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RE: [ai-geostats] bi-Gaussian assumption for non-mathematicians

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  • Pierre Goovaerts
    Well, as the author of the green bible I guess I should help out a little bit here... The key idea is that there exists an analytical expression that allows
    Message 1 of 4 , Mar 23 3:24 PM
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      Well, as the author of the "green bible" I guess I should help out a little bit here...

      The key idea is that there exists an analytical expression that allows you to
      compute a priori, for any threshold of a multigaussian random function,
      the indicator semivariogram models. You only need to know the threshold
      and the normal score semivariogram of the variable. Then, you just compare
      the "expected" or "theoretically-derived" indicator semivariogram models
      to the "empirical" or "derived from the data" ones.

      Note that you don't even need to go through the burden of computing the
      "theoretically-derived" indicator semivariogram models to know that the
      underlying assumptions of the multigaussian model are not fulfilled.
      In many situations, you will notice that your experimental indicator semivariograms
      are not symmetric with respect to the median; for example the 0.1 decile
      semivariogram might have a longer range than the 0.9 decile semivariogram.
      This happens frequently since the low background values tend to be better
      connected in space than the high values...

      The next question is "what do we do with that?"... or in other words "How do we
      know that the differences between expected and empirical indicator semivariograms
      are significant". You could test it, but I don't think it's worth it in practice...
      Well, cross-validation has taught me that even if the indicator semivariograms don't
      look like expected under the multigaussian model, multigaussian kriging might
      still give you better results than indicator kriging.. so it's hard to come up with
      "cast-in-stone" rules regarding the relative merits of parametric and non-parametric
      approaches.. but I am sure that everyone who has some experience with geostatistics
      has already realized that.. As I often say during my short-course, geostatistics provides
      you with a toolbox, and cross-validation and experience will teach you wich tools
      to use in any particular situation...



      -----Original Message-----
      From: Perry Collier [mailto:PCollier@...]
      Sent: Tue 3/22/2005 7:55 PM
      To: ai-geostats@...
      Subject: [ai-geostats] bi-Gaussian assumption for non-mathematicians

      Hi all from Oz (Australia)

      First post on this list. I am a mine geo currently doing some post-grad geostats study (Edith Cowan Uni in WA, hi Dr Ute, Prof. Lyn!).

      Expanding on some very useful feedback from my Uni course director, I would be interested in your learned "from the horse's mouth" comments (what, why, how, when) regarding the bi-Gaussian assumption for Gaussian simulation and the various means of checking it. I am slightly "mathematically challenged", so if anyone could explain the whole thing without too much scary maths, it would be much appreciated. I have Goovaerts' green geostats bible, which is good stuff, but I'm trying to convert some of the maths to English.

      Any comments from mining practitioners would be interesting...


      Perry Collier
      Senior Mine Geologist
      Ernest Henry Mine
      Xstrata Copper Australia
      Ph:(07) 4769 4527
      Fax: (07) 4769 4555
      E-mail: pcollier@...
      Web: http://www.xstrata.com

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