NRCan's Emeritus Scientist lost the variance of his distance-weighted average. That's what made Busang's barren rock and Bre-X's bogus grades look like a gold resource. Just infer ore between bogus grades, krige and smooth a little, and rig the rules of statistics a lot. A National Securities Regulator is urgently required. OSC's qualfied persons do not even know how to derive unbiased confidence limits for mineral inventories in annual reports Degrees of freedom fighters amongst professional engineers and geoscientists are addicted to Matheron's junk science of geostatistics. Hardcore krigers and cocksure smoothers turned exploration into a wonderful game of chance with the stakes of mining investors. 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 mineral sampling expert, consultant, lecturer, author, whistle-blower, 'gadfly', 'pariah', 'iconoclast', CIM Life Member

Dr F P Agterberg himself lost the variance of his zero-dimensional distance- weighted average point grade first in his 1970 paper and once more in in his 1974 Geomathematics. He did refer to Fisher's F-test in several chapters 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. He thinks it's too late to right a wrong! Agterberg is but one of a few geostatistocrats who still preaches that his distance-weighted average point grade has no variance!

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, Past President, International Association for Mathematical Geosciences, and Professor Dr R Dimitrakopoulos, Editor-in-Chief, Journal for Mathematical Geosciences, stand on guard against true variances. The association and its journal were 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 stock.

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 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 should be smart enough to derive the variance of any weighted average. They should know that stochastic modeling with voodoo variances is a scientifc fraud. Ask any professor of mathematical statisticswhether or not stochastic modeling with voodoo 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 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 violate its rules!

The regulators couldn't care less it's a scientific fraud to infer ore between holes because the ostrich rule doesn't apply to them. 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 seems to 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 so called qualified persons accept Matheron's voodoo statistics as much as born geostatistocrats and krigeologists do!

Patricia Dillon and her team of statistically challenged experts talk about confidence but don't know how to derive confidence limits for contents and grades. Classical statistics 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 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 work 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 June 30, 2009, 46,285 visitors called on this web site 92,264 times, looked at 257,043 pages, and downloaded 11.06 GB of tried and tested sampling practices and proven statistical methods.