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1944[ai-geostats] Re: question about kriging with skewed distribution

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  • Isobel Clark
    Mar 5, 2005
      Ruben (et al)

      It is true that Matheron's theory is based on no
      distributional assumptions. In fact, there is no
      requirement for the distribution to be the same at
      every location in the study area.

      The necessity for using traditional geostatistical
      theory is that the 'difference between two values'
      should have a common distribution for a specified
      distance (and possibly direction). The form of this
      distribution is irrelevant but it needs to possess a
      mean and variance.

      The problem lies not with the theory but with the
      practice. If you have the whole 'realisation' you can
      calculate the true average and variance and the shape
      of each distribution is irrelevant. If you have only a
      few samples, then you can only find estimates for the
      means and variances at each distance.

      If the underlying distribution is highly skewed then,
      unless you have ideal conditions (large number of
      samples, regular sampling locations), your estimate of
      the variance will be unstable -- influenced by the
      average of the samples included in the particular
      estimate. There was a huge amount of debate about this
      "proportional effect" back in the 70s [search for
      'relative semi-variogram'].

      So, you have two potential problems:

      (1) you may not get any true picture of the
      semi-variogram due to the uncertainty associated with
      each point exacerbated by the proportional effect;

      (2) you may not wish to use an averaging technique
      such as kriging on skewed samples. All of Sichel's
      (mining) and much of Krige's work was motivated by the
      fact that local averaging is not sensible when your
      data has a coefficient of variation greater than
      around 1.

      The theory is terrific, witness its survival for over
      40 years and its proliferation over many fields of
      application. However, real life isn't so tidy at the
      sharp end ;-)

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