BHP Billiton fell for stochastic sham

Assume that I have invested in BHP Billiton. Surely, I would want to know where my mining giant is going. And most of all I would want to know whether or not Chairman Marcus Kloppers knows what he is doing. Does he have a buddy on his Board who knows a bit about applied statistics? Would she or he know that functions do have variances, and that only measured values do give degrees of freedom? Take a long look at my short story. Assume, krige, smooth, and rig the rules of applied statistics. The roots of geostatistics rest in the archives of CIM Bulletin. What I have done for more than twenty years is keep my story alive. It’s about an invalid variant of applied statistics. It was geostatistics that converted Bre-X’s bogus grades and Busang’s barren rock so smoothly and effortlessly into a massive inferred gold resource. Just the same, Fisher’s F-test proved that the intrinsic variance of gold at Busang was statistically identical to zero. I do not know where Kloppers was when Bre-X Minerals blew up. What I do know is that BHP Billiton was not the only one who put up plenty of play dough to do more with fewer boreholes. So let’s go forward to the play!

McGill Professor Dr Roussos Dimitrakopoulos is Canada Research Chair and BHP Billiton Chair in Mine Planning Optimization at the Department of Mining, Metals and Materials Engineering. He came all the way from Down under in June 1993 to celebrate at McGill University a forum called Geostatistics for the Next Century. When I read about this forum I thought it somewhat premature. That’s why I put together The Properties of Variances and submitted the abstract by registered mail on January 4, 1992. My son and I had studied David’s 1977 Geostatistical Ore Reserve Estimation. The author did not know how to derive unbiased confidence limits for metal contents and grades of volumes of in-situ ore. That’s why we derived confidence limits in Precision Estimates for Ore Reserves. But Dr RD was not at all interested in properties of variances in 1993. And he’s still not interested in 2010!

Professor Dr Roussos Dimitrakopoulos is a Member of IAMG. Once upon a time, IAMG stood for International Association for Mathematical Geology. Nowadays, it stands for International Association for Mathematical Geosciences. The novel tag does make sense. More geoscientists than geologists study this little planet. Dr RD is Editor-in-Chief, the Journal for Mathematical Geosciences.

Editor-in-Chief

As such, he approves what meets his requirements and rejects what is at variance with stochastic mine planning with kriging variances. Much of Behind Bre-X, The Whistleblower’s Story, reviews the works of Matheron, Agterberg, David, Dimitrakopoulos, Journel, and scores of likeminded geostatistical thinkers.

Here’s what I wrote on April 19, 2010 to Dr Marius Kloppers, Chief Executive Officer,
BHP Billiton Plc, London, United Kingdom.

A great deal of my experience was put together in Sampling and Weighing of Bulk Solids. I did so after I had been Assistant to the Chairman of Cominco Ltd. For example, I derived unbiased confidence limits for the mass of metal contained in a mass of mineral concentrate or mined ore. ISO/TC 183 checked and approved this method. ISO published it as ISO 13543:1996 Determination of mass of contained metal in a lot.
Attached is a copy of my letter of November 30, 1994, to the Chairman, CIM Ad Hoc Reserve Definitions Committee. I pointed out that the mass of contained metal in a volume of in-situ ore is a function of volume, in-situ density, and a grade factor. This function, too, does have its own variance. In fact, one-to-one correspondence between functions and variances is a condition sine qua non in mathematical statistics. In geostatistics, however, not all functions do have variances. The variance of the distance-weighted average aka kriged estimate went missing. Drill core sections were crushed and salted at Bre-X’s Busang site when I wrote the enclosed letter in November 1994. Geostatistics converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Mathematical statistics proved the intrinsic variance of gold to be statistically identical to zero.
The purpose of my letter is to suggest that the mining industry should set up and support an ISO Technical Committee on reserve and resource estimation. It is simple to derive confidence limits for masses of metals in reserves, and to derive confidence limits for proved masses of metals in resources. My son and I did set the stage in 1992.

Dr Marius Kloppers, Chairman, BHP Billiton, has not yet replied to my letter.