Dr Frits Agterberg, IAMG's Past President and NRCan's Emeritus Scientist, didn't explain on November 3, 2009, why the variance of his own distance-weighted average point grade went missing. Dr Roussos Dimitrakopoulos, McGill's miracle man and JMG's Editor-in-Chief, talked about stochastic mine planning optimization at APCOM 2009. He should apply his stochastic mine optimization to Gemcom's gold resource at Busang and see what mining plan it cookes up. What kept Bre-X humming along was to assume gold mineralization between salted boreholes, to krige and smooth a little, and to rig the rules of statistics a lot. Canada's newly-minted National Securities Regulator ought to rule against geostatistically engineered mineral inventories in annual reports. Matheron, the self-made wizard of odd statistics, lost the variance of the lenght-weighted grade of core samples in 1954, and the variance of the length-weighted block grade in 1960!

Photo by Nick Didlick Jan W Merks metrologist, author, lecturer, consultant, whistleblower, 'gadfly', 'pariah', 'iconoclast', CIM Life Member

Dr F P Agterberg lost the variance of his distance-weighted average point grade first in his 1970 paper and once more in his 1974 Geomathematics. He did refer to Fisher's F-test elsewhere in this textbook but didn't know how to test for spatial dependence between core samples in a borehole, or between boreholes on a line. He ought to delete Chapter 10 Stationary Random Variables and Kriging. How long does he take to right a wrong? Why does he assume that his distance-weighted average point grade needs no variance? It's time to explain why!

In November 1989, we applied Fisher's F-test in Precision Estimates for Ore Reserves to confirm spatial dependence between gold grades of ordered rounds in a decline. Testing for spatial dependence troubled Professor Dr M David, CIM Bulletin's most dedicated enforcer of Matheronian geostatistics. Scores of similarly gifted geostatistocrats postulated spatial dependence may be inferred unless proven otherwise. All sorts of degrees of freedom fighters were troubled when "classical Fischerian [sic] statistics" proved spatial dependence between gold grades of ordered rounds. Fisher's F-test also proved the intrinsic variance of Bre-X's bogus gold in Busang's barren rock to be statistically identical to zero, as it ought to be. Sound statistics did so several months before Bre-X's boss salter vanished! Bre-X's original and duplicate bogus assays for a few early boreholes could have proved early on that a salting scam was in progress at the Busang project!

Dr F P Agterberg, Past President, International Association for Mathematical Geosciences, does not talk but has others speak on his behalf. Professor Dr R Dimitrakopoulos, Editor-in-Chief, Journal for Mathematical Geosciences, stand on guard against true variances. This association and its journal got new names but the kriged game remains the same. Why should Agterberg revise his 1974 Geomathematics? Mining investors do not question mineral inventories in annual reports, do they?

Dimitrakopoulos is the Canada Research Chair and BHP Billiton Chair in Mine Planning Optimization at the Department of Mining, Metals and Materials Engineering at McGill University. He teaches McGill's students all he knows about stochastic modeling with voodoo variances. When he chaired in June 1993 a forum on Geostatistics for the Next Century, he did not know either that every kriged estimate does have its own variance. JMG's Editor-in-Chief is still playing with pseudo kriging variances. Surely, McGill's students are smart enough to derive the variance of any weighted average. They should know that stochastic modeling with voodoo variances is a scientific fraud. Do all professors of mathematical statistics know that stochastic modeling with invalid variances gives junk statistics?

The world's mining industry is caught in a Catch-22. The problem is not so much that geostatistics overestimate metal grades and contents of mineral inventories but that they are bound to shrink during mining. David dabbled at geostatistical grade control in his 1988 handbook. He was proud that his kriged block was larger than his so-called erratic block. What he did not show is that his kriged block has a significantly lower grade. Less pay dirt and more tailings! Geostatistical grade control in exploration and mining but statistical grade and quality control with ISO standards in smelting and refining! That's a Catch-22! Apply sound statistics in smelting and refining and work with goofy geostatistics in mineral exploration and mining!

Regulators should care that it's a scientific fraud to infer ore between holes. The ostrich rule ought to apply to regulators. Bre-X showed more red flags than a Bolshevist parade. The OSC watched Bre-X's parade with Felderhof in front! Incompetence is common but not a crime. The National Securities and Exchange Commission does make so much sense. I explained to the OSC in 1994 and to the SEC in 2003 why geostatistics is an invalid variant of classical statistics. Infinite sets of kriged estimates with zero pseudo kriging variances and zilch degrees of freedom give goofy statistics! But it seems to make sense to CRIRSCO's Chairman and his Crirsconians!

Matheron's quixotic work is posted with the On-Line Library of the Centre de Géostatistique. He was not a born genius at probability but a self-made wizard of odd statistics. One-to-one correspondence between variances and functions remained beyond Matheron's grasp until his passing in 2000. Matheron fumbled two variances whereas Agterberg fumbled the same variance twice. Yet, scores of so called qualified persons accept Matheron's voodoo statistics as much as born geostatistocrats and krigeologists do!

Teck's Patricia Dillon and her team of statistically challenged experts talk with a great deal of confidence about confidence without confidence limits. Nobody knows how to derive unbiased confidence limits for metal contents and grades of mineral inventories. Classical statistics does give unbiased confidence limits not only for metal contents and grades of reserves but also for proven ore within inferred resources. Borehole Statistics with Spreadsheet Software shows how to derive 95% confidence intervals and ranges for masses of metals in volumes of in-situ.

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