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AI-GEOSTATS: Conditional simulation

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  • Almuth Wameling
    Here is a question about conditional simulations: I am using conditional simulations of a continuous spatial process e.g. by sequential gaussian simulation or
    Message 1 of 2 , Mar 20, 2001
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      Here is a question about conditional simulations:

      I am using conditional simulations of a continuous spatial process
      e.g. by sequential gaussian simulation or LU-decomposition to
      analyse several aspects of spatial variability. According to Chiles
      and Delfiner (1999) I interpret any simulation as a realization
      selected randomly from all realizations that match the sample
      data, or, equivalently, as a simulation of the process Z(.)
      conditional to the observed sample. This conditional process is not
      stationary and its covariance structure is not the structure of the
      unconditional process any more (cf. Cressie, 1991). However, in
      many papers and books the quality of simulations is judged
      according to how good they reproduce the covariance structure of
      the unconditional process. My questions are

      1. Shouldn't I be careful to use the method of moments estimator of
      the variogram as the simulated realizations are non-stationary?

      2. Where is the advantage in post-processing the simulations (e.g.
      by simulated annealing) to match the covariogram of the
      unconditional process? According to the above interpretation as a
      simulation of the conditional process I do not see why I shouldn't
      accept simulations showing the covariance structure of just that
      process, the conditional one.

      Thanks in advance for your comments


      ***************************************************************************
      Cited literature:

      Chiles, J.P. and Delfiner, P. (1999): Geostatistics, Wiley, New York
      Cressie, N.A. (1991): Statistics for Spatial Data, Wiley, New York.



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    • Syed Abdul Rahman Shibli
      ... Perhaps I am misinterpreting your question but in SGS previously simulated values are treated as hard data; this preserves the correlation structure of
      Message 2 of 2 , Mar 21, 2001
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        Almuth Wameling wrote:

        >
        > conditional to the observed sample. This conditional process is not
        > stationary and its covariance structure is not the structure of the
        > unconditional process any more (cf. Cressie, 1991). However, in
        > many papers and books the quality of simulations is judged
        > according to how good they reproduce the covariance structure of
        > the unconditional process. My questions are
        >

        Perhaps I am misinterpreting your question but in SGS previously
        simulated values are treated as "hard" data; this preserves the correlation
        structure of the map. Kriging will, however, result in spatial models
        that are different from the ones you use for the prediction. The former strives
        for realism, the latter for some sort of "best linear unbiased estimate".

        Syed


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