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AI-GEOSTATS: Summary: Log-normal back transform in Webster & Oliver]

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  • Gregoire Dubois
    Hello again, Murray s reply to my question says it all. Thanks again a lot to Isobel Clark (special thanks for the nice explanation on the behaviour of the
    Message 1 of 1 , Jul 29, 2003
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      Hello again,

      Murray's reply to my question says it all. Thanks again a lot to Isobel Clark
      (special thanks for the nice explanation on the behaviour of the Lagrange
      parameter !), Gerard Heuvelink and Murray Lark.

      Gregoire




      ------ Original Message ------
      Received: Mon, 28 Jul 2003 06:22:12 PM CEST
      From: "murray lark (SRI)" <murray.lark@...>
      To: 'Gregoire Dubois' <gregoire.dubois@...>
      Subject: RE: AI-GEOSTATS: Log-normal back transform in Webster & Oliver

      Gregoire,

      Just to follow up my previous email, I have had a word with Dick Webster who
      confirms that the missing Lagrange multiplier in Equation 8.38 was a printing
      error, he thanks you for pointing it out. Also note that the Lagrange
      multiplier should have an argument, bold x_0, since it is specific to the
      kriging target site.

      Murray Lark

      -----Original Message-----
      From: Gregoire Dubois [mailto:gregoire.dubois@...]
      Sent: 28 July 2003 10:39
      To: ai-geostats@...
      Subject: AI-GEOSTATS: Log-normal back transform in Webster & Oliver


      In the book "Geostatistics for Environmental Scientists"
      By Richard Webster & Margaret A. Oliver, Wiley (2000), one will find in page
      180 a brief discussion on the back-transformation of the kriging estimates.

      In ordinary kriging, when the natural logarithm (ln) is used, the
      back-transformation will involve the Lagrange parameter (see equation 8.36).
      No problem so far.

      But... the authors write in equation 8.38 that if one is using common
      logarithms (log10) instead, the unbiased back-transformation of the ordinary
      kriging estimates does not involve the Lagrange multiplier anymore.
      Is this correct ? In the affirmative, can someone point me to a paper
      discussing "natural" log normal kriging versus "common" log normal kriging ?

      Thanks again for any help.

      Regards,

      Gregoire





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