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kriging [SEC=UNCLASSIFIED]

Li Jin 
Hi All,

I have recently reviewed the spatial interpolation methods for environmental
scientists. Regression kriging (RK) is one of over 40 methods reviewed. Here
attached is what I described in the draft of my review. Obviously, RK
described in the review is different from Edzer's approach. Any comment?
Thanks.
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
--------------------------------------------

-----Original Message-----
From: r-sig-geo-bounces at stat.math.ethz.ch
[mailto:r-sig-geo-bounces at stat.math.ethz.ch] On Behalf Of Edzer Pebesma
Sent: Thursday, 3 July 2008 9:33
To: Hengl, T.
Cc: r-sig-geo at stat.math.ethz.ch; Dave Depew
Subject: Re: [R-sig-Geo] kriging
Hengl, T. wrote:
transforms of the original predictors e.g.:
Kriging-with-external-trend algorithm to make predictions (see section 2.1 of
my lecture notes), which is mathematically more elegant, but then it accepts
only a family of linear models (and not GLMs, regreesion-trees etc.). I have
been promoting the concept of regression-kriging (deterministic and
stochastic predictions seperated), but we still did not implement it in any
package so far.
And I can see why, as there are quite a few problems still to solve 
(afaik) ahead of you. When you cut the problem in two, do the regression 
estimation and residual prediction in two separate processes (often 
under different assumptions, e.g. wrt spatial correlation) you ignore 
the correlation between the two. Finding a prediction variance by 
naively adding the variances of the two components e.g. does not yield 
zero variance at observation locations, because a non-zero correlation 
is ignored. At other locations, this correlation is also non-zero. 
Furthermore, if you cut the problem in two for e.g. binomial or Poisson 
distributed cases, in this approach you likely end up with negative 
predictions or predictions above one for the binomial case.

Does the paper you refer to (by yourself) give solutions to these two 
problems?
residuals), but then gstat will not give you the regression-kriging variance,
and you can not run geostatistical simulations.
No, of course not, for the reasons mentioned above. The gstat approach 
is: if you want to make a mess, please take responsibility for it by 
yourself (and don't blame me--through the package). There is a paper I 
did it with count data, though, which is

E.J. Pebesma, R.N.M. Duin, P.A. Burrough, 2005. Mapping Sea Bird 
Densities over the North Sea: Spatially Aggregated Estimates and 
Temporal Changes. Environmetrics 16 
<http://www3.interscience.wiley.com/cgi-bin/jissue/110577560>, (6), p 
573-587 <http://dx.doi.org/10.1002/env.723>.

and (part of) the analysis is found in

library(gstat)
demo(fulmar)

I'm also confused by this term "regression kriging". Would you claim 
that the universal kriging/kriging with (one or more) external drifts 
implemented by gstat is not regression kriging? Are you actually working 
on a package that does do regression kriging as you define it?
--
Edzer

  
    

      
      
    

  


  


  


  
  

    

  

    
      
    
    
Thread (3 messages)

  

  

    
            
        Li Jin
        
        kriging [SEC=UNCLASSIFIED]
      
      Jul 3
    
    
      
            
        Tomislav Hengl
        
        kriging [SEC=UNCLASSIFIED]
      
      Jul 4
    
    
      
            
        Edzer Pebesma
        
        kriging [SEC=UNCLASSIFIED]
      
      Jul 4