thank you very much for the information !
I am analysing plants in grassland and I have the problem, that many researchers here use linear triangulation in r e g u l a r (20 x 20 metres) sampling grids to estimate the population for mapping. Natural Neighbors seems to be very similar.
My question now would be what does surfer do, when the edge parts of a grsslandfield are cross-validated (as you already mentioned there is NO extrapolation) This should result in larger RMSE errors compared to any other extrapolation method !?? I am not shure if I can use these cross-validation results to compare the efficiacy or performance of a interpoolation method in that particular case and in general. (By the way: Do you think it is correct to use the best cross-validation results of a interoplation method to compre its performance to another method? Is a jackknifing nessecary in addition)
Another question I would like to ask you is whether you think that if I would have the spatial location of every single plant in an area; Could I start comparing sampling schemes and interpolators much better ? Which way to do so would you choose ?
I hope you can help me with some of your amazing answers,
Peter
From: Gregoire Dubois <[EMAIL PROTECTED]>
To: "Peter Pinn" <[EMAIL PROTECTED]>, <[EMAIL PROTECTED]>
Subject: Re: [AI-GEOSTATS: Deterministic vs. Stochastic Interpolation Comparison]
Date: Tue, 02 Sep 2003 16:23:25 +0200
Peter,
the RMSE is not THE measure of cross-validation... it is only one of the
possible statistics of the errors you can use. Fundamentaly, what you get from
cross-validations is a set of estimated values that can be compared to the
input data. Hence, you can use various statistics of the errors (error =
observed - estimated value): the RMSE, the MAE (mean absolute error), the
correlation coefficient between observed values and estimates... you can also
focus on the highest values only.
You have to define the criteria that will quantify the "performance" of the interpolators before doing any cross-validation. The RMSE is probably the measure that is the most frequently used.
Surfer's (version 8 only) cross-validation function seems to work fine now
(see my posting in the archives about the bug I found a few months ago). You
have to update your original version to 8.2.
As you mention, a few deterministic interpolators do not allow extrapolations
(estimations outside the boundary defined by the convex hull), but many do
(IDW, polynomes,...).
I don't know what kind of variables you are analysing, but geometrical interpolators (triangulations, thiessen polygons, nearest neighbours) are almost never used for estimation purposes in environmental sciences, unless you have very large data sets.
Gregoire
"Peter Pinn" <[EMAIL PROTECTED]> wrote:
> Hello,
>
> thank you all for the great replies to my questions. This helps very much.
>
> I was wondering whether or not there is a way to compare the performance of
> deterministic interpolation methods such as Linear Triangulation or Natural
> Neighbours to Kriging or IDW !? Is there a measure similar to the RMSE
> resulting from cross-validation ? (e.g. ESRIs Geostatistical Analyst does
> not use these methods, whereas SURFER applies a cross-validation that I do
> not really believe in !) I hope I am not totally wrong assuming that
> cross-validation does not really work fine in deterministic methods, because
> a extrapolation at edge sampling locations will not be computed...
>
> Thanks again :-)
>
> Peter
>
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