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AI-GEOSTATS: Back transforms and simulations

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  • Chris Lloyd
    Hello, The subject of logs and back transforms has been discussed a great deal on the list and I ve seen much material concerning back transforms following
    Message 1 of 3 , Oct 17, 2003
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      Hello,

      The subject of logs and back transforms has been discussed a great deal
      on the list and I've seen much material concerning back transforms
      following kriging of log transformed data (e.g., the approach outlined
      by Cressie in his book 'Statistics for Spatial Data' and many other
      texts). However, I am unsure how to proceed if the objective is
      simulation.

      I have applied sequential Gaussian simulation to log (base 10)
      permeability data and I want to back transform the simulated
      realisations. I would be grateful for any suggests from list members as
      to how best to back transform the values in this case. There are too few
      data to make an indicator approach feasible.

      I will post a summary of answers. Many thanks in advance.

      Chris Lloyd




      [Non-text portions of this message have been removed]
    • Pierre Goovaerts
      Hi Chris, The back transform of simulated values is very easy to perform. Just take the exponential of the simulated values since you are not trying to
      Message 2 of 3 , Oct 18, 2003
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        Hi Chris,

        The back transform of simulated values is very easy to perform.
        Just take the exponential of the simulated values since you are
        not trying to estimate the mean of the local probability distribution
        in the original space, but only a quantile of this distribution.
        Note that if you perform SGS using Gslib, there is a built-in
        normal score transform and back-transform in the program, which is
        more flexible than the lognormal transform.

        Cheers,

        Pierre
        <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

        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 Fri, 17 Oct 2003, Chris Lloyd wrote:

        > Hello,
        >
        > The subject of logs and back transforms has been discussed a great deal
        > on the list and I've seen much material concerning back transforms
        > following kriging of log transformed data (e.g., the approach outlined
        > by Cressie in his book 'Statistics for Spatial Data' and many other
        > texts). However, I am unsure how to proceed if the objective is
        > simulation.
        >
        > I have applied sequential Gaussian simulation to log (base 10)
        > permeability data and I want to back transform the simulated
        > realisations. I would be grateful for any suggests from list members as
        > to how best to back transform the values in this case. There are too few
        > data to make an indicator approach feasible.
        >
        > I will post a summary of answers. Many thanks in advance.
        >
        > Chris Lloyd
        >
        >
        >


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      • Chris Lloyd
        Hello, Many thanks to Isobel Clark and Pierre Goovaerts for sending replies to my email about simulation and back transforms. Both pointed out that in the case
        Message 3 of 3 , Oct 20, 2003
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          Hello,

          Many thanks to Isobel Clark and Pierre Goovaerts for sending replies to
          my email about simulation and back transforms. Both pointed out that in
          the case of simulation the back transform is straightforward. Pierre
          also noted that GSLIB allows normal scores transforms and back
          transforms, which are more flexible than log transforms.

          Both replies are copied below.

          Chris


          Isobel:

          Since your simulated values should have the same distribution as the
          original data, you simply need to anti-log.

          I prefer to use 'natural' logarithms for transformation and then do
          e-to-the-x, but using logs to the base 10 and then 10-to-the-x should
          work just
          as well. The answer is rather more complicated if you krige with logs to
          the base 10.

          Pierre:

          The back transform of simulated values is very easy to perform. Just
          take the exponential of the simulated values since you are not trying to
          estimate the mean of the local probability distribution in the original
          space, but only a quantile of this distribution. Note that if you
          perform SGS using Gslib, there is a built-in normal score transform and
          back-transform in the program, which is more flexible than the lognormal
          transform.



          [Non-text portions of this message have been removed]
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