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Re: GEOSTATS: Non-normal distribution (fwd)

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  • Pierre Goovaerts
    Simon, First, the computation of semivariograms and their use for kriging prediction does not require an assumption of normality, as it has been previously
    Message 1 of 1 , Dec 4, 1998
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      Simon,

      First, the computation of semivariograms and their
      use for kriging prediction does not require an
      assumption of normality, as it has been previously
      mentioned by Don Myers on that list (13 Nov. 1997).
      However, the main problem you face is a spike
      of zero values which can be treated as a separate
      population.

      What I would suggest is to use an indicator approach,
      that is:
      1. discretize the range of variation of your data using
      a given number of thresholds, say 5: the first threshold
      would be 0% (which is close to the median of your sample
      distribution) and 4 other thresholds corresponding to the
      0.6, 0.7, 0.8 and 0.9 quantiles of your distribution.
      2. for each threshold, code each observation into an indicator value
      which is zero if the measured percentage is larger than the threshold
      and one otherwise.
      3. Compute and model the 5 corresponding indicator semivariograms,
      that is the semivariograms of indicator values.
      4. Use indicator kriging to interpolate the probabilities
      to be no greater than each of the 5 thresholds at the nodes
      of your interpolation grid.
      5. At each location, you can now model the conditional cumulative
      distribution function which provides you with the probability
      that the unknown percentage value is no greater than any
      given threshold. You could use the mean of that distribution
      as your estimate and the variance as a measure of uncertainty.

      The method is described at length in the geostat literature,
      as well as in Chapter VII of my recent book. All the computations
      can be carried out using the public domain software Gslib,
      you can download the source code from Deutsch's Website
      http://www.ualberta.ca/~smpe/people/clayton/software.html.

      Since you are a beginner in the world of geostatistics,
      I send you a copy of a review paper that I recently
      wrote for soil scientists in which I present (or try to present!)
      in layman terms a broad overview of main applications of geostat.
      The references are:
      Goovaerts, P. 1998.
      Geostatistical tools for characterizing the spatial variability of
      microbiological and physico-chemical soil properties.
      Biology and Fertility of Soils, 27(4): 315-334.

      Users of the list who are interested in receiving an electronic
      copy of the paper (pdf format) should send me an e-mail since
      the file is too large to be distributed directly through the list.

      Regards,

      Pierre Goovaerts


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      ________ ________
      | \ / | Pierre Goovaerts
      |_ \ / _| Assistant professor
      __|________\/________|__ Dept of Civil & Environmental Engineering
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      On Mon, 30 Nov 1998, Simon Brewer wrote:

      > Hello,
      >
      > I am stuck on the following problem:
      >
      > I am trying to interpolate percentage data on a map. I have
      > approximately 150 samples, of which about 50% are zero values. The
      > distribution is therefore heavily skewed to the right. I have been told
      > that variograms should be based on normally distributed data, and so I
      > have tried to transform the data. A logtransformation gives a normal
      > distribution, but the zero values are unusable. A log(value+1)
      > transformation still appears to leave a non-normal distribution.
      >
      > I am a beginner in the world of geostatistics, so I am not sure where to
      > go from here, or if I am making an elementary mistake. How essential is
      > it that the data is normally distributed? Are there other suitable
      > transformations that apply? If anyone has any suggestions or advice, or
      > ideas about where I might find an answer in the literature, please let
      > me know!
      >
      > Simon Brewer
      > --
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      >
      > Simon Brewer
      >
      > European Pollen Database
      > (Laboratoire de Botanique Historique et Palynologie)
      > (IMEP CNRS URA 1152)
      > (Faculte St Jerome - Aix Marseille III)
      >
      > Centre Universitaire d'Arles
      > Place de la Republique
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