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
Gaussian Variogram Positive Definite?
2 messages · Brian J. Lopes, 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 (Laborat?rio de Estat?stica e Geoinforma??o) Universidade Federal do Paran? 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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