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Re: [AI-GEOSTATS: global vs local ordinary kriging]

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  • Ulrich Leopold
    ... I agree. But then you need to model the experimental semivariogram for all distances. Wouldn t this be a problem to find a reliable model fit? ... The
    Message 1 of 4 , Jul 9, 2003
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      On Wed, 2003-07-09 at 10:06, Gregoire Dubois wrote:

      > I'm surprised we got mainly "pragmatic" answers to your question and
      > would have expected from statisticians and mathematicians more reactions
      > about a possible statistical heresy: the semivariogram model is fitted to an
      > experimental semivariogram which was obtained from a certain number of points.
      > To be mathematically correct in terms of the various hypotheses used, should
      > one not use a search neighbourhood that is equal to the one used to obtain the
      > semivariogram (frequently all points) ?

      I agree. But then you need to model the experimental semivariogram for
      all distances. Wouldn't this be a problem to find a reliable model fit?

      > On the other hand, if the main objective is to compare various algorithms
      > (e.g. ordinary kriging versus indicator kriging, or indicator kriging versus
      > log-kriging) or kriging variances obtained by various models, I would imagine
      > that using a "no search" approach (all neighbours are used) would be the most
      > reasonable approach...

      The objective is to compare different algorithms AND create a most
      realistic map at the same time by using these algorithms. So I guess
      there have to made some compromises. Probably cross-validation could
      help if I use a sub set of the data set.

      Ulrich




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    • Ruben Roa
      ... have expected from statisticians and mathematicians more reactions about a possible statistical heresy: the semivariogram model is fitted to an
      Message 2 of 4 , Jul 10, 2003
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        >Hi Ulrich
        >
        >I'm surprised we got mainly "pragmatic" answers to your question and would
        have expected from statisticians and mathematicians more reactions about a
        possible statistical heresy: the semivariogram model is fitted to an
        experimental semivariogram which was obtained from a certain number of
        points. To be mathematically correct in terms of the various hypotheses
        used, should one not use a search neighbourhood that is equal to the one
        used to obtain the semivariogram (frequently all points) ?

        Okay, as a statistician i would say that the use of a restricted
        neighbourhood search in kriging is akin to the statistical concept of
        'conditioning on a relevant subset'. This concept normally refers to a
        relevant subset in the sample space (i.e. all possible samples not just the
        actually observed one) while in this case it refers to a relevant subset in
        the observed sample given the fitted model. Probably then, an extension of
        the concept of relevant subset in the sample space to the case of the
        observed sample given a model would justify, from a statistical point of
        view, not to use all points in kriging. This seems reasonable too if we
        consider the model as taking the place of the sample space, i.e. as the
        mechanism generating the samples, which in turns seems consistent with the
        general idea of conditioning on an ancillary statistics (the ancillary here
        would be the spatial neighbourhood since these neighbourhood does not
        depend on the parameter to be estimated, namely the density of the random
        variable in the point being interpolated). This is off the top of my head,
        so please 'hande with care'.
        Ruben
        http://webmail.udec.cl

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      • Isobel Clark
        Maybe it is worth pointing out that Ordinary Kriging with a global neighbourhood (using all the points in simple speak) is the same as Simple Kriging with a
        Message 3 of 4 , Jul 11, 2003
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          Maybe it is worth pointing out that Ordinary Kriging
          with a 'global neighbourhood' (using all the points in
          simple speak) is the same as Simple Kriging with a
          neighbourhood which extends to the range of influence
          of the semi-variogram model (if any).

          Given this fact, you would be computationally safer to
          do Simple Kriging - otherwise known as "kriging with
          known mean" and saving yourself the problems of
          enormous and sparse matrix solutions.

          The only overhead to Simple Kriging is producing a
          reliable estimate of the global mean and, to be
          realistic, a standard error associated with it.

          Isobel Clark
          http://geoecosse.bizland.com/courses.htm

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