The Age of Statistics is upon us

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 have a wide range 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. And in Matheron’s tour de force of course!

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 the 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.

Stanford's Journel shed light on geostatistics

Journel got down to shedding some light on October 15, 1992. He did so in a six-page letter to the Editor-in-Chief of the Journal for Mathematical Geology. At that time, JMG’s Editor-in-Chief was Dr Robert Ehrlich, a professor at the Department of Geological Sciences with the University of South Carolina. Journel had “…a bit reluctantly...” agreed to go through my various notes. He left it up JMG’s Editor-in-Chief to decide whether his carefully crafted response should be sent to me. He did point out “…however, I strongly feel that Math Geology has had more than its share of detracting invectives”. Good grief! What could possibly be wrong with geostatistics?

My son and I knew exactly what was wrong in David’s 1977 Geostatistical Ore Reserve Estimation. But it would be the next Millennium before Matheron’s work was posted on the internet. So, I wrote ten letters to JMG’s Editor-in-Chief between November 14, 1990 and August 4, 1992. I had mailed drafts of several papers on different topics, and called him several times. I had also mailed him a copy of my book on Sampling and Weighing of Bulk Solids. I was quite pleased to have received a copy of Journel’s response to my various notes. The more so since JMG’s Editor-in-Chief wrote, “Your feeling that geostatistics is invalid might be correct”. Such a pity that he left. What I still don’t know is whether he jumped or was pushed.

Journel had written “It seems to me that Merks’ anger arises from a misreading of geostatistical theory, or a reading too encumbered by classical “Fischerian” [sic!] statistics”. He really got into the nitty-gritty of geostatistics when he pointed out “The very reason for geostatistics or spatial statistics in general is the acceptance (a decision rather) that spatially distributed data should be considered a priori as dependent one to another, unless proven otherwise.” Journel couldn’t have said it any worse. It’s a textbook case of circular logic. Accept spatial dependence between ordered sets of measured values in sample spaces and sampling units. Do not prove otherwise by applying Fisher’s F-test. What a bunch of blatant blarney! Who wouldn’t get angry?


A peeved student of geostatistics and a friend of mine had gifted me his pre-read copy of Journel & Huijbregts 1978 Mining Geostatistics. On page 1 the authors define what the book is all about. Here’s literally what they wrote: Etymologically, the term geostatistics designates the statistical study of natural phenomena. G Matheron (1962) was the first to use this term extensively, and his definition will be retained: “Geostatistics is the application of the formalism of random functions to the reconnaissance and estimation of natural phenomena.”

In a footnote on the very same page Journel & Huijbregts mentioned J Serra and A Maréchal. David’s 1977 Geostatistical Ore Reserve Estimation, too, mentioned J Serra and A Maréchal. In fact, David took this example from Serra and Maréchal’s 1970 Random Kriging. Matheron’s 1970 Random Functions and their application in Geology, too, was presented at the 1970 Geostatistics colloquium on campus at The University of Kansas in June 1970. And so was Agterberg’s 1970 Autocorrelation Functions in Geology.

That’s when I made up my mind to study the lives and times of the greatest geostatistical minds on our little planet. Journel had gone to Stanford University in 1978 as a Visiting Associate Professor of Applied Earth Sciences. He liked it so much that he never left. As a matter of fact, he has spent more time teaching geostatistics at Stanford than he studied it under Matheron’s humdrum guidance. Journel was Mining Project Engineer at Matheron’s Centre de Morphologie Mathematique from 1969 to 1973. Journel was Matheron’s most gifted disciple by far. His list of honors and awards is striking to say the least. From 1973 to 1978 he did time as Maitre de Recherches at Matheron’s Centre de Geostatistique. Professor Dr A G Journel has been teaching Stanford’s students from 1978 to the present. He has taught them all of his own silly nitty-gritty on Matheron’s novel science of geostatistics.