"Standard Error" GA Layer to Points != "Prediction Standard Error Map"

DaveWetta

I thought I had my head around cross-validation in Geospatial Analyst, but I find the following apparent discrepancy confusing/troubling.

=====

I have split my input data into training and test data sets using "Subset Features".

I have built a simple kriging model using the training data set.

I use GA Layer to Points using the training data set kriging model layer, and select the test data set as Input Point Observation Locations, creating a "Standard Error" field (among others).  My understanding is this is the square root of the kriging variance at those points.

I right-click on my training data set kriging model layer and select "Change Output to Prediction Standard Error".  I thought this was also displaying the square root of the kriging variance.

- The values on the "Prediction Standard Error Map" are significantly lower at my test point locations than the "Standard Error" values from the GA Layer to Points step (loosely 1/5 of the value).

- I've confirmed this by converting the Prediction Standard Error Map to a Raster, and extracting values to the same test data set I used GA Layer to Points on, and comparing both values at all the points.

=====

Are the "Standard Error" values from "GA Layer to Points" not the same as the "Prediction Standard Error" from the "Prediction Standard Error Maps"?

Am I using one of the tools wrong?

Any clarification greatly appreciated.  Let me know if any better description/explanation/elaboration from my end will help.  I'm using ArcGIS 10.1 SP1

Dave Wetta

Eric6346

I was recently reminded that I never followed up on this thread.  We were able to figure out what happened, and I actually learned something I didn't know about our tools.

GA Layer to Points operates slightly differently depending on whether or not you provide a validation field.  If you do not provide one, it is simply extracting the value of the geostatistical layer.

 

If you provide a validation field, things get a little complicated.  In geostatistics, there is a distinction between the true process and the measured process.  We assume that each location does have a true value, but when you attempt to measure it, you introduce measurement error.  We say that the measured value is the sum of the true value plus random noise.  When you provide a validation field, that field is assumed to contain measured values, not true values.  To validate against them correctly, you have to use the standard error of the measured process, which is always larger than the standard error of the true process.

 

Things get extra complicated if you apply a transformation because then the predicted value actually depends on the standard error.  In that case, both the predictions and the standard errors will be different depending on whether you provide a validation field.

 

The issue is discussed thoroughly in this paper:

Krivoruchko, K., A. Gribov, and J. M. Ver Hoef, 2006, "A new method for handling the nugget effect in kriging," T. C. Coburn, J. M. Yarus, and R. L. Chambers, Eds., Stochastic modeling and geostatistics: Principles, methods, and case studies, volume II: AAPG Computer Applications and Geology 5, p. 81–89.