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RE: AI-GEOSTATS: Declustering

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  • Alessandro Gimona
    Isobel wrote: .....The semi-variogram and kriging techniques are not affected by clustering. ... I am slightly confused: ... if sampling is clustered
    Message 1 of 7 , Nov 16, 2001
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      Isobel wrote:

      .....The semi-variogram and kriging techniques are not affected by
      clustering.
      > In fact, one of the main reasons for inventing kriging
      > was to make full use of every one of clustered and/or
      > preferentially sited sampling.
      >
      >
      I am slightly confused:
      ... if sampling is clustered preferentially in e.g. higher values
      areas, would this not bias the semi-variogram for the first few lags?...at
      least if, as it can happen, the variance is related to the mean.
      What about the effects of the possible over-estimation of the global
      mean due to clustering?

      thanks

      Alessandro Gimona

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    • Isobel Clark
      ... The semi-variogram is calculated on the difference between the two sample values. If the basic assumptions for semi-variogram construction are correct,
      Message 2 of 7 , Nov 16, 2001
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        > I am slightly confused:
        > ... if sampling is clustered preferentially in
        > e.g. > higher values
        > areas, would this not bias the semi-variogram for
        > the first few lags?...at
        > least if, as it can happen, the variance is related
        > to the mean.
        The semi-variogram is calculated on the difference
        between the two sample values. If the basic
        assumptions for semi-variogram construction are
        correct, differences are unrelated to the actual value
        of each sample or to the actual absolute location of
        the pair. Therefore, clustering does not influence the
        semi-variogram.

        If you have a situation where variance is related to
        the mean, e.g. with highly skewed data, you need to
        transform these values in some way before constructing
        a semi-variogram. This is true whether or not you have
        clustered sampling. Absolutely regular sampling will
        not give you a valid semi-variogram if you violate the
        assumptions upon which it is based.

        > What about the effects of the possible
        > over-estimation of the global mean due to
        clustering?
        If you are estimating the global mean based on a
        distribution model, you need to decluster. If you are
        estimating the global meaning on the basis of a kriged
        grid, you do not need to decluster as the kriging
        system does that for you.

        You can experiment with these questions using our
        totally free unlimited kriging game. This can be found
        in my 'briefcase' at
        http://uk.geocities.com/drisobelclark/briefcase.html

        Does this help?
        Isobel Clark

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      • oliver.sonnentag@web.de
        hello list, to get the global mean of my data set (484 observation wells) and as a prerequisite for Normal Score Transformation with GSLIB, i declustered my
        Message 3 of 7 , Jul 5, 2003
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          hello list,
          to get the global mean of my data set (484 observation wells) and
          as a prerequisite for Normal Score Transformation with GSLIB, i
          declustered my data with polygonal declustering. When
          standardizing the weights to 1, so that the weights sum up to the
          number of data, I receive some negative weights. this results in
          negative values for the observations (nitrate concentration). how do
          i have to interpret this ? does this require a special treatment? skip
          them? as I mentioned before, i want to normal score transform the
          data set prior to simple kriging.
          many many thanx for some help in advance.
          Regards,
          Oliver




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        • Pierre Goovaerts
          Hi Oliver, I don t know which algorithm you are using to compute these declustering weights but there is something wrong in your rescaling procedure. These
          Message 4 of 7 , Jul 5, 2003
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            Hi Oliver,

            I don't know which algorithm you are using to compute these declustering
            weights but there is something wrong in your rescaling procedure.
            These declustering weights are proportional to the size of the polygon
            of influence of each observation and they can not be negative.

            Regards,

            Pierre Goovaerts

            <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

            Dr. Pierre Goovaerts
            President of PGeostat, LLC
            Chief Scientist with Biomedware Inc.
            710 Ridgemont Lane
            Ann Arbor, Michigan, 48103-1535, U.S.A.

            E-mail: goovaert@...
            Phone: (734) 668-9900
            Fax: (734) 668-7788
            http://alumni.engin.umich.edu/~goovaert/

            <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

            On Sat, 5 Jul 2003 oliver.sonnentag@... wrote:

            > hello list,
            > to get the global mean of my data set (484 observation wells) and
            > as a prerequisite for Normal Score Transformation with GSLIB, i
            > declustered my data with polygonal declustering. When
            > standardizing the weights to 1, so that the weights sum up to the
            > number of data, I receive some negative weights. this results in
            > negative values for the observations (nitrate concentration). how do
            > i have to interpret this ? does this require a special treatment? skip
            > them? as I mentioned before, i want to normal score transform the
            > data set prior to simple kriging.
            > many many thanx for some help in advance.
            > Regards,
            > Oliver
            >
            >
            >
            >
            > --
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            >


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          • Michael Pyrcz
            Good day Oliver, I have another comment on declustering in addition to the previous comment on negative weights. The weights do not actually change the data
            Message 5 of 7 , Jul 5, 2003
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              Good day Oliver,

              I have another comment on declustering in addition to the previous
              comment on negative weights. The weights do not actually change the
              data values. They change the weight of the data values within the
              distribution; therefore, weights change the distribution, but not the
              sample data. One way to think of declustering weights is that they
              would change the height on the bars of a histogram (more precisely, the
              contribution of each of the data to the bar height), but not the
              position of the bars.

              The GSLIB book (Deutsch and Journel) has a lot of practical guides to
              declustering. I have recently written a paper on the specifics of
              declustering, if you are interested.

              All the best,

              Michael

              _____________________________________________

              Michael Pyrcz
              Ph.D. Candidate
              Department of Civil & Environmental Engineering
              University of Alberta
              (780) 492-3153
              mpyrcz@...
              www.ualberta.ca/~mpyrcz


              -----Original Message-----
              From: ai-geostats-list@... [mailto:ai-geostats-list@...] On
              Behalf Of oliver.sonnentag@...
              Sent: July 5, 2003 2:13 AM
              To: ai-geostats@...
              Subject: AI-GEOSTATS: Declustering

              hello list,
              to get the global mean of my data set (484 observation wells) and
              as a prerequisite for Normal Score Transformation with GSLIB, i
              declustered my data with polygonal declustering. When
              standardizing the weights to 1, so that the weights sum up to the
              number of data, I receive some negative weights. this results in
              negative values for the observations (nitrate concentration). how do
              i have to interpret this ? does this require a special treatment? skip
              them? as I mentioned before, i want to normal score transform the
              data set prior to simple kriging.
              many many thanx for some help in advance.
              Regards,
              Oliver




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