Monday, February 14, 2011

How to fingerprint boreholes

I know how to fingerprint boreholes. What’s more, Merks and Merks not only know how to fingerprint boreholes but how to derive unbiased confidence limits for metal contents and grades. We have known all of that since Professor Dr Michel David in February 1990 rejected Precision Estimates for Ore Reserves. He was but one of many similarly gifted geostatistical reviewers with CIM Bulletin. The same paper was praised by and published in Erzmetall, October 1991. What’s more, Borehole Statistics with Spreadsheet Software was approved by and published in SME Transactions 2000. I applied this technique to a large set of test results for a gold deposit in Kazakhstan. When I asked my contact at Barrick Gold what he thought of my report, his response was: “It’s worth its weight in gold”. I didn’t charge quite that much on February 9, 1998.

Here’s what Merks and Merks have decided to propose. We give a short course on how to derive unbiased confidence limits for grades and contents of mineral inventories. Professor Dr Roussos Dimitrakopoulos and all of his staff and students should participate. Of course, Dr Frederik P Agterberg, Emeritus Scientist with Natural Resources Canada, should be invited. Those who are Members of the International Industry Advisory Board ought to attend. McGill staff and students should be given free access. Our fee for this crash course in statistical thinking is C$100,000.
Here's why! It took a long while to unscramble the French sampling school. Here are but a few of the most salient facts. Dr Pierre Gy would put a set of primary increments in a single basket in a manner of speaking. That’s why he didn’t get a single degree of freedom. It may well be why Gy engineered his sampling constant. What he didn’t know was that his sampling constant does have its own variance. Professor Dr Georges Matheron never put a set of core samples from the same borehole in but one basket. So, he was blessed with almost as many degrees of freedom as there were core sections in a borehole. Not quite as many because a set of n boreholes gives df=n-1 degrees of freedom. But Matheron got stuck in a rut. He may have taught his disciples to assume spatial dependence between measured values in ordered sets, and to strip the variance off the distance-weighted average AKA kriged estimate. It would explain why Stanford's Professor Dr Andre G Journel is so unfamiliar with Fisher’s F-test. He never knew that ordered sets of n measured values give dfo=2(n-1) degrees of freedom. Neither did he know that the number of degrees of freedom for a set of measured values with variable weights is a positive irrational. It took a lot of independent statistical thinking to unscramble what French sampling school had cooked up between 1954 and 1974.


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