Born to infer and rig rules of real statistics

The mad world of geostatistics is still as bad as it was when Bre-X’s phantom gold resource was cooked up. All it took was a little placer gold, a lot of barren rock, and a load of junk statistics. When Bre-X’s shareholders were counting their losses, geostatistical ore reserve practitioners were keeping low profiles. The Toronto Stock Exchange and the Ontario Securities Commission tried in vain to sort out the mess. Geostatisticians failed to foil the Bre-X scam early in the salting game. Nowadays, they talk with confidence about mineral reserves and resources. What they won’t talk about is how to derive unbiased confidence intervals and ranges for metal contents and grades of mineral reserves and resources. They would like to bury Bre-X but I don’t want them to forget the role of geostatistics in the Bre-X hoax. Here’s why! To infer ore between boreholes is as much alive today as it was during Bre-X’s hay days. And that was some hoax! Yet, the world’s mining industry is still working with the very same junk statistics. What I want to do is show why geostatistics makes junk statistics of the worst kind. That’s why it ought not to be taught at any university on this planet.

After I found out about the Centre de Geosciences/Geostatistique’s Online Library, I took to a liking to looking at Matheron’s seminal work. I want to grasp what Matheron was thinking when he thought he was working with statistics. When I looked at Matheron’s Note Statistique No 1, I was surprised to find out it had been reborn as Note Géostatistique No 1. When and why did that happen? The scanned copy of Matheron’s Formule des minerais connexes is still marked Note Statistique No 1. Matheron signed it in Algiers on November 25, 1954. Why would anyone want to predate the birth of Matheron’s new science of geostatistics?

What I want to know most of all is why and when Matheron strayed from real statistics into his self-made new science of geostatistics. It was easy to find out when he lost touch with real statistics. When I was a consultant to Cominco long before it got keeviled, I met a geologist who got a headache reading Mining Geostatistics and gave me his copy. That’s when I finally found out why Matheron created geostatistics. It’s all in his Foreword to that 1978 textbook the lead author of which is Professor Dr A G Journel. Journel was Matheron’s protégé and most gifted disciple but also a Stanford professor.

Matheron brooded over structure and randomness, and hypothesized, “Since geologists stress the first of these aspects, and statisticians stress the second, I proposed, over 15 years ago, the name geostatistics to designate the field which synthesizes these two features and opens the way to the solution of problem of evaluation of mining deposits.” I think it’s more intuitive to contrast orderliness and randomness. I prefer text and syntax such as “order in a sample space or in a sampling unit” to clarify what I mean. I took my petite TI calculator and found that Matheron’s new science of geostatistics had been either created or synthesized some time before 1962. Sadly, Matheron in those days didn’t have an HP or TI calculator to derive his odd statistics.

I took several looks at Matheron’s very first paper entitled Formule des minerais connexes and signed in Algiers on November 25, 1954. What Matheron explored in his first paper was the degree of associative dependence between lead and silver grades of core samples of one or more boreholes drilled in a lead deposit. He provided no primary data and but a few questionable statistics. What stands out in his work is obsession with probabilistic symbols and the lognormal distribution. Matheron didn’t show how to check and compare his observed “coefficient de correlation” with the proper value of r0.05;df at 95% probability and with applicable degrees of freedom. Matheron’s predicament in 1954 was that counting degrees of freedom didn’t rank anywhere on his list of things to teach. As a matter of fact, Matheron never in his life got into counting degrees of freedom.

Matheron appended on January 13, 1955 a Rectificative á la Note Statistique No 1 to his Formule des minerais connexes. Neither read like real statistics at all. It did look like geostatistics because degrees of freedom were gone. Matheron talked about µ and σ but those symbols derive from probability theory. The concept of degrees of freedom makes the difference between probability theory with its population parameters and applied statistics with its finite sample statistics. Just the same, Matheron never counted degrees of freedom.

Matheron’s Note Statistique No 2 left me cold but his Note Statistique No 3 did pique my interest. Why did Matheron talk about the standard deviation of a deposit? Why didn’t he derive the 95% confidence interval for the lead and silver contents and grades of his deposit in Algiers? His one-page paper was about the Poisson distribution as it applies to particles of pure minerals and of barren rock, and about the upper limit for the standard deviation of some hypothetical deposit.

Matheron was a mining engineer but also a probabilist of sorts. Six symbol-packed pages with sparse text proved he was also a self-made wizard of odd statistics. How he found a following is bound to go down as a deep mystery in the history of science. His disciples seem to have been born to infer, krige, smooth, rig the rules of real statistics, and beat immeasurable odds. They do all that stuff despite fumbled variances and missing degrees of freedom! Behind Bre-X was not just a salting scam but a unique scientific fraud. And the world’s mining industry just can’t get enough of it!