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[ai-geostats] RE: A banal question...

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  • Isobel Clark
    Simone Not so banal a question. 34 years ago my supervisor gave me some papers to read which said exactly that. Even with a Master s in applied statistics, I
    Message 1 of 1 , May 2, 2005
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      Simone

      Not so banal a question. 34 years ago my supervisor
      gave me some papers to read which said exactly that.
      Even with a Master's in applied statistics, I could
      not make head-nor-tail of the explanation. So I went
      on a three week short course at Fontainebleau and they
      explained it around the middle of the third week!

      A very simplistic explanation: when you calculate an
      ordinary covariance you have two columns of figures,
      say variable g and f. The covariance between g and f
      is calculated (in practice) by multiplying the two
      columns together, summing the results and then
      subtracting the product of the two means. Difficult to
      do in a text email but:

      Sum(g x f)/n - mean(g) x mean(f)

      This is exactly equivalent to:

      Sum (g-mean(g)x(f-mean(f))/n

      {leave out the whole n or (n-1) debate at this point)

      In a geostatistical context, g would be the value of a
      sample (any sample). f would be the value of another
      sample a specified distance away. That is, specify one
      particular distance (h), find pairs of samples that
      distance apart, first sample in pair is g (first
      column), second sample in pair is f (second column).
      Calculate covariance as above with the modification
      that the mean of g and the mean of f will be the same.


      Repeat for many different distances and you end up
      with a graph of how the covariance of the values
      varies with the distance between the samples.

      I, personally, prefer the semi-variogram approach
      because it is a lot easier to explain! Also, you do
      not need to know (or estimate) the mean. More
      explanations in free downloadable Practical
      Geostatistics 1979,
      http://uk.geocities.com/drisobelclark/practica.htm.

      If you have second order stationarity, the covariance
      function is simply the sample value variance minus the
      semi-variogram.

      Does this help?
      Isobel
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