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GEOSTATS: confidence intervals

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  • alister@vt.edu
    Dear group, I read an interesting article about constructing confidence intervals for variograms in order to assess the validity of grouping several sample
    Message 1 of 2 , Sep 30, 1998
      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
      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 2 of 2 , Oct 1, 1998
        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@...
        >
        >--
        >*To post a message to the list, send it to ai-geostats@....
        >*As a general service to list users, please remember to post a summary
        >of any useful responses to your questions.
        >*To unsubscribe, send email to majordomo@... with no subject and
        >"unsubscribe ai-geostats" in the message body.
        >DO NOT SEND Subscribe/Unsubscribe requests to the list!
        >


        ------------------------------------------------------
        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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