[R-sig-Geo] UK, KED or OCK? [SEC=UNCLASSIFIED]

[Edzer Pebesma]

Hi Jin,

Jin.Li at ga.gov.au wrote:
> Hi Edzer,
>
> It is true that demo(cokriging) shows that it is using ordinary cokriging,
> but if we examine its formula, it kriges multiple primary variables without
> secondary information. The ordinary co-kriging (OCK) I mentioned (such as
> those defined in: Goovaerts, 1997. Geostatistics for Natural Resources
> Evaluation.) interpolates one primary variable using one or more secondary
> variables to improve the estimations. I guess that is the key difference.
>   
Ordinary cokriging and multivariate kriging (as e.g. described in the 
original papers by Don Myers in Math Geol, or in Noel Cressie's book, or 
Ver Hoef and Cressie MG) are mathematically equivalent. If you would 
constrain multivariate kriging to kriging of the first variable only 
(the Goovaerts formulation), you end up with exactly the same values 
(and gain a little CPU wise).
> In demo(examples), the multivariate kriging as shown in ex11.cmd claims it is
> using ordinary cokriging, but it actually has no difference with that in
> demo(cokriging), i.e. it kriges multiple primary variables without secondary
> information.
>   
It uses the "secondary" information for the first because a cross 
variogram is defined.
> I thought multiple kriging in ex10.cmd in demo(examples) was the one I was
> after. After a further check, it is the ordinary kriging.  I hope this
> explanation is clear enough. 
>   
No, this "multiple" kriging kriges each variable completely 
independenlty, as no cross variogram is defined. It was introduced in 
gstat stand-alone to speed up multiple kriging settings (think of 
several indicators derived from the same variable) as it re-uses the 
neighbourhood selection. I wasn't aware of it, but it seems to work in 
the R package as well (set up a cokriging gstat object, but don't define 
cross variograms).
> Thanks a lot for any further suggestions.
>
> Best wishes,
> Jin
>
> -----Original Message-----
> From: Edzer Pebesma [mailto:edzer.pebesma at uni-muenster.de] 
> Sent: Monday, 18 August 2008 6:32
> To: Li Jin
> Cc: r-sig-geo at stat.math.ethz.ch
> Subject: Re: [R-sig-Geo] UK, KED or OCK? [SEC=UNCLASSIFIED]
>
> Hi Jin,
>
> Which differences do you exactly refer to? I'd say that what happens in 
> demo(cokriging) is ordinary cokriging. As it says:
> ...
> [using ordinary cokriging]
>
> Best regards,
> --
> Edzer
>
> Jin.Li at ga.gov.au wrote:
>   
>> Hi All,
>>
>>  
>>
>> I am going to compare a few spatial interpolation techniques including
>> kriging with an external drift (KED) and ordinary co-kriging (OCK) (such as
>> those defined in: Goovaerts, 1997. Geostatistics for Natural Resources
>> Evaluation.) to interpolate marine sediment data (mud content in this case)
>> using bathymetry as a secondary variable. However, it seems that the
>>     
> ordinary
>   
>> cokriging in gstat as shown in demo(cokriging) is different from the OCK we
>> planned to use. Is it possible to do such OCK in gstat? Any comments and
>> example? Thanks.
>>
>>  
>>
>> As to KED, I tried 
>>
>>   
>>     
>>> vgm1 <- variogram(sqrt(mud)~bathy, data.file.dev)
>>>     
>>>       
>>   
>>     
>>> model.1 <- fit.variogram(vgm1,vgm(1,"Sph",5,1))
>>>     
>>>       
>>   
>>     
>>> # plot(vgm1, model.1)
>>>     
>>>       
>>   
>>     
>>> coordinates(data.file.pred) = ~LON+LAT
>>>     
>>>       
>>   
>>     
>>> mud.ok <- krige(sqrt(mud)~bathy, data.file.dev, data.file.pred, model =
>>>     
>>>       
>> model.1)
>>
>> [using universal kriging]
>>
>>  
>>
>>   
>>     
>>> vgm1 <- variogram(sqrt(mud)~LON+LAT, data.file.dev)
>>>     
>>>       
>>   
>>     
>>> model.1 <- fit.variogram(vgm1,vgm(1,"Sph",5,1))
>>>     
>>>       
>>   
>>     
>>> # plot(vgm1, model.1)
>>>     
>>>       
>>   
>>     
>>> coordinates(data.file.pred) = ~LON+LAT
>>>     
>>>       
>>   
>>     
>>> mud.ok <- krige(sqrt(mud)~LON+LAT, data.file.dev, data.file.pred, model =
>>>     
>>>       
>> model.1)
>>
>> [using universal kriging]
>>
>>  
>>
>> Both of them are UK. But the first one seems regression kriging. Is it
>> identical to KED in this case? If not, any comments and examples of KED are
>> appreciated.
>>
>>  
>>
>> Cheers,
>>
>>  
>>
>> Jin
>>
>> --------------------------------------------
>>
>> Jin Li, PhD
>>
>> Spatial Modeller/
>>
>> Computational Statistician
>>
>> Marine & Coastal Environment
>>
>> Geoscience Australia
>>
>>
>>
>> Ph: 61 (02) 6249 9899
>>
>> Fax: 61 (02) 6249 9956
>>
>> email: jin.li at ga.gov.au <mailto:jin.li at ga.gov.au> 
>>
>> --------------------------------------------
>>
>>
>> 	[[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/