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AI-GEOSTATS: re:samples in a block

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  • Donald E. Myers
    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
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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 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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