Sunday, August 07, 2011

What's wrong with post-Bre-X standards?

Bre-X’s bogus grades made Busang’s barren rock look like a genuine gold resource. Yet, Professor Dr Michel David didn't know what was wrong with his 1977 Geostatistical Ore Reserve Estimation. He derived a set of sixteen (16) functionally dependent values in a sample space. Each and every one of them is a function of the same set of nine (9) boreholes. That’s why each of them would have been blessed with its own variance in applied statistics. David was inspired by a tale on Random Kriging by A Marechal and J Serra. Matheron himself put on paper Random Functions and Their Application in Geology. He invoked Brownian motion along a straight line to ensure continuity of random functions. This three-some had been brainstorming at the Centre de Morphology Mathematique, Fontainebleau, France. Next, brought Matheron's new science of geostatistics to this continent in June 1970.

Figure 10. –Grades of n samples belonging to
nine rectangles P of pattern surrounding x
Fig. 203. Pattern showing all the points within B,
which are estimated from the same nine holes.

David’s students seem to have thought some 25 years later that he deserved praise for thinking up the first textbook on geostatistics. David’s bash was called Geostatistics for the Next Century. All I wanted David and his buddies to grasp before this century came along were The Properties of Variances. When praise was heaped on David, Bre-X’s rigs were drilling barren rock in the Kalimantan jungle. Good news for Bre-X’s investors kept coming. Soon it was to be bad news!

Applied statistics proved early in 1997 that Bre-X’s crushed core samples were salted with placer gold. That’s why the Mining Standards Task Force (MSTF) was set up. Morley P Carscallen, Vice-Chair, Ontario Securities Commission, and John W Carson, Senior Vice-President, Market Regulation, Toronto Stock Exchange, were MSTF’s Co-Chairs. Here’s what they had pointed out in MSTF’s Interim Report , ”A number of incidents served as an impetus for the formation of a joint task force between the Ontario Securities Commission and the Toronto Stock Exchange. Public confidence in mining stocks was shaken and the industry as a whole suffered a major setback. The most talked about incident was, of course, Bre-X.”

In spite of so much soul searching the Bre-X fraud ended up being the least acted upon incident. The OSC could have acted several years before I proved that Bre-X was a salting scam. I had pointed to the fact that unbiased confidence limits for metal grades and contents can be derived not only for mined ores and mineral concentrates but also for in-situ reserves and resources. I had done so in my letter of November 30, 1994 to John J Drury, PEng and Chairman CIM Ad Hoc Reserve Definition Committee. He responded on October 23, 1995. Who could possibly be against tried, tested and true ISO Standard Methods after the Bre-X salting scam? And why would the world’s mining industry not want unbiased confidence limits for metal contents and metal grades of mineral inventories? Why not turned out to be one very long story!

The Mining Standards Task Force came up with National Instrument 43-101 to define requirements for disclosure of results. It claims to have done so to increase investor confidence. Yet it still doesn’t show how to derive unbiased confidence limits for metal contents and grades of mineral inventories. It’s good news for mining companies but bad news for mining investors. Appendix A in MSTF’s Final Report points to presentations made to the Task Force. I pity those who had to put up with so much mind numbing geostat drivel. Appendix B points to written submissions to the Task Force. AMEC, Geostat Systems International and SNC-Lavalin have not made submissions in writing.

Post-Bre-X standards protect mines much more than investors. Both the OSC and the BCSC knew I had unscrambled the Bre-X fraud. So, I got to meet Ms Deborah McCombe, OSC’s Chief Mining Consultant, and Dr Greg Gosson, BCSC’s Chief Mining Advisor. We met on January 22, 2006 at the BCSC Office in Vancouver, BC. The objective was “to discuss the use of geostatistics in mineral resource and mineral reserve estimates by mining companies.” I handed out copies of my work. I had posted on my website Clark’s hypothetical uranium data in a two-dimensional sample space. She had done what no geostatistician ever got around to doing. She derived the variance of the distance-weighted average aka kriged estimate. Extrapolation shows that the distance-weighted average tends to converge on the arithmetic mean. What she didn’t do was test for spatial dependence. But then, Stanford’s Journel taught her that spatial dependence between measured values in ordered sets may be assumed.

OSC’s Chief Mining Consultant wrote she would appreciate "being apprised of my progress on the development of industry best practices in the application of mathematical statistics to assess the reliability of data." Her letter was copied to OSC’s Chair.