## AI-GEOSTATS: re:samples in a block

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• Unfortunately as Mark has noted, if nothing is known then one will have to design a sampling plan using other criteriia, i.e., essentially meaning
Message 1 of 1 , Aug 28, 2001
Unfortunately as Mark has noted, if nothing is known then one will have
to design a sampling plan using other criteriia, i.e., essentially
meaning non-statistical criteria.

Even if there were no spatial correlation and one only wanted to
estimate the average value for the block one would need the variance. In
such a case one might iterate, i.e., randomly select sample locations
(the number being determined perhaps by budget and difficulty of
sampling). After sampling at those locations, compute the sample
variance and use this to "predict" a sample size (which will almost
certainly be larger than the original size). One can of course use the
data obtained at this stage to estimate the mean and also obtain a
confidence interval, the new sample size will be related to the desired
confidence interval width and desired confidence level. Having
determined a "new" sample size, repeat the process (combining the
original sample with the new data would not correspond to random
sampling), if after several iterations it appears that the predicted
sample size stablizes then you are through. Note that this process only
focuses on the "number" of sample locations, the actual locations being
selected randomly.

This process can be improved on by using the theory of sequential
sampling.

With respect to geostatistics, we need to remember that the data (in
common practice) is used for two different purposes.The first being the
estimation/modeling of the variogram or covariance function, the second
being the kriging (of whatever form or type). An optimal sampling plan
for the one will generally not be an optimal plan for the other.

There is an old issue of "GEOSTATISTICS", the NACOG newsletter, that has
a long list of papers on sampling design. A number of papers have been
written since then as well. There is no definitive answer to the
question since it depends on the question, i.e., what is the data to be
used for?

Donald E. Myers
Department of Mathematics
University of Arizona
Tucson, AZ 85721
http://www.u.arizona.edu/~donaldm

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