[R-sig-Geo] Why is the covariance in Universal Kriging modeled this way in lectures by Prof. Edzer Pebesma?

[Edzer Pebesma]

On 11/22/2017 12:09 AM, Joelle k. Akram wrote:
> Greetings,
> 
> There is code for Universal Kriging from Prof. Edzer Pebesma in GitHub<https://github.com/edzer/mstp/blob/master/lec7.Rmd>.

https://edzer.github.io/mstp/lec7.html

gives you the rendered version.

> 
> The covariance function is defined as follows:
> 
> cov = function(h) exp(-h)
> 
> And defined without any variogram modeling/generation to produce partial sill, range or nugget parameters for defining the covariance matrix.

Well, it implies nugget=0, sill=1 and range parameter=1, it was the
shortest covariance function I could think of.

> 
> If  I want to include a regularization term to account for singularity effects caused due to close spatial points, how do I modify the matrix computation for computing the 'beta' coefficients ?

Add a nugget (i.e. add a constant to the diagonal of V)?

> 
> I know there are standard formulae for different models (e.g. Matern, Exp,etc). But I would like to retain the simple cov function defined above and possibly use a regularizer (like ridge regression) to account for a nugget-like effect.
> 
> thanks,
> 
> Chris
> 
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> 
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-- 
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081