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

[Joelle k. Akram]

thank you for clarifying Prof. Pebesma. I have a couple more question for you regarding the inclusion of a

nugget to the diagonals of V. As we know,there are 2 covariances, V and v; one for the existing coordinates (i.e., V) and the other for the distances between these existing coordinates and other new locations (i.e., v).


I) Assuming unscaled coordinates in latitude/longitude; should the Nugget theoretically be a small value (lets say typically less than <1) or does it depend on other the dataset's spatial distribution,etc?


2) When computing Beta coefficients as in you lecture 7 in github, do we have to add the nugget term to both V and v or only one of them?


thank you,

Chris Akram




________________________________
From: R-sig-Geo <r-sig-geo-bounces at r-project.org> on behalf of Edzer Pebesma <edzer.pebesma at uni-muenster.de>
Sent: November 22, 2017 6:16 AM
To: r-sig-geo at r-project.org
Subject: Re: [R-sig-Geo] Why is the covariance in Universal Kriging modeled this way in lectures by Prof. 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>.

edzer/mstp<https://github.com/edzer/mstp/blob/master/lec7.Rmd>
github.com
mstp - Course slides: modelling spatio-temporal processes




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

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