr
LEG (Laboratório de Estatística e Geoinformação)
Universidade Federal do Paraná
Caixa Postal 19.081
CEP 81.531-990
Curitiba, PR  -  Brasil
Tel: (+55) 41 3361 3573
Fax: (+55) 41 3361 3141
e-mail: paulojus AT  ufpr  br
http://www.leg.ufpr.br/~paulojus

On Fri, 31 Aug 2007, Brian J. Lopes wrote:

> Hello All:
>
> I've been banging my head against the wall about this for quite some
> time now, and I can't seem to find any reference on the matter.  I'm
> trying to calculate MLE estimates for the Gaussian variogram, but it
> seems that I consistently reach the point where the covariance matrix is
> not positive definite, as dictated by the Cholesky decomposition, even
> though the range parameter is indeed positive (note that I am also
> incorporating a nugget to sill ratio as well).  Has anybody else
> experienced this problem?  Better yet, does anybody have any references
> that discuss the situation, or how I can avoid it?
>
> The data is a bit large, so if an example is necessary I'll try to see
> if I can come up with something reasonable.
>
> Thanks,
> Brian
>
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