[R-sig-Geo] maxdist for kriging with an external drift

[Paulo Justiniano Ribeiro Jr]

May be worth adding here that, despite algorithms and the
"funny naming conventions" (good descrition Edzer!)
SK and others are diferent in the following way:

SK, as described in Edzer post, assumes you **know** the mean, in other 
words, there is no uncertainty about it.
On the other hand, variants such as OK, UK, KED, SKlm uses (explicitly 
or implicitly) estimated means.
Therefore, such uncertainty has to be propagated and reflected in the 
predictions.

Suposse the fixed mean in SK is the same as the (implicitly) estimated by 
OK. The point predictions will be the same, however, the uncertainty 
around them will not (and should not) refleting  the uncertainty (or lack 
of it) in the process mean.
The prediction variance expressions for SK ond OK will reflect this
whatever the kriging neighborhood is used.

best
P.J.

On Tue, 26 Jan 2010, Edzer Pebesma wrote:

> Oh, geostatistics and its funny naming conventions!
>
> I see local models vs. global models as a completely different modelling 
> aspect (model decision, basically) then the SK/OK/UK differences. When 
> building on the same tradition / body of literature you quote: in that case 
> KED would be a special form of UK, having only a single non-coordinate 
> predictor called 'external drift'.
>
> In my eyes (and that of the literature with more mathematical statistical 
> grounding, such as Cressie 1993 and others), the difference between SK on the 
> one hand and OK/UK on the other is that SK assumes that you know the mean or 
> mean structure. SKlm is then residual kriging added to a known mean function.
>
> In the gstat R package you obtain SK by specifying a beta value (for the 
> mean); SKlm by specifying one or more predictors and passing the (known) 
> regression coefficients as beta; you obtain OK/UK by not specifying beta; a 
> formula ending on ~1 results in OK with an unknown mean only.
>
> Ah, and then SK = simple kriging, OK = ordinary kriging, UK = universal 
> kriging.
> --
> Edzer
>
> Cutberto Uriel Paredes Hernández wrote:
>> Dear Edzer,
>> 
>> Would it be correct to say then that if a neighbourhood is specified
>> in the krige command the result would be that of Kriging with an
>> External Drift (KED), otherwise it would be that of Simple Kriging
>> with varying local means (SKlm)?
>> 
>> Apologies for posting on this thread but I was about to post a
>> similiar question.
>> 
>> Thanks, Cutberto.
>> 
>> 2010/1/26 Edzer Pebesma <edzer.pebesma at uni-muenster.de>:
>> 
>>> Yes, that is right.
>>> 
>>> Els Verfaillie wrote:
>>> 
>>>> Dear list,
>>>> 
>>>> 
>>>> I want to use Kriging with an external drift for a sedimentological
>>>> dataset
>>>> of grain-size that has a linear relation with the depth.
>>>> Am I correct that when I set a 'maxdist' using the krige command, that a
>>>> trend for the primary variable (grain-size) is calculated as a local
>>>> linear
>>>> function of the secondary variable (depth)? Is this function thus
>>>> different
>>>> for each interpolation window?
>>>> 
>>>> d50.ked.dir50 <- krige(D50F~depth, locations=ds50, newdata=Depth,
>>>> model=d50.fit.var.50, nmin=2, nmax=16, maxdist=9000)
>>>> 
>>>> 
>>>> Thank you for your help.
>>>> 
>>>> 
>>>> Best regards,
>>>> 
>>>> Els Verfaillie
>>>> 
>>>> 
>>>> ______________________________________________
>>>> 
>>>> Dr. Els Verfaillie
>>>> 
>>>> Carto-GIS cluster
>>>> 
>>>> Ghent University (UGent) - Department of Geography
>>>> 
>>>> ______________________________________________
>>>> 
>>>> 
>>>> 
>>>>
>>>>        [[alternative HTML version deleted]]
>>>> 
>>>> _______________________________________________
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>>>>
>>>> 
>>> --
>>> Edzer Pebesma
>>> Institute for Geoinformatics (ifgi), University of Münster Weseler Straße
>>> 253, 48151 Münster, Germany. Phone: +49 251 8333081, Fax: +49 251 8339763
>>>  http://ifgi.uni-muenster.de http://www.52north.org/geostatistics
>>>  e.pebesma at wwu.de
>>> 
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>>>
>>> 
>
> -- 
> Edzer Pebesma
> Institute for Geoinformatics (ifgi), University of Münster Weseler Straße 
> 253, 48151 Münster, Germany. Phone: +49 251 8333081, Fax: +49 251 8339763 
> http://ifgi.uni-muenster.de http://www.52north.org/geostatistics 
> e.pebesma at wwu.de
>
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>

Paulo Justiniano Ribeiro Jr
LEG (Laboratorio de Estatistica e Geoinformacao)
Universidade Federal do Parana
Caixa Postal 19.081
CEP 81.531-990
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Tel: (+55) 41 3361 3573
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e-mail: paulojus AT  ufpr  br
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