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[ai-geostats] Regional estimation - block kriging or conditional simulation?

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  • thomas bishop (RRes-Roth)
    Hello, At the moment I am examining methods for estimating the mean and the variance of the mean of irregularly shaped blocks, in this case soil units and
    Message 1 of 1 , Mar 15, 2006
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      At the moment I am examining methods for estimating the mean and the
      variance of the mean of irregularly shaped blocks, in this case soil
      units and agricultural fields, based on an irregular soil sampling

      The simplest solution is block kriging based on a fine mesh
      discretization of the block. However when the range of the variogram is
      less than the lengths of the block being estimated this is not
      recommended. In this situation conditional simulation is recommended,
      e.g the GSLIB manual and some papers by Goovaerts. This involves
      simulating values, conditional to the samples, onto a fine grid covering
      the block. Over many realizations, the mean and its variance of the
      region may be estimated from the simulated values on the fine grid. In
      particular, LU Decompsition has been mentioned.

      This issue has been raised on the list a few years ago but it was not
      clear which way was best.

      Other than getting a pdf, some reasons for preferring simulation
      (i) numerical instabilities when block kriging with large matrices
      (ii) the semivariogram is most accurate at short lags so to using
      modelled semivariance values beyond the range is unwise.

      I have used both methods (I used LU Decomposition for simualtion) and
      get very similar results which is probably as expected. It seems to me
      that problems with block kriging the regional mean equally apply to
      conditional simulation when using LU Decomposiiton. LU Decomposiiotn
      involves a larger matrix than kriging, and like kriging it uses the
      estimates of the semivariance at longer lags to fill out the covariance
      matrix between the condtioning data and non-conditioning locations.

      I could use other simulation algorithms such as Sequential Gaussian
      Simulation but it all seems an overkill when I just want an estimate of
      the mean and the variance. Especially if I want to extend my work to
      cokrige 4 variables simultaneously, each being equally important. I
      imagine this would take a long time with Sequential Gaussian Simulation
      let alone the time to code this!

      Finally, a good estimate of the variance is equally important as the
      mean in my work so finding the mean value based on dividing the blocks
      into smaller blocks is not appropriate as it does not give an estimate
      of the variance

      So given that I just want the mean and variance, and not the pdf, why
      should I use simulation, especially using LU Decompsition, when the
      results are the same?

      Would it be wise to state that if you only want the mean and variance =
      use block kriging, if you want a pdf = use condtional simulation?

      Thanks for your help in advance.


      Thomas Bishop

      Biomathematics and Bioinformatics Division
      Rothamsted Research
      AL5 2JQ
      United Kingdom
      Tel: + 44 (0) 1582 763 133 ext 2574
      Fax: + 44 (0) 1582 760 981
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