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Re: AI-GEOSTATS: Back transforms and simulations

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  • 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 1 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 2 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.



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