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AI-GEOSTATS: SUM: Sensitivity analysis of automatic variogram fitting

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  • Gregoire Dubois
    Dear all, here is a summary of the two replies I got to my question on robust variograms and automatic mapping: 1) The following reading was suggested by
    Message 1 of 1 , Feb 13, 2003
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      Dear all,

      here is a summary of the two replies I got to my question on robust variograms
      and automatic mapping:

      1) The following reading was suggested by Victor De Oliveira

      Lark, R.M. (2000), A comparison of some robust estimators of the variogram for
      use in soil survey, European Journal of Soil Science, 51, 137-157.

      2) Dan Cornford made the following comments:

      Acronyms used hereafter are:

      SVM: Support Vector Machine
      GP: Gaussian Processes


      SVM are not designed for spatial data. However when treated as
      function approximators (i.e. when the process is real and the noise is
      IID) they are good. However they are not probabilistic models as
      GP's are.


      Dan's group (Neural Computing Research Group, http://www.ncrg.aston.ac.uk)
      have been doing some work on machine learning algorithms for GP's based on
      Bayesian learning algorithms. This allowed them to estimate a GP sequentially
      (using one observation at a time) and also estimate the parameters of the
      covariance (variogram) function.

      It also has a (principled) sparsity heuristic added (which accounts for
      first and second moments), so it works on very large data sets, but
      gives probabilistic prediction.

      However the method is not fully Bayesian in that an approximate MAP
      estimate of the covariance function is used. Also the method would not
      be robust to outliers, since these are not currently incorporated in the
      model. Basically it is very difficult to treat uncertainty in the
      covariance parameters analytically (which is necessary for fast
      computation).

      Dan's suggestion has therefore to do with sampling (i.e. Monte Carlo).
      This still does not address the functional form, although sampling could
      again be used, but would be painfully slow.

      Implementing cost functions to cope with kriging with outliers might be a
      solution but this would require the use of prior information to set the
      covariance.

      Thanks again

      Gregoire

      PS: For those interested about SVM and geostatistics, I have in my bookmarks
      the following reference:

      Nicolas Gilardi's publications (as well as his PhD thesis, 2002, which are
      available online at http://www.idiap.ch/~gilardi/publi.html and
      ftp://ftp.idiap.ch/pub/gilardi/these_gilardi.ps.gz)


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