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AI-GEOSTATS: Declustering

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  • amazot@ulb.ac.be
    Hello, I would like to know what is the declustering, why we used this method and how we proceed to decluster a set of data? Thank you -- * To post a message
    Message 1 of 7 , Nov 15, 2001
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      Hello,

      I would like to know what is the declustering, why we used this
      method and how we proceed to decluster a set of data?

      Thank you

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    • Isobel Clark
      ... If your data is clustered spatially (in location) this may bias any histograms or probability plots which you draw and, therefore, any conclusions you make
      Message 2 of 7 , Nov 15, 2001
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        > I would like to know what is the declustering, why
        > we used this
        > method and how we proceed to decluster a set of
        > data?
        If your data is clustered spatially (in location) this
        may bias any histograms or probability plots which you
        draw and, therefore, any conclusions you make about
        what kind of distribution the values come from.

        For example, in mining projects geologists tend to
        drill a lot more holes in the good bits than the bad
        bits. This means that a histogram contains a lot more
        samples than it should in the higher end.

        If you try to fit a model to such data, or use a
        transform or 'anamorphosis' it will not really reflect
        the values in the whole of the area. Backtransforms
        will be biassed like the original samples.

        Declustering is one way to get rid of the bias. There
        are various ways to decluster but the most common ones
        revolve around laying a grid of squares over your map
        area and either (a) selecting one sample per square or
        (b) averaging all the samples in each square. (b) is
        not very sensible given what we are trying to do with
        the data, but is very common (again) in mining. If you
        use (a) it is a good idea to choose which sample to
        'keep' in the histogram at random.

        You may still use all of the clustered sampling for
        geostatistical analysis, of course. 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.

        The term 'declustering' became popular around 1982/83
        and is first used widely in the proceedings of the
        geostatistical congress held at Lake Tahoe in
        September 1983.

        Isobel Clark
        http://uk.geocities.com/drisobelclark

        __________________________________________________
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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 3 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 4 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

            __________________________________________________
            Do You Yahoo!?
            Everything you'll ever need on one web page from News and Sport to Email and Music Charts
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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 5 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 6 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
                >
                >
                >
                >
                > --
                > * To post a message to the list, send it to ai-geostats@...
                > * As a general service to the users, please remember to post a summary of any useful responses to your questions.
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                > * Support to the list is provided at http://www.ai-geostats.org
                >


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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 7 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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