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Re: AI-GEOSTATS: Regression slope in kriging

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  • Isobel Clark
    Joe ... Simple kriging as invented by Danie Krige in the 1950 s was exactly a linear regression method. The kriging system has a left-hand-side consisting
    Message 1 of 3 , Apr 29, 2003
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      Joe

      > 1.Kriging is often cited as least squares regression
      Simple kriging as invented by Danie Krige in the
      1950's was exactly a linear regression method. The
      'kriging' system has a 'left-hand-side' consisting of
      the variance/co-variance matrix between sample pairs
      and a 'right-hand-side' consisting of the co-variances
      between each sample and the unknown value. Krige
      derived the variances and co-variances empirically
      from 50 years of historical data.

      In the early 1960s, Matheron's work put this on a
      modelling (theoretical) footing by suggesting that the
      co-cariances could be modelled by a function -- the
      semi-variogram reversed. Thus the l.h.s became
      co-variances or semi-variograms depending on your
      personal preference and likewise the r.h.s.

      However, Matheron also introduced the notion that the
      weights should add up to one and invented 'ordinary'
      kriging which is not (strictly) classical linear
      regression.

      > 2.I read in seveal papers that it is possible to
      > calculate the slope of
      > regression from parameters of the krigin system.
      All explained in my 1983 paper 'regression revisited'
      in Mathematical Geology. I can send you a copy if you
      can't find it or you can download it from:

      http://uk.geocities.com/drisobelclark/resume/Publications.html

      (note capital P)

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

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    • Digby Millikan
      Joe, What is the formulae for the regression slope for punctual kriging, you only cited the case for block kriging. By block variance do you mean the
      Message 2 of 3 , Apr 29, 2003
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        Joe,
        What is the formulae for the regression slope for punctual kriging,
        you only cited the case for block kriging. By block variance do you
        mean the dispersion variance of points within blocks or the distribution
        variance of block grades.

        Digby

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