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AI-GEOSTATS: Log normal kriging (2)

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  • Gregoire Dubois
    Dear all, my last posting on lognormal kriging was either stupid, tricky or unclear but I didn t get any reply to it. Were the readers shocked that I planned
    Message 1 of 4 , May 13, 2003
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      Dear all,

      my last posting on lognormal kriging was either stupid, tricky or unclear but
      I didn't get any reply to it. Were the readers shocked that I planned to do a
      biased back transformation ? :)

      If one is browsing the literature presenting case studies involving lognormal
      kriging, one would be amazed by the lack of information the authors provide on
      the back transformation of their estimates. I simply cannot believe that the
      authors used the unbiased back transformation (see the correct transformation
      in Journal and Huybregts, 1989, p. 572 or in Saito, H. and P. Goovaerts. 2000.
      Geostatistical interpolation of positively skewed and censored data in a
      dioxin contaminated site. Environmental Science & Technology, vol.34, No.19:
      4228-4235).

      The unbiased back transformation involves the kriging standard deviation as
      well as the Lagrange parameter. This renders the transformation rather tricky
      (hence my plan to use a biased transformation). Since the Lagrange parameter
      is not provided in the output files, I wonder how the authors who have
      published case studies with lognormal kriging did their transformation (a few
      case studies were even done with software that were not providing the kriging
      variance). Are there any free/cheap geostats package I'm not aware off that
      are performing log-normal kriging and the unbiased back transformation? (there
      are none listed on the AI-GEOSTATS web site).

      I also saw case studies where the back transformation did not take the
      Lagrange parameter into account. How can this be justified and how much would
      such an approach affect the transformation?

      Thanks for any clarification about this matter.

      Best regards,

      Gregoire

      PS: as a colleague told me, geostatistics is often closer to black magic than
      to any scientific discipline...



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    • Isobel Clark
      Gregoire I am hurt and disappointed after all this time that you can say that there is no (cheap) software listed on ai-geostats which uses the unbiassed
      Message 2 of 4 , May 13, 2003
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        Gregoire

        I am hurt and disappointed after all this time that
        you can say that there is no (cheap) software listed
        on ai-geostats which uses the unbiassed lognormal
        backtransform in kriging.

        I am forbidden by the list rules from mentioning our
        (commercial) software, but we consider our prices as
        cheap as we can go and still provide a reliable
        service. Lognormal backtransforms are carried out on
        request for ordinary and universal kriging in our
        software. For (free) examples of lognormal kriging
        anyone can use our completely public domain 'kriging
        game' which provides all of the equations, the
        weights, lagrange multipliers etc. This can be
        downloaded from http://geoecosse.bizland.com/softwares
        and can read geo-eas and csv files as well as our
        standard data file.

        The lognormal back transform is discussed at length in
        several of my papers which can be found at
        http://uk.geocities.com/drisobelclark/resume/Publications.html

        Isobel Clark
        http://geoecosse.bizland.com/whatsnew.htm

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      • Edzer J. Pebesma
        ... What I did for mapping groundwater quality variables during my PhD research was: 1. estimate block mean concentrations on the log scale, and std.errors 2.
        Message 3 of 4 , May 14, 2003
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          Gregoire Dubois wrote:
          >
          > I also saw case studies where the back transformation did not take the
          > Lagrange parameter into account. How can this be justified and how much would
          > such an approach affect the transformation?
          >

          What I did for mapping groundwater quality variables during my PhD research
          was:
          1. estimate block mean concentrations on the log scale, and std.errors
          2. calculate approximate 95% predictions intervals by est +/- 2 * std.err
          3. back-transform both sides of the interval by taking the exponent.
          What results is not an interval estimate of the block mean value (which
          may be outside this interval!) but an estimate of the block geometric
          mean value. When, on the log scale block mean and block median coincide
          (e.g. when log-concentrations within a block are symmetrically distributed)
          this value coincides with the block median value. The full story is in
          Journal of Hydrology 200, p. 364-386; reprints available from me.

          Now what I wonder is how much it matters if you ignore the lagrange
          parameter but only use the kriging variance: isn't this parameter usually
          much smaller than the kriging variance? Isobel?

          >
          > PS: as a colleague told me, geostatistics is often closer to black magic than
          > to any scientific discipline...
          >
          I try to explain kriging usually as prediction using regression models
          with spatially correlated errors (modelled as stationary random functions).
          In this context, you are practically in the field of statistics. Authors
          to read are: Cressie, Christensen, Diggle, M. Stein, Ribeiro, and probably
          many others.

          A good friend of mine who already was in this area before I was even born
          once told me that his impression was that geostatistics suffers from
          "boosterism" by a number of important authors: each small step is
          sold with many new names, new jargon, exclamation marks, and so on. This
          puts off many scientists who are interested from the outside, but who are
          not in the main stream, like statisticians. I, for example, cannot read
          the BME papers.

          Two days ago I had a discussion with a PhD student here. He had been
          studying Goovaerts' 1997 reference book, and came to the conclusion that
          the difference between simple and ordinary kriging was that simple
          kriging uses global neighbourhoods, whereas ordinary kriging uses
          local neighbouhoods. I apologized, and had to admit that I'd advised
          him to read the wrong book, at least for this issue.
          --
          Edzer

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        • Edzer J. Pebesma
          ... geoR, an excelent package for R (both GPL and available at no cost from http://www.r-project.org/ ) seems to do this. Paulo, could you confirm this? See
          Message 4 of 4 , May 14, 2003
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            Isobel Clark wrote:
            >
            > Gregoire
            >
            > I am hurt and disappointed after all this time that
            > you can say that there is no (cheap) software listed
            > on ai-geostats which uses the unbiased lognormal
            > backtransform in kriging.
            >

            geoR, an excelent package for R (both GPL and available at no
            cost from http://www.r-project.org/ ) seems to do this. Paulo,
            could you confirm this? See http://www.est.ufpr.br/geoR/

            Gregoire, could you include geoR on ai-geostats.org ?
            --
            Edzer

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