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

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  • Lucy Roberts
    Hi Perry (from just down the road at JCU Townsville!) A few references I have found useful are: Rivoirard, J. (1994) Introduction to Disjunctive Kriging and
    Message 1 of 4 , Mar 22, 2005
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      Hi Perry

      (from just down the road at JCU Townsville!)

      A few references I have found useful are:

      Rivoirard, J. (1994) Introduction to Disjunctive Kriging and Non-Linear Geostatistics.  Clarendon Press, Oxford. 181pp.

      which has some good case studies at the back, and

      Humphreys, M. (1998) Local recoverable estimation: A case study in uniform conditioning on the Wandoo Project for Boddington Gold Mine in Proceedings of Symposium on Beyond Ordinary Kriging, Perth, Western Australia (Geostatistical Association of Australasia).

      which again is case study based, so quite easy to read.

      I'm sure lots of people will be able to help with more in-depth stuff.

      Cheers,  Lucy

      ***************************************************************
      Lucy Roberts
      PhD Candidate
      "Sampling and Estimation of Archaean Lode-Gold Deposits"
      Department of Earth Sciences
      James Cook University
      Townsville
      QLD 4811
      Australia
      Phone:  +61 (0)7 4781 6151
      Fax:      +61 (0)7 4725 1501
      ***************************************************************





      -----Original Message-----
      From: Perry Collier [mailto:PCollier@...]
      Sent: Wednesday, 23 March 2005 10:56 AM
      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...
      Cheers
      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
       
      PO Box 527
      Cloncurry QLD 4824
      Australia
       
      "I like rich people. I like the way they live. I like the way I live when I'm with them..."
      From Roger & Hammerstein's Sound of Music


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    • Digby Millikan
      bi-Gaussian assumption for non-mathematiciansPerry, I am not familair with simulation, but your post would be a good starting point for discussion, I assume
      Message 2 of 4 , Mar 23, 2005
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        bi-Gaussian assumption for non-mathematiciansPerry,

        I am not familair with simulation, but your post would be a good starting
        point for discussion,
        I assume simulation is carried out by kriging values generating a kriged
        estimate and an
        estimation variance at each point. I assume the next step is to adjust the
        kriged values using
        the estimation variance at each point? It is assummed that the grade data
        has a gaussian
        distribution, it is also assumed the error described by the estimation
        variance at each point
        has a gaussian distribution. Is this the bi-gaussian assumption, which page
        of Pierre's book
        are you looking at? You could plot a distribution plot of your grade data to
        see if it has a normal
        (gaussian) distribution, this would confirm the first assumption, and I
        guess there is some
        mathematical implication that the confidence or error of grade estimates
        described by the
        estimation variance at each point also has a normal distribution. Sorry I
        take my first course
        in geostatistics next summer school at WASM, so this is only a guess, maybe
        someone can
        confirm or comment on these?

        Regards Digby
        ----- Original Message -----
        From: Perry Collier
        To: ai-geostats@...
        Sent: Wednesday, March 23, 2005 11:25 AM
        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...

        Cheers

        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

        PO Box 527
        Cloncurry QLD 4824
        Australia

        "I like rich people. I like the way they live. I like the way I live when
        I'm with them..."
        From Roger & Hammerstein's Sound of Music



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        If you receive this e-mail in error, any use, distribution or
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        Support Centre phone: Australia 1800 500 646
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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 3 of 4 , Mar 23, 2005
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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...

          Cheers,

          Pierre

          -----Original Message-----
          From: Perry Collier [mailto:PCollier@...]
          Sent: Tue 3/22/2005 7:55 PM
          To: ai-geostats@...
          Cc:
          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...

          Cheers

          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

          PO Box 527
          Cloncurry QLD 4824
          Australia

          "I like rich people. I like the way they live. I like the way I live when I'm with them..."
          From Roger & Hammerstein's Sound of Music



          **********************************************************************
          The information contained in this e-mail is confidential and is
          intended only for the use of the addressee(s).
          If you receive this e-mail in error, any use, distribution or
          copying of this e-mail is not permitted. You are requested to
          forward unwanted e-mail and address any problems to the
          Xstrata Queensland Support Centre.
          Support Centre e-mail: supportcentre@...
          Support Centre phone: Australia 1800 500 646
          International +61 2 9034 3710
          **********************************************************************
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