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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.
Thanks, Eric. This really helps me.
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?
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.