To have or not to have true variances

It all depends on who applies what! Statisticians apply true variances but geostatisticians work with false variances. The problem is that geostatistocrats call theirs kriging variances. The matter of true variances versus kriging variances came up at a seminar sponsored by the PDAC (Prospectors and Developers Association of Canada). The PDAC had set the stage at the Royal York Hotel in Toronto, Ontario, on Saturday, March 23, 1991. It was organized by H E (Buzz) Neal, PEng, William A Roscoe, PhD, PEng, Henrik Thalenhorst, PhD, and Lorne A Wrigglesworth. I had called my talk Sampling in Exploration, Theory and Practice. I was slated first to speak. As luck would have it, I would give the same talk at Mount Isa, Queensland, Australia, on November 3-7, 1992. That’s where I also presented the Conference Dinner address. But that’s one more part of my story!

During my talk Professor Dr Michel David was sitting sort of face to face with me on the first row. A few of his buddies were close by. David himself had put on paper the very first work on Matheron’s new science of geostatistics. He had simply called it Geostatistical Ore Reserve Estimation. Elsevier Scientific Publishing Company had printed in 1977. David himself had predicted in this book that it was not for professional statisticians. He also predicted that statisticians would find many unqualified statements. And he did get that right too! What David did not predict is that he would blow a fuse if and when he was to review a paper that was short on references to geostatistical literature. But that’s exactly what he did as a reviewer for CIM Bulletin. David did so when he reviewed in September 1989 our paper on Precision Estimates for Ore Reserves.

We had decided not to point out what was wrong with geostatistics but to show what made sense in applied statistics. We had tested for spatial dependence between gold grades of bulk samples taken from a set of ordered rounds in a drift. We had done so by applying Fisher’s F-test to the variance of the set and the first variance of the ordered set. We pointed out that each function does have its own variance in applied statistics and that variances of gold contents are additive. What we didn’t do was estimate the intrinsic variance of gold. It would have required that a pair of interleaved primary samples be taken from every crushed round. We mentioned that extraneous variances such as those for dividing whole core sections into halves, and for selecting and assaying test portions of test samples may be subtracted before deriving unbiased confidence limits for contained gold. We were tickled pink that Precision Estimates for Ore Reserves was praised by and published in Erzmetall, October 1991.

David has made peer review at CIM Bulletin a shameful sham. Read what he wrote about our paper: “The authors present their own method for calculating precision estimates for ore reserves without a single reference to 20 years of work in geostatistical ore reserve estimation (see attached references)”. What he had missed were references to Dagbert & Myers, to himself, and to Journel & Huijbregts. In his 1977 Geostatistical Ore Reserve Estimation he did praise “the famous Central Limit Theorem”. What he didn’t show was how to test for spatial dependence between measured values in ordered sets. Neither did he show how to derive unbiased confidence limits for masses of contained metals.

David may have reviewed A study on Kriging Small Blocks. Its authors called attention to the fact that mine planners are often tempted to over-smooth small blocks. Armstrong and Champigny failed to show how to smooth both small and large blocks to perfection. Good grief! That sort of bogus science was approved by and published in CIM Bulletin of March 1988. Nowadays, mineral analysts are blamed when geostatistically predicted grades mess up metallurgical balances in mineral processing plants. It’s all a huge game of chance for mining investors!

Marechal and Serra showed in 1974 how to derive a set of sixteen (16) distance-weighted averages from a set of nine (9) boreholes. David shows the same set on page 286 of his book. Each distance-weighted average is a function of the same set of nine (9) holes. As such, each is blessed with its own variance in applied statistics. Here’s where statistics went missing in geostatistics. The variance-deprived distance-weighted average morphed into a kriged estimate. What’s more, geostatisticians never took to counting degrees of freedom.

Infinite set of kriged estimates within B

David got into calling a kriged estimate a simulated value. Here’s literally what he wrote on page 324 of his 1977 work, “The criticism to this model is obvious. The simulation is not reality. There is only one answer: The proof of the pudding is …! So far the few simulations made which it has been possible to check have a posteriori proved to be adequate”. Nobody knows all of the nonsense I've had to put up with!

Who's to protect mining investors?

The Bre-X fraud made it clear that mining investors ought to be protected! Mining investors in Canada may well be the first in the world to be so protected. The National Securities Regulator takes on this task once the Supreme Court approves it for all of Canada. Now let’s take a quick look at a scenario. A mining investor may have thought that a mineral resource in an annual report looked like a good bet. But what went wrong if its mined grade is significantly lower than predicted? Here’s a cute catch-22! Confidence limits for metal grades and contents of mineral resources need not be disclosed. Yet public opinion polls are reported with 95% confidence limits. Why does the mining industry not do likewise? I did so in 1997 for Barrick Gold. The mining industry ought to revisit what was once hailed as Matheron’s new science of geostatistics. It made landfall on this continent in 1970. It is simple to prove that geostatistics is an invalid variant of applied statistics. Surely, mining investors in Canada would want a National Securities Regulator to investigate the validity of geostatistics.

Our National Securities Regulator launched its Transition Office in June 2009. Mr Douglas M Hyndman was appointed the NSR Chair. The Supreme Court of Canada has not yet ruled on the constitutional validity of a national securities regulator. It seems to make sense at a glance but is fraught with practical pitfalls. Alberta and Quebec prefer provincial fiefdoms. Here’s what I find funny. David’s 1977 Geostatistical Ore Reserve Estimation was put on paper in La Belle Province. Alberta’s oil patch has taken to geostatistics with reckless abandon. That’s why I am pleased that NSR’s Chair is bringing 25 years of experience to this position.

Mining investors do remember the Bre-X fraud but too few grasp how geostatistics converted bogus grades and barren rock into a massive gold resource. I’m not one to search for moral integrity. Searching for scientific integrity is good enough for me. I am pleased that the BCSC Chair has been appointed to chair the NSR Transition Office. He does have what it takes to unravel a scientific fraud. I do so wish the Supreme Court of Canada to rule in favor of a National Securities Regulator.

I drew the attention to the BCSC Chair in my letter of March 24, 2006 to the fact that I had called on the Canadian Council of Professional Engineers and the Canadian Council of Professional Geoscientists to examine whether geostatistics is a scientific fraud or sound science. Neither CCPE nor CCPG took to the task. I also pointed out to have met in Vancouver, BC on January 22, 2006 with Ms Deborah McCombe, PGeo and Dr Greg Gossan, PGeo. At that time both were on staff with securities commissions in Ontario and in British Columbia.

I pointed out that Dr Isobel Clark derived in her 1979 Practical Geostatistics the variance of the distance-weighted average AKA kriged estimate. She was the first and only scholar who derived the distance-weighted average. I pointed out that the author didn’t test for spatial dependence within her sample space by applying Fisher’s F-test to the variance of the set and the first variance term of the ordered set. I made it clear that all distance-weighted averages converge on the arithmetic mean as the distance between Clark’s sample space and a selected position converges on infinity. That’s why testing for spatial dependence in sample spaces and sampling units is so critical in applied statistics. All I want to know is why professional engineers and professional scientists accept that spatial dependence between measured values may be assumed simply because Stanford’s Professor Dr Andre Journel has said so.

The Supreme Court of Canada is to decide whether or not a National Securities Regulator is in the best interest of Canadian investors. Meanwhile the Chair of NSR’s Transition Office in June 2009. He no longer has to rely on Dr Greg Gossan, his former Chief Mining Advisor.

Dr Gregory J Gossan
Formerly: BCSRC Chief Mining Advisor
Presently: Chief Geologist, AMEC

Mr Douglas M Hyndman, Chair, NSR Transition Office, ought to ask the Canadian Council of Professional Engineers and the Canadian Council of Professional Geoscientists whether or not a statistical fraud does violate any Code of Ethics.