Dear Diane,
 
As far as I know, the sample variance for the semivariogram is not theoretically defined. One cannot simply calculate the variance as if the sample points were identical independent data, because, by definition, they are not independent when spatial dependence exists!
There is an approximation in Cressie that I have used to test for spatial dependence, but I believe that it is sensitive to various assumptions in the data.
The alternative is to use a Monte Carlo test, i.e. randomly allocate the data to the spatial locations many times, calculate semivariograms for each randomization, and see how the sample semivariogram compares with the simulations. If the sample semivariogram for a particular lag is below the simulation semivariogram 95 % of the time, you would conclude that there is spatial structure at this lag.
 
Dan Bebber
___________________________________
Dr. Daniel P. Bebber
Department of Plant Sciences
University of Oxford
South Parks Road
Oxford OX1 3RB
UK
Tel. 01865 275060
----- Original Message -----
From: diane poon
Sent: Monday, January 23, 2006 3:01 PM
Subject: [ai-geostats] variograms iwth error bars?

Dear AI-geostats list,

These may be a silly questions...but why do variograms appear without error bars to each sample variogram lag point?
I understand that each point in the sample variogram illustrates the mean of all pairs of points at that lag distance in the sample area and the scatter increases with larger lags.
But how does this not compromise our interpretation of the sample variogram (i.e. sill, range, etc...)? 
Why aren't error bars applicable or shown on variograms like we see in many other type of statistics?
What are the assumptions?
and where can I cite these from the litterature?

Thank you
Diane



--
The period of greatest gain in knowledge and experience, is the most difficult period in one's life.


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