Geostatistical Analyst kriging standard error

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06-24-2010 07:00 AM
DelvoieSimon
New Contributor
I am interpolating altitud values from point data to recreate a DEM. I use the ordinary kriging method to predict these values. Moreover I would like to understand the standard error related to the predicted values. To get information on standard errors related to the predicted values, the Geostatistical Analyst Tool in ArcGIS 9.2. provides different information:
- In the cross-validation step, ArcGIS gives us a standard error value (as named on the column on the table of the detailed results of the interpolation process) related to each point data;
- Always in the cross-validation step, ArcGIS computes an average standard prediction error;
- We can also create a prediction standard error map.

So, my questions are simple but the answers should be much more complex...
What is the difference between these different standard errors (punctual standard error, average standard prediction error and prediction standard error mapping)?
Especially, how are they computed in practice and statistically?

Cheers,

Simon
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3 Replies
PageWeil
New Contributor
In order to support and defend the work I do with Geostatistical Analyst, I would also like to know the underlying statistical methods used to create Predictive Standard Error.  A toolbox as advanced as Geostatistical Analyst needs to have some description of what underlies it in order for the outputs to be respected/believed in scientific circles.

Please point me to a paper or documentation of what each of the various GA error maps indicate and the mathematical basis for forming them

Thanks

Page
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EricKrause
Esri Regular Contributor
http://resources.arcgis.com/content/product-documentation?fa=viewDoc&PID=48&MetaID=778

Appendix A contains the mathematical details of methods available at ArcGIS 9.
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EricKrause
Esri Regular Contributor
As for the differences between the different standard errors, the prediction standard error map that can be created in the Wizard refers to the standard deviation of the prediction for any individual point (formulas are in the pdf I just posted).

The cross-validation statistics are calculated for each input location (suppose there are n points).  To calculate the error for some point x, the software removes the point and recalculates the kriging weights based on the on the remaining (n-1) points and generates a prediction at point x.  The error is the difference between the prediction at point x and its actual value.  The software does this for all n points.  The root mean square, for example, is the average squared error for the n points.

Be careful not to confuse "standard error" with "standardized error."  They aren't the same.

Page 35 of the pdf talks more about it.
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