Bamboozled by French sampling gurus

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 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. The question is then why French sampling gurus did not count degrees of freedom.

SGS Geneva had asked me on February 17, 1978 to peruse Gy’s paper on Unbiased Sampling from a Falling Stream of Particulate Material. I was to “possibly correct any English wording which may seem inappropriate”. Gy’s terminology was unusual to say the least. So what I decided to do was jot down handwritten notes in Gy’s draft. My scribbles were mailed on March 1, 1978. SGS Geneva had supported Gy’s test program to derive the optimum width and speed of linear cutters. What Gy had not done is cover coarse particles with fines. A coarse particle that impacts the leading edge of a cutter has a higher probability to become part of the primary sample than a similar particle that bounces off its trailing edge. That’s but one of several reasons why cross belt samplers have become so popular.

Gy’s Sampling of Particulate Materials, Theory and Practice ended up on my desk at SGS Vancouver. It did so close to Christmas 1979. Gy had graced my copy with his compliments, his signature, and his invoice. It was Volume 4 in Developments in Geomathematics. Three volumes had already been released by Elsevier Scientific Publishing Company. David’s 1977 Geostatistical Ore Reserve Estimation was the second volume. Our assay lab had just unscrambled the Tapin Copper salting scam. I wanted to know how to test for spatial dependence between gold grades of ordered core samples. But David did not know how to test for spatial dependence.

I scrutinized Gy’s work from cover to cover. Elsevier had not typeset Gy’s first take on sampling theory and practice. So Gy had had to paste corrections on a number of pages. Scores of his literary gems boggled my mind. Stunning terms are bi-univocal relationship, degenerate splitting process, durationless instant, increment reunion, maximum maximorum, punctual sample and zero-dimensional lot. It was a good omen that the Central Limit Theorem was mentioned twice in his Index. I couldn’t find it on one of those pages but did find it on the other. The term “degrees of freedom” was missing between “degenerate splitting processes” and “degree of representativeness”. Surprisingly, it did surface under “variogram”. Gy rambled on about, “Statistical analysis of a sequence of data by means of the Student-Fisher (SF) test”. Sir R A Fisher and W S Gosset would have found it uncool!

I need to digress before unscrambling Gy’s sampling constant. I spoke German and French a bit better than English when we came to Canada in 1969. So I decided to take survey sampling at Simon Fraser University. Later on my son really studied at SFU. Ed Merks completed his BSc (Honours) in 1986 and his MSc in 1987. He obtained his PhD in Computing Science. He was awarded the Graduate Dean’s Medal from the Faculty of Applied Science in 1986 and 1992. My son knows at least as much as I do about applied statistics. And he knows a lot more about computing science! It was a while before Precision Estimates for Ore Reserves got under David’s skin and was rejected by CIM Bulletin. And that was a scientific fraud! The variance of Gy’s sampling constant is another scientific fraud. The French sampling school still does not know that each and every function does have its own variance. Quelle domage!


I’ll move fast forward to the 1990s. My work with Cominco left me mesmerized by confidence limits for metal grades and contents of in-situ ores and mined ores. So I had thought that David’s 1977 Geostatistical Ore Reserve Estimation and Clark’s 1997 Practical Geostatistics would come in handy. A friend gave me Journel and Huijbregts’s 1978 Mining Geostatistics. That’s when Merks and Merks found out why Professor Dr Georges Matheron, Dr Pierre M Gy and Professor Dr Michel David were birds of a feather. I work with applied statistics simply because I have studied Volk’s Applied Statistics for Engineers. It taught me all I needed to know about one-to-one correspondence between functions and variances.

Stay tuned for more about the first sampling gurus who ignored the properties of variances, and who assumed, kriged, smoothed, and rigged the rules of applied statistics with impunity!

NSERCC to grant Access to Information Request

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:

Access to Information Request

Professor Dr Michel David’s work is based on research funded by the Natural Science and Engineering Council of Canada (Grant 7035). The author mentioned this grant in his 1977 Geostatistical Ore Reserve Estimation (364 pages) and in his 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation (216 pages). David shows on page 286 of his 1977 work how to derive a set of sixteen (16) distance-weighted averages from a set of nine (9) holes. What he did not derive was the variance of each distance-weighted average. On the contrary, he postulated, “Writing all the necessary covariances for that system of equations might be a good test to find out whether one really understands geostatistics!” As a matter of fact, counting degrees of freedom for that system of equations is a good test to find out whether one really grasps applied statistics.

Geostatistics is an invalid variant of applied statistics. As such it is a scientific fraud. Lord Kelvin (William Thomson 1824-1907) once said, “…when you can measure what you are speaking about, and express it in numbers, you know something about it, but when you cannot express it in numbers your knowledge is of the meagre and unsatisfactory kind…” Lord Kelvin knew more about degrees Kelvin and degrees Celsius than about degrees of freedom and the study of climate change. Lord Kelvin and Sir Ronald A Fisher (1890-1960) were marginal contemporaries. Lord Kelvin would have wondered about the wisdom behind assumed spatial dependence between measured values in ordered sets. Sir Ronald A Fisher could have verified spatial dependence by applying his F-test to the variance of a set of measured values and the first variance term of the ordered set.

What I want to know is whether or not any mutation of Matheron’s new science of geostatistics is applied to study climate dynamics or to monitor pollution of lakes and waterways.

Yours truly,
J W Merks, President
Matrix Consultants Limited
1357 Napier Place
Coquitlam, BC
Canada V3B 7A3
Phone: 604-941-1213

http://geostatscam.com/statistics_for_geoscientists.html
http://blog.bulk-online.com/general/nrc-shelled-out-real-dough-for-bogus-statistics.html http://cosmo.mcgill.ca/people/faculty.php

NRC shelled out real doug for bogus statistics

The National Research Council did 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”. The author mentioned it on page VII of what he had come to call Geostatistical Ore Reserve Estimation. But why didn’t he ask a genuine statistician to read his draft? I found out that the author was right after having read my own copy of his book.

David was as smitten with geostatistics in the 1970s as young Matheron was with applied statistics in the 1950s. Alas, Matheron’s pursuit of applied statistics was not to last. On the contrary, Professor Dr Georges Matheron in the 1970s praised geostatistics as a new science. He did so because he had failed to grasp that functions do have variances. Thus, each and every distance-weighted average has its own variance in applied statistics. Just the same, Matheron got hooked on his variance-deprived distance-weighted average. So much so that he got into calling it a kriged estimate. He did it to honor D Krige who worked with distance-weighted averages at Witwatersrand gold mines in South Africa. What went wrong with Matheron’s new science is that the variance of the kriged estimate has gone missing!

A strong case can be made that eulogies be written long before one’s time on this planet comes to an end. One might ask a lawyer to assist in assuring the veracity of one’s credentials. A case in point is Professor Dr George Matheron’s 2000 eulogy. Dr F P Agterberg was his eulogist. He remembered him as the founder of spatial statistics. As luck would have it, Matheron never tested 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. Given that Matheron’s magnum opus is posted on the web, one might spend a life time to study his work.

Professor Dr Michel David passed away on May 10, 2000. His obituary was put together by Professor Dr Roussos Dimitrakopoulos and Michel Dagbert. The International Association for Mathematical Geology awarded David the W C Krumbein medal in 1988. David became a Fellow of the Royal Society of Canada in the same year. Moreover, CIMMP recognized David’s worldwide achievements in 1989 with the award of the Selwyn G Blaylock medal.

My son and I knew precisely what had gone wrong with geostatistics when I was face-to-face with David on Saturday, March 23, 1991. It was at a seminar on Sampling and Ore Reserves at the Royal York Hotel, Toronto, Ontario. CIM Bulletin in 1990 rejected Precision Estimates for Ore Reserves. We had shown how to test for spatial dependence and how to derive unbiased confidence limits for gold content and grade. David saw fit to nitpick that twenty years of geostatistical literature went missing. He did not ask me a single question. Take a look at what is wrong in Matheron’s new science of geostatistics.

Marechal & Serra, Random Kriging, 1970, Figure 10
David, Geostatistical Ore Reserve Estimation, 1977, Figure 203

David wrote: Writing all the necessary covariances for that system of equations might be a good test to find out whether one really understands geostatistics! Merks and Merks claim: Deriving the variance of each distance-weighted average AKA kriged estimate, and counting degrees of freedom for that his system of equations might be a good test to find out whether one really grasps applied statistics.

The National Research Council is the Government of Canada’s institute for research and development. As such it has been active since 1916. NRC’s task is to stand on guard for ethics and integrity. It did not know in the 1970s that Matheron’s new science of geostatistics is an invalid variant of applied statistics. Neither did Dr Roger A Blais, a Professor in Economic Geology and a Fellow of the Royal Society of Canada. He made it possible for David to write so much about so little. David also confessed to be indebted to Matheron. David’s writing added up to a batch of bogus statistics. NRC7035 was in place not only for his 1977 Geostatistical Ore Reserve Estimation but also for his 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation.

Dr Isobel Clark in her 1979 Practical Geostatistics derived the variance of the distance-weighted average AKA kriged estimate. Professor Dr Michel David wrote about the famous Central Limit Theorem but did not apply it. Professor Dr Roussos Dimitrakopoulos wrote a touching farewell to Michel David (1945-2000). David is no longer listed under Obituaries of Deceased Fellows. Sic Transit Gloria Mundi!

To have or not to have true variances

It all depends on who applies what! Statisticians apply true variances but geostatisticians work 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 PDAC had set the stage at the Royal York Hotel in Toronto, Ontario, on Saturday, March 23, 1991. It was organized by 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. But that’s one more part of my story!

During my talk Professor Dr Michel David was sitting sort of face to face with me on the first row. A few of his buddies were close by. David himself had put on paper the very first work on Matheron’s new science of geostatistics. He had simply called it Geostatistical Ore Reserve Estimation. Elsevier Scientific Publishing Company had printed in 1977. David himself had predicted in this book that it was not for professional statisticians. He also predicted that statisticians would find many unqualified statements. And he did get that right too! What David did not predict is that he would blow a fuse if and when he was to review a paper that was short on references to geostatistical literature. But that’s exactly what he did as a reviewer for CIM Bulletin. David did so when he reviewed in September 1989 our paper on Precision Estimates for Ore Reserves.

We had decided not to point out what was wrong with geostatistics but to show what made sense in applied statistics. We had tested for spatial dependence between gold grades of bulk samples taken from a set of ordered rounds in a drift. We had done so by applying Fisher’s F-test to the variance of the set and the first variance of the ordered set. We pointed out that each function does have its own variance in applied statistics and that variances of gold contents are additive. What we didn’t do was estimate the intrinsic variance of gold. It would have required that a pair of interleaved primary samples be taken from every crushed round. We mentioned that extraneous variances such as those for dividing whole core sections into halves, and for selecting and assaying test portions of test samples may be subtracted before deriving unbiased confidence limits for contained gold. We were tickled pink that Precision Estimates for Ore Reserves was praised by and published in Erzmetall, October 1991.

David has made peer review at CIM Bulletin a shameful sham. Read what he wrote about our paper: “The authors present their own method for calculating precision estimates for ore reserves without a single reference to 20 years of work in geostatistical ore reserve estimation (see attached references)”. What he had missed were references to Dagbert & Myers, to himself, and to Journel & Huijbregts. In his 1977 Geostatistical Ore Reserve Estimation he did praise “the famous Central Limit Theorem”. What he didn’t show was how to test for spatial dependence between measured values in ordered sets. Neither did he show how to derive unbiased confidence limits for masses of contained metals.

David may have reviewed A study on Kriging Small Blocks. Its authors called attention to the fact that mine planners are often tempted to over-smooth small blocks. Armstrong and Champigny failed to show how to smooth both small and large blocks to perfection. Good grief! That sort of bogus science was approved by and published in CIM Bulletin of March 1988. Nowadays, mineral analysts are blamed when geostatistically predicted grades mess up metallurgical balances in mineral processing plants. It’s all a huge game of chance for mining investors!

Marechal and Serra showed in 1974 how to derive a set of sixteen (16) distance-weighted averages from a set of nine (9) boreholes. David shows the same set on page 286 of his book. Each distance-weighted average is a function of the same set of nine (9) holes. As such, each is blessed with its own variance in applied statistics. Here’s where statistics went missing in geostatistics. The variance-deprived distance-weighted average morphed into a kriged estimate. What’s more, geostatisticians never took to counting degrees of freedom.

Infinite set of kriged estimates within B

David got into calling a kriged estimate a simulated value. Here’s literally what he wrote on page 324 of his 1977 work, “The criticism to this model is obvious. The simulation is not reality. There is only one answer: The proof of the pudding is …! So far the few simulations made which it has been possible to check have a posteriori proved to be adequate”. Nobody knows all of the nonsense I've had to put up with!

Who's to protect mining investors?

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 would want a National Securities Regulator to investigate the validity of geostatistics.

Our National Securities Regulator launched its Transition Office in June 2009. Mr Douglas M Hyndman was appointed the NSR Chair. The Supreme Court of Canada has not yet ruled on the constitutional validity of a national securities regulator. It seems to make sense at a glance but is fraught with practical pitfalls. Alberta and Quebec prefer provincial fiefdoms. Here’s what I find funny. David’s 1977 Geostatistical Ore Reserve Estimation was put on paper in La Belle Province. Alberta’s oil patch has taken to geostatistics with reckless abandon. That’s why I am pleased that NSR’s Chair is bringing 25 years of experience to this position.

Mining investors do remember the Bre-X fraud but too few grasp how geostatistics converted bogus grades and barren rock into a massive gold resource. I’m not one to search for moral integrity. Searching for scientific integrity is good enough for me. I am pleased that the BCSC Chair has been appointed to chair the NSR Transition Office. He does have what it takes to unravel a scientific fraud. I do so wish the Supreme Court of Canada to rule in favor of a National Securities Regulator.

I drew the attention to the BCSC Chair in my letter of March 24, 2006 to the fact that I had called on the Canadian Council of Professional Engineers and the Canadian Council of Professional Geoscientists to examine whether geostatistics is a scientific fraud or sound science. Neither CCPE nor CCPG took to the task. I also pointed out to have met in Vancouver, BC on January 22, 2006 with Ms Deborah McCombe, PGeo and Dr Greg Gossan, PGeo. At that time both were on staff with securities commissions in Ontario and in British Columbia.

I pointed out that Dr Isobel Clark derived in her 1979 Practical Geostatistics the variance of the distance-weighted average AKA kriged estimate. She was the first and only scholar who derived the distance-weighted average. I pointed out that the author didn’t test for spatial dependence within her sample space by applying Fisher’s F-test to the variance of the set and the first variance term of the ordered set. I made it clear that all distance-weighted averages converge on the arithmetic mean as the distance between Clark’s sample space and a selected position converges on infinity. That’s why testing for spatial dependence in sample spaces and sampling units is so critical in applied statistics. All I want to know is why professional engineers and professional scientists accept that spatial dependence between measured values may be assumed simply because Stanford’s Professor Dr Andre Journel has said so.

The Supreme Court of Canada is to decide whether or not a National Securities Regulator is in the best interest of Canadian investors. Meanwhile the Chair of NSR’s Transition Office in June 2009. He no longer has to rely on Dr Greg Gossan, his former Chief Mining Advisor.

Dr Gregory J Gossan
Formerly: BCSRC Chief Mining Advisor
Presently: Chief Geologist, AMEC

Mr Douglas M Hyndman, Chair, NSR Transition Office, ought to ask the Canadian Council of Professional Engineers and the Canadian Council of Professional Geoscientists whether or not a statistical fraud does violate any Code of Ethics.

What's wrong with post-Bre-X standards?

Bre-X’s bogus grades made Busang’s barren rock look like a genuine gold resource. Yet, Professor Dr Michel David didn't know 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 of them 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 Random Functions and Their Application in Geology. He invoked Brownian motion along a straight line to ensure continuity of random functions. This three-some had been brainstorming at the Centre de Morphology Mathematique, Fontainebleau, France. Next, brought Matheron's new science of geostatistics to this continent in June 1970.

Figure 10. –Grades of n samples belonging to
nine rectangles P of pattern surrounding x
Fig. 203. Pattern showing all the points within B,
which are estimated from the same nine holes.

David’s students seem to have thought some 25 years later that he deserved praise for thinking up the first textbook on geostatistics. David’s bash was called Geostatistics for the Next Century. All I wanted David and his buddies to grasp before this century came along were The Properties of Variances. When praise was heaped on David, Bre-X’s rigs were drilling barren rock in the Kalimantan jungle. Good news for Bre-X’s investors kept coming. Soon it was to be bad news!

Applied statistics proved early in 1997 that Bre-X’s crushed core samples were salted with placer gold. That’s why the Mining Standards Task Force (MSTF) was set up. Morley P Carscallen, Vice-Chair, Ontario Securities Commission, and John W Carson, Senior Vice-President, Market Regulation, Toronto Stock Exchange, were MSTF’s Co-Chairs. Here’s what they had pointed out in MSTF’s Interim Report , ”A number of incidents served as an impetus for the formation of a joint task force between the Ontario Securities Commission and the Toronto Stock Exchange. Public confidence in mining stocks was shaken and the industry as a whole suffered a major setback. The most talked about incident was, of course, Bre-X.”

In spite of so much soul searching the Bre-X fraud ended up being the least acted upon incident. The OSC could have acted several years before I proved that Bre-X was a salting scam. I had pointed to the fact that unbiased confidence limits for metal grades and contents can be derived not only for mined ores and mineral concentrates but also for in-situ reserves and resources. I had done so in my letter of November 30, 1994 to John J Drury, PEng and Chairman CIM Ad Hoc Reserve Definition Committee. He responded on October 23, 1995. Who could possibly be against tried, tested and true ISO Standard Methods after the Bre-X salting scam? And why would the world’s mining industry not want unbiased confidence limits for metal contents and metal grades of mineral inventories? Why not turned out to be one very long story!

The Mining Standards Task Force came up with National Instrument 43-101 to define requirements for disclosure of results. It claims to have done so to increase investor confidence. Yet it still doesn’t show how to derive unbiased confidence limits for metal contents and grades of mineral inventories. It’s good news for mining companies but bad news for mining investors. Appendix A in MSTF’s Final Report points to presentations made to the Task Force. I pity those who had to put up with so much mind numbing geostat drivel. Appendix B points to written submissions to the Task Force. AMEC, Geostat Systems International and SNC-Lavalin have not made submissions in writing.

Post-Bre-X standards protect mines much more than investors. Both the OSC and the BCSC knew I had unscrambled the Bre-X fraud. So, I got to meet Ms Deborah McCombe, OSC’s Chief Mining Consultant, and Dr Greg Gosson, BCSC’s Chief Mining Advisor. We met on January 22, 2006 at the BCSC Office in Vancouver, BC. The objective was “to discuss the use of geostatistics in mineral resource and mineral reserve estimates by mining companies.” I handed out copies of my work. I had posted on my website Clark’s hypothetical uranium data in a two-dimensional sample space. She had done what no geostatistician ever got around to doing. She derived the variance of the distance-weighted average aka kriged estimate. Extrapolation shows that the distance-weighted average tends to converge on the arithmetic mean. What she didn’t do was test for spatial dependence. But then, Stanford’s Journel taught her that spatial dependence between measured values in ordered sets may be assumed.


OSC’s Chief Mining Consultant wrote she would appreciate "being apprised of my progress on the development of industry best practices in the application of mathematical statistics to assess the reliability of data." Her letter was copied to OSC’s Chair.

Praise for ASTM Committee E11

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. How about that? 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.

Greg Gould’s friends called him GG. When I met Greg for the first time he told me that his number one textbook was Volk’s Applied Statistics for Engineers. I still have my first copy. Volk explores all properties of variances in a chapter called Analysis of Variance. Visman applied the additive property of variances to partition his sampling variance into its composition and distribution components. I divided the set of primary increments into interleaved pairs so as to get a single degree of freedom. Gy would put his set of primary increments in a single basket. Clearly, the French sampling school didn’t respect the concept of degrees of freedom nearly as much as do statisticians. That’s why I put together a paper called The Properties of Variances. I wanted to prove that kriging variances and classical variances are as different as night and day.

GG’s grasp of sampling and statistics made him a valuable member of ASTM Committee E11 on Quality and Statistics. He didn’t attend the meeting of ISO/TC27 at Vancouver, BC in 2009. Here’s where and when SGS’s Charles D Rose talked about multivariate analysis when testing for bias between paired data. He didn’t talk about trace elements in rocks or soils but about bias test data for total moisture and dry ash in coal. The power of Student’s t-test to detect a bias is best defined in terms of Bias Detection Limits and Probable Bias Ranges. C D Rose and R M Srivastava seemed to have solved in 1993 some sort of sampling problem. They did it with a fractal correlation function but without degrees of freedom. Scores of degrees of freedom deprived papers were presented in 1993 at David’s bash. Thus it came to pass that David’s 1977 Geostatistical Ore Reserve Estimation was praised for no reason whatsoever.

British Columbia got stuck with environmental guidelines cooked up by R Mohan Srivastava and his FSI pals. Mo ticked me off by dismissing degrees of freedom. He put up a squabble when Sandra Rubin’s “Whistleblower Raises Doubts over Ore Bodies” was published in the National Post of September 30, 2002. Mo beats around the bush with the best when talking about degrees of freedom. All the same, a gifted geostatistocrat thought Mo was witty.

Geovariances’ Dr M Armstrong
Past Editor: De Geostatisticis
Coauthor: A Study on Kriging Small Blocks

Both Armstrong and her coauthor failed to grasp why kriging variances rise and fall. They thought mine planners were over-smoothing small blocks. So they cautioned against over-smoothing. As luck would have it, testing for spatial dependence didn’t play much of a role in Matheronian geostatistics.

Stanford’s Journel made geostatistics a piece of cake by assuming spatial dependence between measured values in ordered sets. So, he didn’t even teach his students how to apply Fisher’s F-test.

Stanford’s Professor Dr A G Journel
Unencumbered with Fisher’s F-test

Mineral analysts, too, are blamed when metal grades of mined ores are lower than geostatistically “engineered” grades. Mineral analysts do know that interpolation without justification makes no sense in any science. I have talked about sampling and statistics at several of their annual meetings. I even put together a paper on Self-defense for Mineral Analysts.

ASTM awarded me in 1995 for 25 years of continuous membership. Peter S Unger, Vice Chairman, Committee E-11, had written on March 4, 1995, that Ricardo Stone, 1st Vice Chair, would review my notes and contact me. Hennie and I enjoyed luncheon with Carol and Ricardo. I explained that measured gold grades of mined ore were lower than geostatistically engineered gold grades at Hecla’s Grouse Creek mine. Hecla's chief geologist and his dad were both into geostatistics. That’s why the assay laboratory was blamed for low gold grades. I had met its chief assayer at some other mine in the USA. He asked me to visit the Grouse Creek mine and figure out what was wrong. All I did was apply Fisher’s forbidden F-test to gold grades of ordered blast holes. Spatial dependence dissipated into randomness between 20 and 30 m. Yet, the geostatistical model was based on assumed spatial dependence at 100 m. Hecla’s Grouse Creek never made the predicted grade. As fate would have it, geostatistical software was already converting Bre-X’s bogus grade and Busang’s barren rock into a massive phantom gold resource. ASTM Committee D-18 on Soil and Rock is still kriging and smoothing as much as does the world’s mining industry.