CIM stands for Canadian Institute of Mining, Metallurgy and Petroleum. Once upon a time I was a proud CIM Member. Today I am the accidental CIM Life Member. My first message to CIM`s President was snail mailed on March 20, 1992. CIM`s President was William E Stanley of The Coopers & Lybrand Group in Vancouver. He was the first of many whom I had told why geostatistics is an invalid variant of applied statistics. We met, he listened to my story, and I wrote him a letter. CIM Bulletin of March 1989 had published Armstrong and Champigny’s A Study on kriging Small Blocks. Both authors were at that time geostatistical scholars at the Centre de Géostatistique, France. They thought up the study since, “The kriging variance rises up to a maximum and then drops off.” What they found out is that “…mine planners are often tempted to kriging very small blocks.” How about that? Smoothing a little is good but smoothing very small blocks is bad. That sort of a pass-the-buck study did pass David’s peer review with red flags blazing.
Early in 1990 we found out that Precision Estimates for Ore Reserves was rejected. Our paper showed how to test for spatial dependence between gold grades of ordered rounds in a drift. David’s 1977 textbook didn’t show how to test for spatial dependence, or how to count degrees of freedom. Neither did his work show how to derive unbiased confidence limits for metal contents and grades of in-situ ores. So, I put Geostatistics or Voodoo Science on paper, and The Northern Miner printed it on March 20, 1992. Champigny was no longer a geostatistical scholar at the Centre de Géostatistique in France but a Senior Consultant with The Coopers & Lybrand Group in Toronto. He never lost his passion for kriging and smoothing. As a matter of fact, he rounded up a team of anonymous ore reserve practitioners to stand on guard against the rise and fall of kriging variances. What he and his team did prove was that the properties of variances were far beyond their grasp. The Northern Miner put Champigny’s rambling tale in print on May 18, 1992. Armstrong went beyond the pale and lectured on scientific integrity in De Geostatisticis of July 1992.
About twenty years ago I reported to CIM that geostatistics is an invalid variant of applied statistics. Geostatistocrats with CIM Bulletin promptly put up a spirited battle to salvage the new science of geostatistics. And a fine job they did! Matheron’s madness of surreal geostatistics even survived the Bre-X fraud. Statistics turned into geostatistics under the guidance of Professor Dr Georges Matheron, a French probabilist who became a self-made wizard of odd statistics in the 1950s. A brief history of my 20-year campaign against the geostatocracy and its army of degrees of freedom fighters is chronicled on my website.
Dr Frederik P Agterberg, Past President, International Association for Mathematical Geosciences formerly know as International Association for Mathematical Geology, called Matheron (1930-2000) the Founder of Spatial Statistics. Agterberg ranked Matheron on a par with giants of real statistics such as Sir Ronald A Fisher (1890-1962) and Professor Dr J W Tukey (1915-2000). Agterberg was wrong! Matheron fumbled the variance of the length-weighted average in 1954. Agterberg himself fumbled the variance of the distance-weighted average first in his 1970 Autocorrelation Functions in Geology and once more in his 1974 Geomathematics. Agterberg is Emeritus Scientist with Natural Resources Canada. He ought to but has yet to explain why his distance-weighted average point grade does not have a variance. After all, Gemcom‘s geostatistical software converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. I applied Fisher’s F-test to prove that the intrinsic variance of Bre-X’s phantom gold resource was statistically identical to zero. Duplicate test results for gold by cyanide leaching determined in a few boreholes would have been enough to unravel the Bre-X fraud in a timely manner.
I make a clear and concise case for real statistics. Test for spatial dependence by applying Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set. Chart a sampling variogram to show where spatial dependence in a sample space (or in a sampling unit) dissipates into randomness. We applied Fisher’s F-test in Precision Estimates for Ore Reserves. And we did it again in our APCOM 2009 paper entitled Metrology in Mineral Exploration.
Geostatisticians assume spatial dependence between measured values in ordered sets, interpolate by kriging, smooth some kind of least biased subset of an infinite set of Agterberg’s zero-dimensional and variance-deprived distance-weighted average point grades AKA kriged estimates or kriged estimators, and rig the rules of real statistics with reckless abandon. I urge CIM to investigate whether or not geostatistics is a scientific fraud. I do so as a CIM Life Member. Please do not assume that CIM need not resolve this matter.
CIM Bulletin approved Abuse of Statistics for publication. Dr Frits Agterberg wanted to know when and where Wells spoke so highly about statistical thinking. I wasn’t about when Wells said what he did. What I do know is that Darrell Huff said Wells did. That’s good enough for me. Huff did so in his 1954 How to Lie with Statistics. It was the very same year that young Matheron didn’t know how to test for spatial dependence between metal grades of ordered core samples, how to derive the variance of the set of metal grades, and how to derive the variance of the central value of the set. Huff never found out what Matheron did wrong. But then, neither did Matheron himself! And Agterberg, Armstrong, David, Journel and scores of geostatistocrats never broke rank with Matheron.
I want to move fast forward to the present. Michael J Allan, CIM President in 2010, writes under President’s Notes about A time of renewal. Let’s read what else he wrote. “Our work in providing standard reserve and resource definitions that are used by the country’s securities regulators is an example of the ongoing technical contributions CIM makes to the industry at large”. For heaven’s sake! Geostatistics is as alive and flawed as it was in the 1970s. So it seems that CIM is not about to kill the incredible kriging machine. For infinite sets of kriged estimates and zero kriging variances set the stage for boundless krige and smooth fests. APEGBC ‘s Code of Ethics is not written to rule against scientific fraud. What will kill the kriging machine is the study of climate dynamics on our little planet. No ifs and buts!