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1019Re: AI-GEOSTATS: Log normal kriging (2)

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  • Edzer J. Pebesma
    May 14, 2003
      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
      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.

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