How to do cross-validation in Moving Window Kriging

[zhaochengzeng]

It is really great that Moving Window Kriging(MWK) can be implemented in Arcgis. 
There are two questions that puzzle me,
1. How can I generate an appropriate geostatistical model source input for the WMK? is there an tutorial?
2. WMK is not included in the geostatistical Wizard. How can I get the cross-validation(CV) result from WMK? is WMK able to do the CV?

Thanks a lot.

zeng
from CEODE, CAS

[EricKrause]

Despite its name, MWK is not actually an interpolation method, so you can't perform crossvalidation.  It is designed to calculate local semivariogram parameters (nugget, range, sill) at locations you specify.  There is an optional prediction raster output, but that is using Local Polynomial Interpolation.  The model source parameter is typically a Kriging layer that you created in the Geostatistical Wizard.  It needs this layer so that it can pull things like semivariogram model type (Spherical, Exponential, etc).  You can learn how to make a geostatistical layer in our tutorial.

However, in ArcGIS 10.1, we have Empirical Bayesian Kriging.  While it's not exactly a moving window, it builds local, overlapping models, so it has many of the advantages of MWK.

[zhaochengzeng]

Thank you Eric.
I think MWK is an interpoaltion method though it is sometimes hard to implement in practice. Crossvalidation in WMK is feasible, see
[1]http://www.sciencedirect.com/science/article/pii/S009830040700091X
[2]http://www.stat.purdue.edu/~zhanghao/MASSData/Projects/project1.pdf
[3]http://www.science.mcmaster.ca/geo/faculty/paez/additional_info/Spatial_Effects_v2.1_(US_handout).pd...

Empirical Bayesian Kriging is really amazing. are there any publications about the Empirical Bayesian Kriging used in Arcgis 10.1? If I want to use this method for my data, how can I cite it?
Thanks a lot.

Despite its name, MWK is not actually an interpolation method, so you can't perform crossvalidation.  It is designed to calculate local semivariogram parameters (nugget, range, sill) at locations you specify.  There is an optional prediction raster output, but that is using Local Polynomial Interpolation.  The model source parameter is typically a Kriging layer that you created in the Geostatistical Wizard.  It needs this layer so that it can pull things like semivariogram model type (Spherical, Exponential, etc).  You can learn how to make a geostatistical layer in our tutorial.

However, in ArcGIS 10.1, we have Empirical Bayesian Kriging.  While it's not exactly a moving window, it builds local, overlapping models, so it has many of the advantages of MWK.

[EricKrause]

You can use this reference to learn about and cite EBK:

Krivoruchko K. and Gribov A. (2014) Pragmatic Bayesian kriging for non-stationary and moderately non-Gaussian data. In Mathematics of Planet Earth. Proceedings of the 15th Annual Conference of the International Association for Mathematical Geosciences. Eds: Pardo-Igúzquiza, E.; Guardiola-Albert, C.; Heredia, J.; Moreno-Merino, L.; Durán, J.J.; Vargas-Guzmán, J.A. Springer 2014, pp. 61-64.

[EricKrause]

And you're correct that MWK can be implemented as an interpolation method.  In our implementation, it allows you to make predictions at a particular set of points, along with getting their estimated range, nugget, and sill.  You actually can get it to create a surface if your set of points is on an evenly spaced grid.  You can then run the Point to Raster geoprocessing tool to turn the gridded points into a raster surface.  However, I don't think there is any way to perform crossvalidation on this surface with ArcGIS tools.

That being said, you should probably still use EBK over MWK.