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GEOSTATS: Re: Non-colocated datasets. MUCK

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  • Isobel Clark
    ... Deepest apologies. I was unaware that the geocities sites were case sensitive!! Link is: http://uk.geocities.com/drisobelclark/resume/Publications.html
    Message 1 of 1 , Oct 29, 2000
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      > Hi. what is MUCK? I couldn't access the
      > publications section of your web
      > page. thanks. Brian Gray
      Deepest apologies. I was unaware that the geocities
      sites were case sensitive!! Link is:

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

      Just when I think I've mastered this Web stuff it
      turns around and does something different! You can get
      there and to my other pages from the base home page

      http://uk.geocities.com/drisobelclark

      Back in 1985 or so, when Bill Harper and I invented
      non-co-located kriging we didn't know that was what we
      were supposed to call it. At the time there was a joke
      going round the community about the excessive use of
      intials (IK, OK, DK, SK and so on) and there was a
      rumour that someone was out there looking into Fuzzy
      Universal Co-Kriging (work it out). To distinguish our
      approach from the traditional co-kriging, we called it
      Multivariable Universal Co-Kriging (MUCK).

      The major difference between MUCK and traditional
      co-kriging is simply in the definition of the
      semi-variogram. We could not use the traditional
      approach because we were looking at pressure heads in
      water wells in two different aquifers. From the two
      surfaces kriged individually, we could see that the
      pressure surfaces were highly related. However, we
      could not get a semi-varogram which demanded both
      measurements at the same location. So we invented the
      other one. For a more formal coverage, check out the
      relevant section in Noel Cressie's book where he gives
      the non-co-located as the standard approach and the
      co-located as a historical background.

      The kriging equations remain the same. The major
      differences are these:

      (a) you can use all of your data all of the time to
      estimate the semi-variogram

      (b) you get a positive definite shape like a normal
      semi-variogram. there is no possibility to get
      negative values as with the traditional one

      (c) the intercept (nugget effect) is directly
      analagous to the correlation coefficient which you
      woul dget for co-located pairs

      The drawbacks are:

      (1) if the two measurements are of wildly different
      scales, any structure in the semi-variogram would be
      masked (same as with all covariance approaches)

      (2) the difference between the means of the two
      variables is a factor in the MUCK approach. We did not
      have this problem in our application, because both
      surface had a high degree of trend which had to be
      removed, leaving the average for both variables
      (residuals) as zero.

      Both of these problems can be solved by using a
      standardisation (say Normal score) or rank transform
      on all of the variables. This will give the correct
      model for the semi-variogram (theoretically) which can
      then be scaled if necessary or desirable. In the
      statistical world an auto-correlation approach such as
      this is always given as preferable to a co-variance
      approach such as that generally used in kriging.

      Does this help?
      Isobel Clark


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