[R-sig-Geo] gstat: block kriging variance

[Edzer Pebesma]

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: julian.burgos at hafogvatn.is
> 
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-- 
Edzer Pebesma
Institute for Geoinformatics
Heisenbergstrasse 2, 48151 Muenster, Germany
Phone: +49 251 8333081