The original brains behind the French sampling school were those of Dr Pierre Gy and of Professor Dr Georges Matheron. Gy’s L’Échantillonage des Minerais en Vrac is deeply troubling. Matheron’s Synopsis to Gy’s opus is dated January 15, 1967. It was translated into English, Spanish, and German. Gy’s work consists of Volume 1 with but 168 pages of dense text, and of Volume 2 with a whopping 470 pages.

Gy did refer to a pair of articles by G Gould and a set of eight (8) by Dr J Visman. Both of them were true experts who did grasp the properties of variances. Gy and Matheron have never grasped why degrees of freedom play a key role in sampling practice. In fact, confidence limits for metal contents and grades of in-situ ores and mined ores demand that degrees of freedom be taken into account. But one question is why French sampling gurus do not count degrees of freedom. Another is why not all functions do have variances!

National Science and Engineering Research Council of Canada had funded David’s 1988 work with NSERCC Grant 7035. National Research Council of Canada had earlier funded David’s 1977 work with NRC Grant 7035. Professor Dr Michel David’s 1977 work did not respect the requirement of functional independence and ignored the concept of degrees of freedom. His 1988 work was just as flawed but a bit more slipshod. My case against geostatistics has been brought to the attention of several NSERCC officials. One of those thought my message should have been sent to Natural Resources Canada. I had done so long ago but to no avail.

Dr Frederik P Agterberg
Ex Emeritus Scientist
Natural Resources Canada

The text that had been transmitted on December 14, 2011 reads as follows:

The National Research Council of Canada had done so in the 1970s. Professor Dr Michel David was awarded Grant NRC7035 to advance geostatistics.  So he plodded away and got his work printed in 1977. But he came up with a peculiar caution. He pointed out that “professional statisticians would find unqualified statements”. How about that? He mentioned it on page VII of what he had come to call Geostatistical Ore Reserve Estimation. He should have asked a statistician to scrutinize his draft. I found scores of unqualified stuff when I perused my own copy of David’s book.

It all depends on who applies what! Statisticians apply true variances whereas geostatisticians play with false variances. The problem is that geostatistocrats call theirs kriging variances. The matter of true variances versus kriging variances came up at a seminar sponsored by the PDAC (Prospectors and Developers Association of Canada). The stage was set at the Royal York Hotel in Toronto, Ontario, on Saturday, March 23, 1991. The organizers were H E (Buzz) Neal, PEng, William A Roscoe, PhD, PEng, Henrik Thalenhorst, PhD, and Lorne A Wrigglesworth. I had called my talk Sampling in Exploration, Theory and Practice. I was slated first to speak. As luck would have it, I would give the same talk at Mount Isa, Queensland, Australia, on November 3-7, 1992. That’s where I also presented the Conference Dinner address. And that’s but one more part of my long story!

Here’s why my friend so richly deserves a tribute! He was Editor of Trans Tech Publications in 1985 when my work on Sampling and Weighing of Bulk Solids was put in print. It was Volume 4 in the Series on Bulk Materials Handling. I derived confidence limits for masses of metals contained in shipments of mineral concentrates. What underpins this method is the interleaved sampling protocol. ISO/TC183 on Ores and Concentrates incorporated it in ISO/DIS 13543, Determination of Mass of Contained Metal.

What happened next was that my work was translated into Mandarin. This variant was published in November 1989. Given that it was published without authorization I decided to visit the Consulate-General of the People’s Republic of China in Vancouver, BC.  I got a friendly smile, a cup of green tea but no royalties.

The Bre-X fraud made it clear that mining investors ought to be protected! Mining investors in Canada may well be the first in the world to be so protected. The National Securities Regulator takes on this task once the Supreme Court approves it for all of Canada. Now let’s take a quick look at a scenario. A mining investor may have thought that a mineral resource in an annual report looked like a good bet. But what went wrong if its mined grade is significantly lower than predicted? Here’s a cute catch-22! Confidence limits for metal grades and contents of mineral resources need not be disclosed. Yet public opinion polls are reported with 95% confidence limits. Why does the mining industry not do likewise? I did so in 1997 for Barrick Gold. The mining industry ought to revisit what was once hailed as Matheron’s new science of geostatistics. It made landfall on this continent in 1970. It is simple to prove that geostatistics is an invalid variant of applied statistics. Surely, mining investors in Canada want the National Securities Regulator to investigate the validity of geostatistics.

Bre-X’s bogus grades made Busang’s barren rock look like a genuine gold resource. Yet, Professor Dr Michel David never knew what was wrong with his 1977 Geostatistical Ore Reserve Estimation. He derived a set of sixteen (16) functionally dependent values in a sample space. Each and every one of them is a function of the same set of nine (9) boreholes. That’s why each would have been blessed with its own variance in applied statistics. David was inspired by a tale on Random Kriging by A Marechal and J Serra. Matheron himself put on paper his take on Random Functions and Their Application in Geology. He invoked Brownian motion along a straight line to ensure the continuity of his random functions. This three-some had been brainstorming at the Centre de Morphology Mathematique, Fontainebleau, France. The next step was to bring Matheron’s new science of geostatistics to this continent. They did so in June 1970.

Praise for ASTM is also due for correcting the first name of Dr Jan Visman. I had reported on May 22, 2011 to ASTM’s President that it was misspelled. Catharine Allan, Administrative Assistant, Technical Committee Operations, made the correction and kept me posted. Now that’s the iconic society I got to know so well. ASTM Committee D05 on Coal and Coke has been working with applied statistics ever since Greg Gould became its driving force. One reference in Visman’s 1947 PhD thesis reads, Gould, G B, How to use laboratory tests in judging coal values, Combustion 11, 31-37, 1939-1940. Visman was already aware of Gould’s work! Gy’s 1967 and 1971 works do refer to Visman but his 1979 Sampling of Particulate Matter no longer does. On the contrary, Gy praised in his Introduction not only Matheron’s theories but also David’s 1977 textbook. Gy’s praise may well be the reason why David blew a fuse when Merks & Merks showed how to test for spatial dependence between gold assays of ordered round in a drift.

ASTM Committee D18 on Soil and Rock had arranged an International Symposium on Geostatistics for Environmental and Geotechnical Applications. The stage was set at the Hyatt Regency, Phoenix, Arizona on January 24-25, 1995. One of its co-chairs was R Mohan Srivastava. His point of view on geostatistics was already an integral part of BC Environment Guidelines. Environment Canada has a handbook called The Inspector’s Field Sampling Manual. I read it when EC took a client of mine to court. Here’s what EC’s inspectors are taught, “Systematic samples taken at regular intervals can be used for geostatistical data analysis, to produce site maps showing analyte locations and concentrations. Geostatistical data analysis is a repetitive process, showing how patterns of analytes change or remain stable over distance or time spans”. It refers to shellfish samples taken at 1-km intervals along a shore, and to water samples taken from varying depths in a water column. It’s just as short of primary data sets and derived statistics as is Matheron’s whole magnum opus. The question is then why geostatistical data analysis underpins the joint study of the Great Lakes by Canadian and US governments. It boils down to blind ambition and blatant contempt for the properties of variances.

The American Society for Testing and Materials fell for geostatistics in the 1990s. It came about when statistically challenged soil and rock experts had cooked up ASTM D5549-Standard Guide for Reporting Geostatistical Site Investigations. I had brought my case against what Professor Dr Georges Matheron himself had come to call a new science to the attention of Mr James A Thomas, President of the American Society for Testing and Materials. I had done so by snail mail on April 19, 1994.

ASTM President