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

[Joelle k. Akram]

hi Prof. Pebesma,


just to follow up on my question about adding the nugget term to both V and v from your lecture 7 on github.

I do not want an exact interpolator. Instead I want to do a smoothing interpolator using UnivKrig. Would you

recommend only adding the nugget to V only ? and set the nugget=0 for defining v (whilst retaining the same psill and range used for defining V).

thanks
Chris Akram

________________________________
From: Edzer Pebesma <edzer.pebesma at uni-muenster.de>
Sent: November 22, 2017 2:55 PM
To: Joelle k. Akram; 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 10:23 PM, Joelle k. Akram wrote:
> 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?
>

I would say it should depend on the data.

>
> 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?

For a nugget, by definition to each of them; if you'd only add it to V
you no longer obtain an exact interpolator (i.e., you no longer predict
the data value at data locations); if your measured process is subject
to a measurement error, this may however be preferred.

>
>
> 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>.
[https://avatars2.githubusercontent.com/u/520851?s=400&v=4]<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



>
> edzer/mstp <https://github.com/edzer/mstp/blob/master/lec7.Rmd>
[https://avatars2.githubusercontent.com/u/520851?s=400&v=4]<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



> 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
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
R-sig-Geo Info Page - SfS – Seminar for Statistics | ETH ...<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
stat.ethz.ch
A mailing list for discussing the development and use of R functions and packages for handling and analysis of spatial, and particularly geographical, data.




--
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081

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