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[ai-geostats] Re: Geostats Scam continued

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  • Isobel Clark
    O boy, I wish my world included the kind of data which would allow modelling of anisotropy on a 10m scale! I am full of envy. Isobel
    Message 1 of 1 , Feb 14 2:13 PM
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      O boy, I wish my world included the kind of data which would allow modelling of anisotropy on a 10m scale! I am full of envy.

      Edward Isaaks <ed@...> wrote:
      Hello List

      FYI, a few comments related to the ongoing discussion re Geostats Scam.

      Stephen Henley makes some valid points on the shortcomings of geostatistics.
      In particular, I have also been troubled by the application of models
      "invariant under spatial translation" to real world data.

      "The proper selection of data" for estimation is considered by many to be
      the fundamental mantra of ore resource estimation. Typically, the selection
      of data for variography and the estimation of block model grades is
      controlled through manually interpreted models of lithology, alteration,
      grade shells, structural domains and so on. Although these models are
      practical at the scale of the deposit, they are not practical at local
      scales where local scale is defined by distances as short as 10 m, over
      which abrupt changes in the direction of geologic trends such as grade,
      fault direction, fracture patterns, and rock type contacts are observed.
      Obviously, it is not practical to control the selection of data at this
      scale using manually interpreted models.

      However, the good news is that the proper selection of data for kriging can
      be achieved at a local scale by aligning an anisotropic search ellipsoid
      with the local geologic trend(s) on a block by block basis.

      The idea is simple. Before each block is estimated, the anisotropy ratios of
      the local search neighborhood are adjusted and the axes aligned with local
      trends in the data. The method has come to be known as local anisotropy
      kriging or LAK. The results are remarkable. I have an example where LAK
      applied to grade control out performs ordinary kriging by reducing dilution
      and ore loss. You can read more about this relatively new implementation of
      an old idea by visiting www.isaaks.com and clicking on "Geo Docs".

      I would also add a note regarding popular geostatistical misconceptions, and
      there are several. For example, Krige, Deutsch, Vann and many others have
      published papers admonishing conditional bias. However, in mining
      applications (where geostatistics has its roots) conditional bias is
      actually irrelevant, unless the estimates are used for grade control. See
      "The Kriging Oxymoron" at www.isaaks.com "Geo Docs" for a peer reviewed
      paper on the subject.

      I recently read a paper by J Vann, S Jackson, and O Bertoli (2003) that
      actually proposes a method for designing the kriging search neighborhood
      based on minimizing conditional bias. Horrifying - do they not realize that
      such practice actually increases the estimation error of the predicted
      tonnes and grade above cutoff? This paper is probably the worst (best?)
      example I have seen of a faulty misconception in 25 years of ore resource
      assessment. One can almost understand why geostatistics might be labeled a

      However, I'm not sure I agree with Stephen where he appears to suggest that
      the "vast array of methods and an array of intensely mathematical published
      papers" are somewhat responsible for providing the means to deliver
      "whatever the client wants". The difference between a professional and an
      amateur practitioner is knowing which is the correct tool for the job and
      how to use it properly. I'd argue that a packed toolbox is not the problem
      but rather, the inexperienced or dishonest practitioner is the problem.

      And finally, I have done some research on the subject of computing "weighted
      variances" since a number of "weighted variance" estimators can be found in
      the literature including Mr. Merks' version. Each of the estimators I found
      provided a different estimate of the weighted variance and to make matters
      worse, not one was shown to be a valid statistical estimator -- they were
      simply stated without derivation(see footnote). However, the good news is
      that with careful work and with help from Colin Daly and Don Myers, I now
      have the mathematical derivation of an unbiased estimator for the population
      variance given a sample of N (iid) observations with associated weights.
      Now, it turns out that in spite of all the huffing and puffing by our
      colleague Mr. Merks, the "weighted variance" estimator that he so loudly
      champions is biased under the iid model! Perhaps Mr. Merks' time could have
      been better spent looking for an unbiased variance estimator rather than
      stalking the "lost variance". :-)

      A copy of this work will be made available to the list following

      Derivation -- A logical or mathematical process indicating through a
      sequence of statements that a result such as a theorem or a formula
      necessarily follows from the initial assumptions.

      Edward Isaaks

      J Vann, S Jackson and O Bertoli, (2003), "Quantitative Kriging Neighbourhood
      Analysis for the Mining
      Geologist - A Description of the Method With Worked Case Examples", 5th
      International Mining Geology Conference, AusIMM.

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