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

Edzer Pebesma edzer.pebesma at uni-muenster.de
Tue Aug 26 08:36:19 CEST 2008


Jin, you are right. A suggestion (or my usual question here) is to 
carefully look at the neighbourhood selection settings for the secondary 
variable(s), when they come as coverage rather than points.

A typical answer is "use collocated cokriging". To find out how to do 
that, look into the help of function gstat and search for the "merge" 
parameter.
--
Edzer

Jin.Li at ga.gov.au wrote:
> Hi Edzer,
> Thank you very much for the clarification.
> In my current study, I am going to use a few variables like bathymetry,
> distance to coastline, as secondary information to interpolate one primary
> variable (e.g. mud content). To get the estimations as from OCK for only one
> primary variable, I guess I need to feed all these primary and secondary
> variables in the multivariate kriging as in the ex11.cmd in demo(examples),
> retain the prediction and associate se for the primary variable and treat the
> prediction and associate se for the secondary variables as redundant
> information. Am I right? Or any further suggestions? 
> Thanks,
> Jin
>
>
> -----Original Message-----
> From: Edzer Pebesma [mailto:edzer.pebesma at uni-muenster.de] 
> Sent: Monday, 25 August 2008 5:07
> 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,
>
> 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]]
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> R-sig-Geo at stat.math.ethz.ch
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>   
>>>     
>>>       
>>   
>>     
>
>   

-- 
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/




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