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GEOSTATS: Cross validation vs. semivariogram comparison?

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  • Yetta Jager
    Andrew and others, We are interested in this issue as well in the context of subsampling from a GIS coverage to conduct semivariogram analysis. My colleagues
    Message 1 of 2 , Oct 1, 1998
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      Andrew and others,

      We are interested in this issue as well in the context of
      subsampling from a GIS coverage to conduct semivariogram
      analysis. My colleagues are concerned by the idea that we
      would be throwing away data and want to compare semivariograms
      from the whole set with those estimated from samples (I'm
      suggesting sampling with a mixed design of regular and more
      closely spaced nearest neighbors).

      In the past, I've assumed that the best way to test the
      adequacy of the semivariogram is to do cross-validation --
      krig based on the estimated semivariogram(s) leaving out
      one point at a time, sum the squared errors (predicted Z - actual)
      and compare with the kriging variance estimate (which is based
      on the semivariogram and the spacing of data). This ensures
      that the distances that will actually be used most are given
      the correct weight. For example, if the data are all fairly
      closely spaced, it doesn't matter if the semivariogram is way
      off at large distances. If comparing semivariograms is the
      issue, then I'd just be inclined to pick the one that does
      a better job of producing accurate kriging variances.

      I'd be interested in dissenting or confirming opinions, since
      we are dealing with the same controversy.

      Yetta


      At 11:16 AM 9/30/98 -0400, you wrote:
      >Dear group,
      >
      >I read an interesting article about constructing confidence intervals for
      >variograms in order to assess the validity of grouping several sample sites
      >together to estimate one composite variogram. (Kabrick et al. 1997.
      >spatial patterns of carbon and texture .....Soil Science Society of America
      >Journal 61:541-548.
      >
      >I would like to do a similar thing: to see if it's valid to group
      >variograms calculated from data from each of several smaller, non
      >contiguous plots in a forest into one composite variogram. Basically, the
      >Kabrick article points out that assessing confidence interval overlap is
      >not really a statistical test of similarity of two regression lines, so
      >they give a z test to further support a conclusion of similarity or
      >dissimilarity; I was, however, confused by this.
      >
      >I was a little unclear on their approach and was wondering if anybody had
      >any more straightforward approach to comparing variograms. It seems like
      >one could estimate confidence intervals by calculating the standard errors
      >of all of the (xi-xi+h)^2/2n's, and multiply this std error by t (1.96 for
      >large n) to define the limits of the CI. Is this overly simplistic? I'm
      >sort of an intermediate geostatistics (and classical statistics for that
      >matter) user.
      >
      >Thanks for any advice.
      >Andrew
      >alister@...
      >
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      ------------------------------------------------------
      Yetta Jager
      Environmental Sciences Division
      Oak Ridge National Laboratory
      P.O. Box 2008, MS 6036
      Oak Ridge, TN 37831-6036
      OFFICE: 423/574-8143
      FAX: 423/576-8543
      Work email: jagerhi@...
      Home email: hjager@...
      WEBpage: http://www.esd.ornl.gov/~zij/
      -----------------------------------------------------

      "One man's mean is another man's Poisson" J.W. Haeffner
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