## Re: AI-GEOSTATS: Kriging with External Drift

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• Hi, a little off the original topic, but one question that puzzles me is the computation of the semivariogramm for Kriging with external drift. If I understand
Message 1 of 13 , Dec 7, 2001
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Hi,

a little off the original topic, but one question that puzzles me is the
computation of the semivariogramm for Kriging with external drift.

If I understand correctly, a relation of type
m*(x) = a1(x) + a2(x)*s(x)
is assumed between the mean of the primary variable at location x
(drift) and secondary variable (s). Now, the a's are dependent on the
location and are not computed explicitly. But in the kriging system the
residual covarince is needed. To compute the residuals, I would need to
calculate the equation explicitly, right?

How do I compute the residual semivariogramm when I don't know the
residuals? Or have I misunderstood something in the concept of external
drift?

Best regards
Andreas

--
Andreas Hartmann
RWTH Aachen, Angewandte Geophysik
Lochnerstr. 4-20
52056 Aachen, Germany
(+49) (-0) 241 8094835
mailto:Andreas@...-aachen.de
http://www.geophysik.rwth-aachen.de

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• ... you got it. Plus the constraint that the drift components in the samples have to balance with the drift component at the point being estimated. Isobel
Message 2 of 13 , Dec 7, 2001
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> So are you saying that the external drift variable
> in the matrix is just the
> magnitude of the the drift variable at that point?
you got it.

Plus the constraint that the drift components in the
samples have to balance with the drift component at
the point being estimated.

Isobel

________________________________________________________________
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The competition ends 16 th of December 2001.

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• ... There is a nice section (Chapter 5.4) in Cressie s textbook (Statistics for Spatial Data) that discusses the potential bias of estimating semivariograms
Message 3 of 13 , Dec 7, 2001
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On Friday, December 7, 2001, at 10:05 AM, Andreas Hartmann wrote:
>
> How do I compute the residual semivariogramm when I don't know the
> residuals? Or have I misunderstood something in the concept of external
> drift?

There is a nice section (Chapter 5.4) in Cressie's textbook (Statistics
for
Spatial Data) that discusses the potential bias of estimating
semivariograms from residuals and Matheron's formulation of
IRF-K kriging as an alternative means to krige in the presence of
a trend. The iterative fitting of the covariance is usually
non-graphical,
which is a drawback in itself, and Fig. 5.1 in the same section shows
Cressie's bold attempt at showing the pitfalls of doing such an
"automatic" fit. I have not used IRF-K kriging very much in practice,
for the above reasons. Better to live with the devil that I know, i.e.
my -- albeit biased -- residual variogram.

Regards,

Syed

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• Hi, Just to add to that Gotway and cressie I can t remember the exact citation did a large simulation study and showed that the bias from using the residual
Message 4 of 13 , Dec 8, 2001
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Hi,
Just to add to that Gotway and cressie I can't remember the exact citation
did a large simulation study and showed that the bias from using the
residual variogram is very small in most cases.

Nicholas

On Fri, 7 Dec 2001 sshibli@... wrote:

>
> On Friday, December 7, 2001, at 10:05 AM, Andreas Hartmann wrote:
> >
> > How do I compute the residual semivariogramm when I don't know the
> > residuals? Or have I misunderstood something in the concept of external
> > drift?
>
> There is a nice section (Chapter 5.4) in Cressie's textbook (Statistics
> for
> Spatial Data) that discusses the potential bias of estimating
> semivariograms from residuals and Matheron's formulation of
> IRF-K kriging as an alternative means to krige in the presence of
> a trend. The iterative fitting of the covariance is usually
> non-graphical,
> which is a drawback in itself, and Fig. 5.1 in the same section shows
> Cressie's bold attempt at showing the pitfalls of doing such an
> "automatic" fit. I have not used IRF-K kriging very much in practice,
> for the above reasons. Better to live with the devil that I know, i.e.
> my -- albeit biased -- residual variogram.
>
> Regards,
>
> Syed
>
>
>
> --
> * To post a message to the list, send it to ai-geostats@...
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>

CH3
|
N Nicholas Lewin-Koh
/ \ Dept of Statistics
N----C C==O Program in Ecology and Evolutionary Biology
|| || | Iowa State University
|| || | Ames, IA 50011
CH C N--CH3 http://www.public.iastate.edu/~nlewin
\ / \ / nlewin@...
N C
| || Currently
CH3 O Graphics Lab
School of Computing
National University of Singapore
The Real Part of Coffee kohnicho@...

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