Dr Isobel Clark derived the variance of a distance-weighted average but didn't test for spatial dependence between measured values in her ordered set. Dr Roussos Dimitrakopoulos, McGill's miracle man and JMG's Editor-in-Chief, knows all about stochastic mine planning optimization with kriging variances. He has yet to apply it to Bre-X's phantom gold resource to find out what mining plan pops up with voodoo variances. 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. The National Securities Regulator ought to rule that unbiased confidence limits for contained metal be reported. Matheron, the self-made wizard of odd statistics, lost the variance of the length-weighted grade in 1954. He didn't test for spatial dependence. Nor did he take to counting degrees of freedom.	Photo by Nick Didlick Jan W Merks metrologist, author, lecturer, consultant, whistleblower, 'gadfly', 'pariah', 'iconoclast', CIM Life Member

Dr F P Agterberg stripped the variance off his distance-weighted average point grade in his 1970 paper and once more in his 1974 Geomathematics. He mentioned degrees of freedom and Fisher's F-test in this textbook. Why didn't he show 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. Surely, a distance-weighted average grade without a variance is a genuine scientific fraud!

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 others do speak on his behalf. Professor Dr R Dimitrakopoulos, Editor-in-Chief, Journal for Mathematical Geosciences, stand on guard against genuine variances. This association and its journal got new names but the kriged game remains the same. Why should Agterberg revise his 1974 Geomathematics? After all, mining investors accept mineral inventories in annual reports without demanding confidence limits.

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 that each and every kriged estimate does have its own variance. JMG's Editor-in-Chief is still playing games 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 scientific fraud. Of course, geoscientists ought to know why stochastic modeling with voodoo variances gives junk statistics.

The world's mining industry is caught in a Catch-22. The problem is that metal grades and contents of mineral inventories in annual reports 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 in mined ores and more tailings in ponds! Geostatistical grade control in exploration and mining but statistical grade and quality control with ISO standards in smelting and refining! It's a a Catch-22! Apply sound statistics in smelting and refining and work with goofy geostatistics in mineral exploration and mining!

The National Securities Regulator ought to rule it a scientific fraud to assume ore between boreholes. Bre-X showed more red flags than a Bolshevist parade. The OSC watched the parade with Felderhof in front! Incompetence runs rampant but is not deemed a crime. I explained to the OSC in 1994 and to the SEC in 2003 why Matheronian geostatistics is a flawed variant of applied statistics. Infinite sets of kriged estimates, zero pseudo kriging variances and no degrees of freedom make goofy statistics! But it seems to make sense to CRIRSCO's new Chair and her flock of Crirsconians!

Matheron's quixotic work is posted with the On-Line Library of the Centre de Géostatistique. Matheron 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 his grasp until his passing in 2000. Matheron fumbled two variances whereas Agterberg fumbled the same variance twice. Scores of somehow qualified persons accept voodoo statistics as much as do born geostatistocrats and krigeologists!

Teck's Patricia Dillon and her team of statistically challenged experts talk confidently about confidence without limits. Applied statistics does give unbiased confidence limits for metal contents of mined ores and mineral concentrates. It does so not only for metal contents and grades of ore 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 ores. It's high time to set up an ISO Technical Committee on reserve and resource estimation. But Barrick Gold, BHP Billiton, Rio Tinto and a few others prefer the geostatus quo.

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