Some 600,000 visitors looked at blogs such as Going GIGO with CRIRSCO. Geostatistics converted Busang's barren rock and Bre-X's bogus grades into the largest phantom gold resource the world has never seen. Just infer ore between holes, krige and smooth a little, and rig the rules of classical statistics a lot. It takes a National Securities Regulator to sort out why OSC's qualified persons have a penchant for geostatistics. Degrees of freedom fighters amongst professional engineers and geoscientists embraced Matheron's junk science of geostatistics. Hardcore krigers and cocksure smoothers turned it into a wonderful game of chance with the stakes of mining investors. Matheron, the self-made wizard of odd statistics, fumbled the variance of the lenght-weighted average grade of core samples in 1954, and the variance of the length-weighted block grade in 1960!

Photo by Nick Didlick Jan W Merks mineral sampling expert, consultant, lecturer, author, whistle-blower, 'gadfly', 'pariah', 'iconoclast', CIM Life Member

Dr F P Agterberg fumbled the variance of his zero-dimensional distance- weighted average point grade first in his 1970 colloquium paper and then in his 1974 Geomathematics. He did refer to Fisher's F-test but didn't show how to test for spatial dependence, either within holes or between holes. He should delete Chapter 10 Stationary Random Variables and Kriging. Agterberg believes it's too late to right a wrong! Agterberg is wrong!

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 a salting scam was in progress at the Busang project!

Pseudo kriging variances are protected. Agterberg, President, International Association for Mathematical Geology, and Professor Dr R Dimitrakopoulos, Editor-in-Chief, Journal for Mathematical Geology, stand on guard against real variances. The association and its journal are reborn with new names but the kriged game remains the same. Agterberg has yet to announced he will revise Geomathematics. Meanwhile, don't apply Fisher's F-test but infer mineralization between boreholes to keep mining investors buying.

Dimitrakopoulos surfaced from Queensland University to become Canada Research Chair and BHP Billiton Chair in Mine Planning Optimization at the Department of Mining, Metals and Materials Engineering at McGill University. He is teaching McGill's students all he knows about stochastic modeling with pseudo kriging variances. When Dimitrakopoulos chaired in June 1993 a forum on Geostatistics for the Next Century, he did not even know that each kriged estimate does have its own variance. In 2007, JMG's Editor-in-Chief still plays with pseudo kriging variances. Surely, McGill's students are smart enough to derive the variance of a distance-weighted average. They ought to know why stochastic modeling with pseudo kriging variances is a game of chance. They may have to get ready for geometallurgy by stochastic simulation. Ask the opinion of any professor of mathematical statistics! Stochastic modeling with voodoo variances is 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 know 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 the Catch-22! Apply sound statistics or breach its rules!

Regulators couldn't care less it's a scientific fraud to infer ore between holes. Why doesn't the ostrich rule 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. This is why a National Securities and Exchange Commission makes so much sense. I told the OSC in 1994, and 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 does make sense to CRICSCO''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 qualified persons accept Matheron's voodoo statistics as much as born geostatistocrats and krigeologists do!

Patricia Dillon and her team of statistically challenged experts talked a lot about confidence but don't know how to derive confidence limits for metal contents and grades. Statistics does give unbiased confidence limits not only for contents and grades of a reserve but also for proven ore within an inferred resource. Borehole Statistics with Spreadsheet Software shows how to derive confidence intervals and ranges. All the same, A J Sinclair is still teaching how to apply Matheron's mad statistics in Mineral Reserve Estimation at UBC's Norman B Keevil Institute of Mining Engineering.

Geoscientists who grew up with semi-variograms should click here and study why degrees of freedom are important when deriving sampling variograms and measuring changes in climate as a function of space and time. Between January 1, 2007, and Juy 31, 2008, 36,004 visitors called on this web site 78,794 times, looked at 214,810 pages, and downloaded 8.18 GB of proven sampling practices and sound statistical methods.