How I wish it were true! But that`s what W J Reichmann thought in 1961. It’s the very title of Chapter 1 in his delightful Use and abuse of statistics. The first line of its Preface points out: `Very few people nowadays can progress very far without at some point coming in contact with statistics`. Now that’s what I have been trying to tell the geostatistocracy since the early 1990s. So I pointed to Reichmann’s work in Abuse of Statistics. I own several scores of books on sampling and statistics. Applied statistics underpins sampling practice just as much as probability theory does sampling theory. As such, degrees of freedom play a key role in sampling practice but none at all in sampling theory. No ifs or buts! Except in CIM Bulletin. In Matheron’s tour de force of course. And in Cressie’s Statistics with upper-case S.
The Editor of CIM Bulletin wrote on September 21, 1992 that “articles of a controversial nature” may be published under the heading Forum. It’s hard to believe that applied statistics was controversial in those days. Of course, The Geological Society of CIM has got to be vigilant when deciding what GEOSOC members get to read. So I was pleased that Abuse of Statistics was approved for publication with the proviso that the source of my most favorite quote be disclosed. That’s what Dr Frits P Agterberg wanted. In those days, Agterberg was Associate Editor with CIM Bulletin. In due course, he would wish not only geologists but geoscientists at large to work with geostatistics. Here’s what H G Wells (1866-1946) once said, “Statistical thinking will one day be as necessary for efficient citizenship and the ability to read and write.” How about that? I do not know when or even if Wells said it and to whom. But Darrell Huff thought Wells had said so. Surely, the author of How to lie with statistics would not tell a lie. So I put Huff’s book on my short list of references. And I put Wells’ thought on statistical thinking on top of my brief but somehow controversial article.
Peer review at The Geological Society of CIM in those days was a sham. Not only was it blatantly biased but it was also shamelessly self-serving. Why did it see fit to reject Precision Estimates for Ore Reserves? It did so because we didn’t refer to twenty years of geostatistical literature! And why didn’t we do that? We didn’t because Professor Dr Michel David’s 1977 Geostatistical Ore Reserve Estimation didn’t show how to derive unbiased confidence limits for metal grades and contents of in-situ ores. As a matter of fact, geostatisticians still do not know how to derive unbiased confidence limits for metal contents and grades of ore reserves. All the same, The Geological Society of CIM rejected Dependencies and degrees of freedom and The properties of variances just as brazenly as did the Journal for Mathematical Geology.
CIM’s GEOSOC failed to grasp in 1992 why the properties of variances and the concept of degrees of freedom cannot be ignored with impunity. That’s when Bre-X Minerals was getting ready to explore for gold in Kalimantan, Indonesia. I’m sick and tired thinking of Bre-X’s salting scam. The more so because Bre-X’s massive phantom gold resource was cooked up by assuming the same gold grades between step-out lines of boreholes as within lines of boreholes. It’s the doctrine of Stanford’s Journel. Agterberg argued in 2009 that Bre-X’s test results for gold are “no real data”. The problem was that the Ontario Securities Commission thought they were. And many Bre-X investors thought likewise!
I’m still tickled orange that applied statistics played a key role in unraveling the Bre-X fraud. I have large sets of bogus gold assays determined by cyanide leaching 250 g test portions taken from crushed and salted drill core sections. I’ll show why it makes sense to test for rather than assume spatial dependence between measured values in ordered sets.
The first step was to insert three (3) lines of kriged boreholes between two lines of (2) salted boreholes in Busang’s South-East Zone. The second step was to derive statistics for two (2) lines of salted boreholes and three (3) lines of kriged boreholes. A little applied statistics was enough to show that geostatistics creates spatial dependence where it does not exist.
Neither line of salted boreholes displays a significant degree of spatial dependence. In contrast, all lines of kriged boreholes display a significant degree of spatial dependence. What a shame it’s all bogus gold. What’s real is that even test results for gold in salted boreholes do give degrees of freedom. In contrast, functionally dependent values such as kriged estimates are never blessed with degrees of freedom. All of that is old hat in applied statistics! The age of applied statistics may still not be upon us but the age of the internet is. The worldwide net has made it easy to find out who messed up what, when, where and why. Geostatistics is about to look a lot worse.