[R-sig-Geo] indicator kriging with R

[Tim Peterson]

Hi Dafne and Edzer,

I too have been looking into gstat indicator kriging and simulation. My 
interest is because indicator simulations can (at least in GSLib) 
account for systems where extreme values are more/less spatially 
correlated than median values; that is the upper and lower threshold 
variograms can have a very different range to the mean values.

However, following 
http://rstudio-pubs-static.s3.amazonaws.com/10216_57cb0ffbb2e94586b29dfb1849dd49f0.html, 
I've just realised that gstat indicator kriging requires all indicator 
variograms to have an intrinsic correlation or be a linear model of 
coregionalisation, and hence requiring each variogram to have at least 
an equal range (FYI, to test this change line 'meuse.fit = fit.lmc(x, 
meuse.i)' to 'meuse.fit = fit.lmc(x, meuse.i,fit.ranges=TRUE)'). This is 
most likely because, unlike GSLib, gstat uses cokriging but this 
limitation defeats one of the advantages of indicator simulation over 
Gaussian simulation.

Anyway, can anyone propose a work around to this limitation? The only 
solution I can see is to krige each threshold independently but this 
does eliminate the option of accounting for cross-correlations between 
the thresholds or more advanced indicator feature; such as including 
spatially varying constraints eg 
http://www.mssanz.org.au/modsim2011/I9/peterson.pdf

Cheers

Tim


On 22/10/15 20:12, Dafne Berg wrote:
> Dear Edzer,
> yes it is exactly what I meant. Thanks for the confirmation that it is not
> yet implemented in gstat. I will have a look to gslib and the book.
>
> Thanks a lot
>
> Dafne
>
> On 22 October 2015 at 09:38, Edzer Pebesma <edzer.pebesma at uni-muenster.de>
> wrote:
>
>> Yes, this is what indicator kriging does.
>>
>> What you want is probably going back from the [0..1] estimated
>> probabilities to the original Z values. Gstat doesn't help here, but it
>> shouldn't be too hard to write a function for this. You need to make
>> assumptions about the distribution between different cutoff values, in
>> particular about both extreme (open) classes. I think the GSLIB and
>> Goovaerts books would be the first ones to look into.
>>
>> On 22/10/15 10:19, Dafne Berg wrote:
>>> Dear list,
>>> I am trying to do a indicator kriging of a continuous variable. I am
>>> especially interested in performing the "order relation correction". In
>> the
>>> documentation of "predict" in gstat it is mentioned as debug level 64
>>> (order relation violations (indicator kriging values before and after
>> order
>>> relation correction).
>>>
>>> However, when running predict I can only get the values in the range 0 to
>>> 1, as expected for indicator kriging.
>>>
>>> I am probably missing something very basic here, but I will be grateful
>> for
>>> any pointers in the right direction
>>>
>>> Thank you very much in advance
>>>
>>> Best wishes
>>>
>>> Dafne
>>>
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>>>
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>>>
>> --
>> Edzer Pebesma
>> Institute for Geoinformatics (ifgi),  University of Münster,
>> Heisenbergstraße 2, 48149 Münster, Germany; +49 251 83 33081
>> Journal of Statistical Software:   http://www.jstatsoft.org/
>> Computers & Geosciences:   http://elsevier.com/locate/cageo/
>> Spatial Statistics Society http://www.spatialstatistics.info
>>
>>
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-- 
----------------------
Dr. Tim Peterson

The Department of Infrastructure Engineering
The University of Melbourne, 3010 Australia
T: +61 3 8344 9950 <tel:%2B61%203%208344%209950>, M: +61 0438 385 937 
<tel:%2B61%200438%20385%20937>

Dept. profile : 
http://www.ie.unimelb.edu.au/people/staff.php?person_ID=141135
Research Gate : https://www.researchgate.net/profile/Tim_Peterson7
Google Scholar: 
http://scholar.google.com.au/citations?user=kkYJLF4AAAAJ&hl=en&oi=ao

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