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

[Brian J. Lopes]

Paulo,

Sorry for the delay in response, but making the changes you recommended 
opened a whole bunch of other bugs in my C code.  Thank you very much 
for the advice, it indeed did help me to get my MLE to converge 
consistently by incorporating a small nugget.  I'm still having trouble 
getting consistent estimates with the Matern model, but that's beyond 
the scope of the email.

I should also thank Terry for the advice as well.

Thanks,
Brian

Paulo Justiniano Ribeiro Jr wrote:
> 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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>>


-- 
Brian J. Lopes
PhD Student
Department of Statistics and Operations Research
University of North Carolina at Chapel Hill

To know that we know what we know, and that we do not know what we do
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Confucius): Walden