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1535GEOSTATS: Summary: Jacknife, Bootstrap

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  • Gregoire Dubois
    Sep 6, 1905
    • 0 Attachment
      Dear all,

      here is a first summary of the replies I received to my first question (on the
      use of resampling techniques & cross-validation techniques applied to spatial
      dependent data) and that have not been sent to the list.
      Thanks a lot to all who contributed.

      1st question:

      Denis Marcotte ( Denis.Marcotte@... )write

      "It is still an open question. Some have suggested to work with
      orthogonal residuals. The problem is that the orthogonalization calls
      for the covariance function which is precisely what we want to estimate with
      these techniques. Journel (1994) suggested to produce conditional realizations
      and then to resample from these realizations. This calls
      for a knowledge of the covariance function (to use in the conditional
      simulation) and of the sampling strategy used to get the original
      sample that will be applied to the various realizations
      (But, of course not at the same points, as these are perfectly
      reproduced by the conditional simulations). Naraghi and Marcotte (1996) used
      the fact that increments computed for variogram computation are rather weakly
      correlated in average for small lags and when the same
      data point is not used for the construction of more than one increment
      for a given lag distance. They then resampled the increments within
      each lag distance class. A bad idea is certainly to resample directly
      the data points, as this biased strongly the covariance function toward
      a pure nugget effect."

      Two other references are given by Edzer Pebesma

      A. Solow, bootstrapping correlated data,
      Math. Geol. early eighties.

      P. Kitanidis, something with `Orthogonal residuals' in the title, also
      Math. Geol., year unknown.

      For what concerns the use of cross-validation applied to geostatistical
      data,Donald Myers writes

      There have also been a couple of papers by Bruce Davis, A. Solow and
      Kathryn Campbell (all in Math Geology) with warnings about the use of
      The cross-validation statistics are not equally sensitive to changes in the
      variogram model and or the parameters of the variogram. Some of them are
      sensitive to changes in the search neighborhood. In the case of simple
      kriging and cross-validation, the theoretical maximum value of the
      correlation between the observed and estimated values is 1. However if
      ordinary kriging is used then the theoretical maximum value is less because of
      the LaGrange multiplier. Similarly if simple kriging is used the theoretical
      minimum for the correlation between estimated and the
      estimation error is zero, this is not true if ordinary kriging is used.
      Again the LaGrange multiplier has an effect.

      1992, Myers, D.E., Selection of a radial basis function for data
      interpolation. in
      Advances in Computer Methods for Partial Differential Eq. VII, R.
      Vichnevetsky, D. Knight and G.Richter (eds), IMACS, 553-558

      1991, Myers,D.E., On Variogram Estimation. in Proceedings of the First
      Inter. Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II,
      American Sciences Press, 261-281

      1991, Myers,D.E., Interpolation and Estimation with Spatially
      Located Data, Chemometrics and Intelligent Laboratory Systems 11, 209-228

      Gregoire Dubois
      Section of Earth Sciences
      Institute of Mineralogy and Petrography
      University of Lausanne

      Currently detached in Italy


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