gstat: block kriging variance

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gstat: block kriging variance

Julian M. Burgos
Dear list,

I am doing block kriging using the gstat package in order to estimate
the mean and variance of a variable over an irregular polygon. I do this
by passing to the krige function a SpatialPolyons object under the
newdata argument. The krige block variance is calculated (as I
understand) using the point-to-point, point-to-block and within-block
variograms.

My question is about how this calculation is done in gstat. It seems that
gstat's krige function deals with an irregular polygon by discretising
it using the spsample function to select a number of regular nodes in
the polygon (~500 by default).  But according to Goovaerts (1999,
Geostatistical Tools for Deriving Block-Averaged Values of Environmental
Attributes, p.91), this approach is difficult because "the variance of the
global estimator cannot be derived as a mere combination of the kriging
variances at each discretizing point".  But clearly gstat is producing a
krige variance estimate.  So how it is done?

At the end, what I want is to be sure that the variance estimate is
valid. :)

Many thanks for the clarification,

Julian

--
Julian Mariano Burgos, PhD
Hafrannsóknastofnun, rannsókna- og ráðgjafarstofnun hafs og vatna/
Marine and Freshwater Research Institute
Botnsjávarsviðs / Demersal Division
Skúlagata 4, 121 Reykjavík, Iceland
Sími/Telephone : +354-5752037
Bréfsími/Telefax:  +354-5752001
Netfang/Email: [hidden email]

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Re: gstat: block kriging variance

edzer


On 12/07/2017 05:28 PM, Julian M. Burgos wrote:

> Dear list,
>
> I am doing block kriging using the gstat package in order to estimate
> the mean and variance of a variable over an irregular polygon. I do this
> by passing to the krige function a SpatialPolyons object under the
> newdata argument. The krige block variance is calculated (as I
> understand) using the point-to-point, point-to-block and within-block
> variograms.
>
> My question is about how this calculation is done in gstat. It seems that
> gstat's krige function deals with an irregular polygon by discretising
> it using the spsample function to select a number of regular nodes in
> the polygon (~500 by default).  But according to Goovaerts (1999,
> Geostatistical Tools for Deriving Block-Averaged Values of Environmental
> Attributes, p.91), this approach is difficult because "the variance of the
> global estimator cannot be derived as a mere combination of the kriging
> variances at each discretizing point".  But clearly gstat is producing a
> krige variance estimate.  So how it is done?

It does exactly as what Goovaerts points to (read Journel & Huijbregts).

>
> At the end, what I want is to be sure that the variance estimate is
> valid. :)

Of course it is approximate, but that is what happens with most
numerical integration. It is easy to think of weird cases where the
whole thing is not so valid, but I think it is unlikely that you
spontaneously create them.

>
> Many thanks for the clarification,
>
> Julian
>
> --
> Julian Mariano Burgos, PhD
> Hafrannsóknastofnun, rannsókna- og ráðgjafarstofnun hafs og vatna/
> Marine and Freshwater Research Institute
> Botnsjávarsviðs / Demersal Division
> Skúlagata 4, 121 Reykjavík, Iceland
> Sími/Telephone : +354-5752037
> Bréfsími/Telefax:  +354-5752001
> Netfang/Email: [hidden email]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>

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

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