topic Back log transform in Geostatistical analysis tool in ArcGIS GeoStatistical Analyst Questions

Back log transform in Geostatistical analysis tool

LilyWang — Tue, 19 Jul 2011 15:22:44 GMT

Hello,
I'm using Geostatistical analysis tool to do spatial analysis (ordinary Kriging). I log transformed my data point within the wizard before I go ahead to do the analysis. I know analysis tool will be back log transform my data by the end of analysis. But I'm wondering if the back log transform algorithm built-in with ArcGIS software considered variance when it calculated back transformed data. I searched through google, I couldn't find any information for it. I'll really apppreciate it if anyone could answer my question promptly. Thanks.

Lily

Re: Back log transform in Geostatistical analysis tool

EricKrause — Tue, 19 Jul 2011 18:43:48 GMT

Hi Lily,

Yes, the variance is taken into account in the back transformation. If you'd like to learn more about exactly what is happening behind the scenes, our method is described in the following paper:

Cressie, N. 2006. "Block Kriging for Lognormal Spatial Processes." Mathematical Geology 38: 413-43

Good luck, and thanks for the interest in geostatistics.

-Eric

Re: Back log transform in Geostatistical analysis tool

LilyWang — Thu, 21 Jul 2011 17:00:24 GMT

Thanks, Eric. This really helps me.

Lily

Re: Back log transform in Geostatistical analysis tool

MikeWild — Wed, 02 May 2012 15:43:25 GMT

Eric,
I purchased the article by Cressie that you mentioned and want to make sure that I am looking at the correct formula for the back transformation of point estimates using ordinary kriging. From what I can gather, the back transformed value is:
Exp (estimated value + 1/2* estimation variance)
Is this assumption correct?
Is there a way to see both the estimated value and the estimation variance, separately, before this transformation?
Thanks,
Mike Wild

Re: Back log transform in Geostatistical analysis tool

EricKrause — Wed, 02 May 2012 21:50:26 GMT

The formula you posted is for simple kriging, not ordinary kriging. The formula for ordinary kriging looks similar, but it uses a Lagrange multiplier, which makes it a lot harder to understand.

For simple kriging, if you want to get the expected value and variance in the log-space (before the back transformation), then you should do the transformation manually. Create a new field in your feature class, and calculate the log of the data with the Field Calculator. Then perform simple kriging (with no transformation) on the logged data. The prediction surface will correspond to the estimated value, and the prediction standard error surface corresponds to the square root of the estimated variance.