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AI-GEOSTATS: Regression slope in kriging

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  • Joe Geo
    Dear ai-geostat follows I have some questions regarding kriging. 1.Kriging is often cited as least squares regression method - this I understand for liner
    Message 1 of 3 , Apr 28, 2003
      Dear ai-geostat follows

      I have some questions regarding kriging.

      1.Kriging is often cited as least squares regression method - this I
      understand for liner regression but how does this actually occur in the
      kriging matrix ? Are the covariances the square values that are being
      minimised ?

      2.I read in seveal papers that it is possible to calculate the slope of
      regression from parameters of the krigin system. Specifically:

      (Block variance-kriging variance + abs(lagrangian))/(block varaince -
      kriging variance + 2 x abs(lagrangian))

      I can follow the derivation of the kriging variance and I can see the
      purpose of the lagrangian, where does the block variance come from and how
      (in conceptual terms) does this equation give the regression slope of true
      versus actual block grades ?

      Thanks in advance

      Joe





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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 2 of 3 , Apr 29, 2003
        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 3 of 3 , Apr 29, 2003
          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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