The stage was set in 1964 to teach junk statistics at the University of British Columbia. It was the year Professor Dr Alastair J Sinclair took on his duty to teach earth sciences to UBC’s students. It was but a few years after Matheron dabbled at his own kind of unreal statistics and fumbled real variances. Just the same, Matheron’s junk statistics was hailed as new science on campus at the University of Kansas in June 1970. His tour de force at that time was to call on Brownian motion to infer the continuity of his famed stationary random function. UK’s campus was a fitting venue because that’s where Agterberg failed for the first time to derive the real variance of his distance-weighted average point grade. Here’s why it gives too rich an abundance of data in mineral exploration. As few as a pair of measured values, when determined in samples taken at positions with different coordinates in a finite sample space, gives an infinite set of Agterberg’s point grades, a zero voodoo variance, and not a single degree of freedom. How about that? Some kind of perpetual motion in mineral exploration!
Sinclair details in Applied Mineral Inventory Estimation how his “exciting and invigorating career” took off when he was exposed to Matheron’s ideas, and how he had had “the good fortune to work with Journel, Huijbregts and Deraisme.” Those were Matheron’s earliest students who took his musings for dogma, and who didn’t have a clue which variances were lost on Matheron’s watch. Sinclair’s list of folks he was “fortunate to have worked with at various times” reads like a Who’s Who in the geostatistical fraternity. He credits all of them to have contributed to his education. I’m all in favor of giving credit where credit is due. But to give credit to everybody who taught him junk statistics is over the top. Some geostatistocrats on Sinclair’s list now know each weighted average has its own variance. And the odd one might even know why! One cannot help wonder how the cream of Matheron’s crop saw fit to make junk statistics look so good to Sinclair starting in 1972. So much so that Sinclair felt compelled to write his own textbook. Of course, all of that spelled bad news for UBC’s students.
When I met Sinclair at his UBC office in August 1992, I talked about real statistics. I showed how to count degrees of freedom for the set of nine holes in Figure 203 of David’s 1977 Geostatistical Ore Reserve Estimation. In Sinclair’s world, the concept of degrees of freedom breaks down in matters of spatial dependence. But it’s alive and well in my world. Sinclair did not see much of a difference between Matheron’s surreal geostatistics and Fisher’s real statistics. In fact, he knew as much about real statistics in August 1992 as he did in September 1989. That’s when CIM Bulletin entrusted Sinclair and David with the review of Precision Estimates for Ore Reserves. David blew a fuse because our paper was “without a single reference to 20 years of work in geostatistical ore reserve estimation.” And we didn’t even know we had written a geostatistical paper! So, we were baffled when Dr L R Fyffe, Editor, CIM’s Geology Division wrote on November 23, 1989, “Both reviewers recommend publication with major revisions.”
But big troubles were looming in the esoteric universe of those who infer, krige, smooth, and rig the rules of real statistics with reckless abandon. When I was working on Sampling and Weighing of Bulk Solids in the early 1980s, I studied David’s 1977 Geostatistical Ore Reserve Estimation. I found way too many symbols and far too few measured values. Brownian motion, too, played some kind of cameo role in this work of geostatistical fiction. The author confessed his work is "not for professional statisticians." In fact, he even predicted, “…statisticians will find many unqualified statements…” What David didn’t predict was he would deny anything was wrong in surreal geostatistics.
So what were we to do? Spice our paper with symbols? Scrap measured values? Delete Fisher’s F-test for spatial dependence? Call David to the task? Ask him to put in plain words his “good test to find out whether one really understands geostatistics” on page 286 of his 1977 textbook? Or try to pacify CIM Bulletin’s keepers of Matheron’s tablets with a few tidbits of token stuff? So we huffed and puffed a lot and added but a few references to works of geostatistical scholars such as Dagbert, David, Journel and Huijbregts. Our marginally revised paper was rejected on February 7, 1990. My son completed his PhD in computing science. I resolved to raise a stink. I did it then. And I still do now! Sinclair is but one reason. Bre-X’s phantom gold resource is another!
On November 23, 1989, CIM Bulletin’s editor wrote “Both reviewers recommend publication with major revisions.” Sinclair started some charade of sorts on November 22, 1989, at 08:30AM. He welcomed those who attended my short course on Sampling Precious Metal Deposits: Metrology-A New Look. The venue was Room 330A at UBC’s Department of Geological Sciences. The course was sponsored by its Mineral Deposits Research Unit. Sinclair didn’t have time to listen and moved about a lot. In fact, he popped in and out of Room 330A like a Jack-in-the-Box. Sinclair didn’t ask any questions. Was it because the paper he rejected was part of my notes? Did he worry others might ask questions? Did he worry I would talk too much about real statistics and too little about Matheronian geostatistics?
Dr J A McDonald, Interim Director, Mineral Deposits Research Unit, on February 21, 1990, wrote, “We certainly were pleased with the response to your course and have elected to maintain the theme with a 5-day course to be held April 23-27, 1990, entitled Geostatistics for the Mining Industry, New Concepts, New Tools.” How about that for cruel and unusual punishment? Sinclair was in damage control mode. So much more has happened in our stand-off on real statistics ever since I met Sinclair in his UBC Office in August 1992. Much of it will stay untold for some time to come.
Dr Alastair J Sinclair, PEng, PGeo, has striking credentials. He is a former Member of the Discipline Committee of the Association of Professional Engineers and Geoscientists of British Columbia with its Code of Ethics to protect the public at large. He was CIM’s Distinguished Lecturer for 2000-2001. He taught a short course at the UBC Robson Square Campus, Vancouver, BC, on May 15-16, 2008. What he didn’t teach was that each distance-weighted average has its own variance. He didn’t teach how to verify spatial dependence by applying analysis of variance and how to count degrees of freedom. Neither did he teach how to derive unbiased confidence interval and ranges for metal grades and contents of mineral inventories. Sadly, Sinclair is still teaching junk statistics!
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