Why Westray Mine trial was stayed

The methane gas explosion at the Westray Mine in Plymouth, Nova Scotia, Canada on May 9, 1992 caused the death of 26 miners. Mine managers Gerald Philips and Roger Parry were charged with manslaughter and criminal negligence causing death. The mills of justice ground to a halt when the Crown had failed to give full disclosure of all of its exhibits by November 15, 1994.

Mr Duncan R Beveridge, QC, with Beveridge, Lambert & Duncan, called during the summer of 1999 to find out what I knew about sampling and statistics. I pointed to Sampling and Weighing of Bulk Solids, my activities on ISO Technical Committees, and my savvy in solving scams such as the Bre-X fraud. I transmitted a facsimile of my curriculum vitae which was similar to the one currently posted on my website.

I went to work on the Westray file shortly after October 1, 1999. It consisted of twenty–two (22) pages of text and ten (10) schedules marked A to F. I was pleased with the description of how post-explosion samples had been taken. Test results determined by Canmet and other participants in an interlaboratory test program were statistically identical. The Nova Scotia Department of Labour and the RCMP had selected test samples at intervals of 0.9 m in accordance with the Coal Mines Regulations Act. Test results for all test samples proved the average percentage combustible matter to be significantly higher than the maximum allowable limit of 35%. My report is titled Post-Explosion Sampling Procedures at the Westray Mine and was submitted on November 2, 1999.

What piqued my interest was the testimony of Andy Liney, PEng and a former mine manager and ventilation specialist from the United Kingdom. He testified that too few post-explosion samples had been taken to obtain a precise estimate for the average percentage combustible for all locations. Post-explosion samples had been taken at 0.9 m intervals. A statistical analysis of test results in samples taken by the Nova Scotia Department of Labour and the RCMP proved beyond reasonable doubt that the average percentage combustible matter in the underground workings at the Westray mine exceeded the maximum allowable limit of 35%.

Spatial dependence between measured values in ordered sets such as those taken after the explosion at the Westray Mine may or may not exist. As a matter of fact, testing for spatial dependence plays a key role in sampling practices for mined ores and mineral concentrates as defined in ISO Standards. The lead prosecutor was Herman C Felderhof. He knew as much about testing for spatial dependence at the Westray coal mine as did John B Felderhof at the Bre-X phantom gold project.

On-stream analysis of slurries in mineral processing plants became a powerful tool in the 1980s. That’s why I put together Simulation Models for Mineral Processing Plants. It was reviewed by The Metallurgical Society of CIM and published in CIM Bulletin of September 1991. On September 28, 1989 my son and I submitted for review our take on Precision Estimates for Ore Reserves. Here’s what I wrote to the Editor of CIM Publications, “The authors believe that their methodology provides a reliable measure for the risk to encounter less than the predicted grade”. What had troubled Professor Dr Michel David was that we had not only applied “our own method” but had also failed to refer to twenty years of geostatistical literature. Professor Dr A J Sinclair, PEng, PGeo was troubled because he deemed the variance of a general function a bit dated. He has been teaching generations of UBC students all he knows about geostatistics.

Variance of a general function

What I taught at UBC on November 22-24, 1989 was Sampling Precious Metal Deposits: Metrology-A New Look. Professor Dr A J Sinclair, PEng, PGeo welcomed the participants in Room 330A at 8:30AM. He didn’t object to anything I taught nor did he ask any questions. Yet, he had earlier reviewed for CIM Bulletin our take on Precision Estimates for Ore Reserves. His review was dated November 15, 1989. Surely, Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo ought to explain how Gemcom software converted bogus grades and barren rock into Bre-X’s phantom gold resource. APEGBC ought to get a copy as soon as UBC's Emeritus Professor has explained why the variance was stripped off the distance-weighted average AKA kriged estimate!

Professionals pine for public trust

Professional designations are powerful symbols. The public at large tends to trust those who do qualify. Noblesse oblige, bien sur! Here’s what the public ought to know! The current code of ethics does not always protect the public at large. I was aware of this code long before I read the Vancouver Sun of March 1, 2012. Much of it is posted under Correspondence on my website. The National Engineering and Geoscience Month (NEGM) was this year held in Vancouver, BC. Its members have as strong a need to be appreciated and understood as I do! But far too few of its members remember as well as I do how geostatistics converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Kilborn Engineering Pacific Ltd cooked up Bre-X’s phantom gold resource here in Vancouver, BC. I had given my short course on sampling and statistics at Kilborn’s Office long before Bre-X Minerals got into drilling holes at its gold property in Borneo, Indonesia. It bothered but few professionals that geostatistics as Kilborn knew it in the 1990s morphed into stochastic mine planning at McGill University in 2010s. Among those who couldn’t care less whether or not functions have variances is UBC Emeritus Professor Dr Alastair J Sinclair, PEng. He took a liking to Matheron’s thinking in the 1970s. He has been teaching Matheronian geostatistics to scores of students at the University of British Columbia.

Dr A J Sinclair, PEng, PGeo
Professor Emeritus

Since the 1990s I have explained in rich detail on my website and in my blogs why geostatistics is a scientific fraud. Why then do so many APEG Members ignore one-to-one correspondence between functions and variances? One would expect that sort of scientific fraud to be at variance with APEG’s Code of Ethics. What I want to know most of all is whether or not the properties of variances have ever been a matter of any concern to APEG’s Members. So I tend to ask a lot of questions. Where have degrees of freedom gone? Who lost the Central Limit Theorem? What has happened to unbiased confidence limits for masses of contained metals? Dr Alastair J Sinclair, PEng, PGeo still does not accept one-to-one correspondence between functions and variances. He is still teaching his students all about assuming spatial dependence between measured values in ordered sets, interpolating by kriging, smoothing to perfection, and rigging the rules of applied statistics with impunity.

Assume, krige, smooth and be happy!

Here’s what Mr Tom Sneddon, MSc, PGeol, Manager of Geoscience Affairs, APEGGA Calgary wrote in response to my emessage of March 2, 2012:

“The Vancouver Sun article you refer to was placed by our sister organization, the Association of Professional Engineers and Geoscientists of British Columbia, but its content applies equally to the practice of geosciences anywhere in Canada as we pledge a common code of ethics and we all play by the same rules of conduct. You are quite right in saying that geologists and geoscientists in Alberta are bound to use only techniques and software that the practitioner is completely familiar with and understands. That is a fundamental rule of professional practice. Further, Alberta geoscientists are mostly industrial practitioners who are pretty pragmatic about what kind of methods they use in exploring for oil, gas and minerals. If a particular body of knowledge or set of techniques or algorithms don’t find dollars, their ultimate objective, they are not going to use those techniques.

As your publications suggest, good science (and by extension applied science) depends on a healthy load of skepticism and debate before an idea or concept can even be conditionally accepted as good professional practice. APEGGA provides one particular platform where ideas are openly and enthusiastically discussed, sometimes at great length: the Readers’ Forum in our bi-monthly magazine, the PEG. If you would like to have your views known and engage in a debate with our over 63,000 members, please send a note to George Lee, The Editor in Chief of the PEG (glee@apegga.org) allowing him to print you letter. Since many of our members use geostatistics as a tool for mineral exploration and development, I look forward to hearing the range of views they will surely express.”

PEG's Editor in Chief wrote: “This is not a debate we’ll get into, for at least three reasons. First, the subject matter is not part of our mandate as a non-technical publication. Second, the complexity of the subject and the need to present both sides, in fairness to UBC and Dr Sinclair, would require a full story, which we don’t have the space or the mandate for. And finally, it’s set in B.C. – our focus is Alberta. Sorry we can’t help you. All the best”.

Sound statistics or goofy geostatistics?

It took a while to post on my website much of what I know about sampling and applied statistics in mineral exploration, mining, mineral processing, smelting and refining. My webmaster and I have done so in the format of downloadable PDF files. Cash flow is used to derive unbiased confidence limits for content and grade of a reserve, and of the proven part of a resource.

The Canadian Institute of Mining, Metallurgy and Petroleum in 2007 made me a Life Member. I am the most irate Life Member of that iconic institution. Every year CIMMP asks its Life Members for donations. It wants to teach students all about mineral exploration, mining, mineral processing, smelting and refining. Sounds familiar, doesn’t it! But I have never donated a penny. Not as long as UBC’s Emeritus Professor Dr Alastair J Sinclair, PEng is teaching students to assume spatial dependence between measured values in ordered sets. Why doesn’t he grasp that each distance-weighted average does have its own variance? Did he ever peruse Clark’s 1979 Practical Geostatistics? She derived the variance of her distance-weighted average hypothetical uranium concentration. Alas, what she didn’t do was test for spatial dependence between measured values in her wacky sample space. So it seems that Clark’s take on applied statistics is imperfect.

Practical geostatistics

The odd mining mogul seems to pine for moral integrity but I pine for scientific integrity. Scores of scientists pay attention to my take on geostatistics. On November 14, 1990 I mailed the first of several letters to Professor Dr Robert Ehrlich, Editor of the Journal of Mathematical Geology. I did so by snail mail and enclosed copies of Precision Estimates for Ore Reserves and of Sampling and Weighing of Bulk Solids. On October 26, 1992 JMG’s Editor wrote, “Your feeling that geostatistics is invalid might be correct”. Attached to his letter was what Stanford’s Professor Dr A G Journel had written “a bit reluctantly”. I have also posted the letter on my website under Correspondence. It seemed to Journel that “my anger arises fro a misreading of geostatistical theory, or a reading too encumbered by classical “Fischerian” statistics”.

The next paragraph shows another ad verbatim example of goofy geostatistical thinking:

1 – Data and degrees of freedom

"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. It is that spatial dependence which allows differentiated local interpolation and mapping in general. Were the data independent one from another then only global statistics can be retrieved. In presence of dependence the classical notion of degrees of freedom vanishes; n spatially dependent data do not provide n degrees of freedom”.

Another stunning farce was Geostatistics for the Next Century. Geostatisticians from far and wide had flocked to McGill, Montreal, Canada on June 3 to 5, 1993. They had come to honor Professor Dr Michel David for his contribution to Matheron’s new science of geostatistics. I tried to get on the program but my paper on The Properties of Variances didn’t arouse any interest.

Way too many years I have been exposed to geostat drivel. It has made me a perfect cynic. But I do have friends. A true friend is a precious gift. Sometimes it’s tough to find out who your true friends are. Dr.-Ing Reinhard Wohlbier is a true friend. Trans Tech Publications in 1985 printed my textbook on Sampling and Weighing of Bulk Solids. Thanks to Reinhard it has now been posted on my website as a PDF file. Various papers I have put together for Trans Tech Publications through the years are about to be posted on my website. Reinhard has formidable knowledge of the handling of materials in bulk. I wish Reinhard and Ute well.

Todd Higden, too, is a true friend. He is Creative Director of Frontline Multimedia. He has set up most of my first take on Geostatscam.com. My website went online in September 2005. Todd has posted scores of downloadable PDF files in 2012. It takes less than ten minutes at legal speed to drive to Todd’s Office. I have more papers to scan and to post on my website. I want my readers to know the difference between sound statistics and surreal geostatistics. Todd does not need to know much about either but he'll get to know a little!

My partner for life and my son are far more than true friends. Hennie has never been awarded a PhD in Psychology for putting up with her driven hubby. In contrast, Ed was awarded a PhD in Computing Science at Simon Fraser University in 1992. He was also awarded the Dean’s Medal in 1986 and in 1992. My son and I did put together Precision Estimates for Ore Reserves. It was thrashed by our geostatistical peers at CIM Bulletin. In spite of that Erzmetall praised it for “splendid preparation” and published it in October 1991. We have also put together Precision and Bias for Mass Measurement Techniques. ISO did like it. So much so that it became ISO 12745:2008. Nowadays Ed leads the top-level Eclipse Modeling Project as well as the Eclipse Modeling Framework subproject. He has put on the same page his blog, my blog and the bulk-online blog. Now that’s cool!

A tale of two papers

CIM Bulletin approved and published in 1999 a paper called Simulation models for mineral processing plants. In contrast, CIM Bulletin did reject in 1990 what Merks and Merks had called Precision estimates for ore reserves. Professor Dr Michel David (1945-2000) decided to reject our paper because we had applied our own method and had given too few references to the geostatistical literature. Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo found the variance of a general function a bit dated!

Variance of a general function

Dr Sinclair frowned on functions whose roots are traceable to applied statistics. He is Emeritus Professor at the University of British Columbia. He may still be teaching students that working with variance-deprived distance weighted averages AKA kriged estimates does make sense in Matheronian geostatistics.

Applied statistics has always played a key role in my teaching. The published paper was based on process simulation with the pseudo-random number generator of the standard uniform distribution. The variance of the general function as defined by Volk in his Applied Statistics for Engineers was of critical importance. This function made it simple to derive confidence limits for metal contents of mined ores and mineral concentrates. So I was delighted that the Metallurgical Society of the Canadian Institute of Mining had approved my paper. The more so since MetSoc had not found any errors. That’s how it came to pass that CIM Bulletin did publish this paper in September 1999.

A few years later I did spot a mistake not only in Simulation models for mineral processing plants but also in my book on Sampling and Weighing of Bulk Solids. The number of degrees of freedom for the first variance term of measured values in an ordered set is df=2(n-1) rather than df=2n-1. I also found out that the number of degrees of freedom for sets of measured values with variable weights are no longer positive integers but become positive irrationals. Both my book and my paper have been corrected.

Merks and Merks’s Precision estimates for ore reserves was the first paper on this topic that my son and I had put together. When Gy had sent me a copy of his 1979 Sampling of particulate materials, Theory and practice, I found out about David’s 1977 Geostatistical ore reserve estimation. It struck me as odd for any author to predict “…statisticians will find many unqualified statements…” Why hadn’t he asked a real statistician to peruse his work? And why had geostatistics been hailed as a new science in the 1970s? What I decided to do at that time was to keep David’s 1977 opus for scrutiny. The time for scrutiny came about in the late 1990s!

One would expect those who ignore degrees of freedom not to be entrusted with the works of those who do count degrees of freedom. CIM Bulletin did trust geostatistical peer review but I called it a blatantly biased and shamelessly self-serving sham. Let me briefly explain why! We had submitted our paper on September 28, 1989. We did expect the Geology Division of CIM to review our paper in an unbiased manner. I was tickled pink when the Editor of CIM Bulletin wrote on November 23, 1989 that both reviewers recommended publication with major revisions. But I turned red when I read what “mayor revisions” were necessary. So who had asked for major revisions? Professor Dr Michel David and Professor Dr Alastair J Sinclair had been entrusted with the task to protect the central tenets of Matheron’s new science of geostatistics.

David was in a tiff when he wrote “the authors had presented their own method”. Good grief! Whose method had David expected? What the author of the first textbook on geostatistics did expect most of all were scores of references to the geostatistical literature. We did find what David himself had predicted that statisticians would find. He wrote:"...statisticians will find many unqualified statements here". We did indeed! What David also felt is that we should have made reference to Gy’s 1979 Sampling of Particulate Materials, Theory and Practice. We should have pointed out that Gy's sampling constant does have its own variance whether his followers like it or not! Too few scientists and engineers are grasping what problems the French sampling school has caused!

Goofing with Gy's sampling errors

Searching for sound sampling practices always deserves praise. Sampling experts in South Africa have tried to put into plain words what sound sampling practices are all about. What a shame that they took a shine to Pierre Gy’s sampling errors. So much so that they have decided to put together a study of Gy’s sampling errors. Gy had grasped but little of what he had come to call “sampling errors”. What a pity that sampling experts in South Africa, too, have failed to come to grips with Gy’s sampling errors as much as had Gy himself.

What irked me is that sampling experts in South Africa praised Gy’s unpublished tale on “Minimum mass of a sample needed to represent a mineral lot”. Gy didn’t refer to it in his 1979 Sampling of Particulate Materials. But why didn’t he refer to Visman’s 1947 PhD Thesis anymore? And why did he take to praising David’s 1977 Geostatistical Ore Reserve Estimation? Famous French sampling scholars such as Professor Dr G Matheron, Dr P M Gy and Professor Dr M David have left no doubt that the properties of variances were far beyond their shared grasp. That’s why they never were familiar with one-to-one correspondence between functions and variances. And that’s why degrees of freedom have become such a burden!

Part 1 and Part 2 of this 2007 review of Pierre Gy’s sampling errors were strung together by R C A Minnitt, P M Rice and C Spangenbergs. All that is necessary to get goofy statistics is to pay no attention to those who do grasp applied statistics. I have sent an email to Professors F Cawood and R Minnitt. I spelled out why mining students ought not to be taught to assume spatial dependence between measured values in ordered sets, to interpolate by kriging, and to ignore the rules of applied statistics with impunity. Added to my email was a link to pre-read copies of Volk’s textbook on Applied Statistics for Engineers for the benefit of those who are studying mining engineering at the Witwatersrand University.

It feels at times as if I grew up with Volk’s Applied Statistics for Engineers under my pillow. I bought my first copy when a friend told me he liked it a lot. I did so before moving to Canada in 1969. Volk’s Chapter Seven Analysis of Variance deals in rich detail with all of the properties of variances. Section 7.3 Confidence range of variances shows how to derive lower and upper confidence limits for an observed variance as a function of the number of degrees of freedom. The odd inquisitive student may wonder why statisticians do count degrees of freedom. Those who are against counting degrees of freedom are bound to score passing grades wherever Gy’s sampling errors are taught.

Volk’s 1980 reprint is still as sound as was his 1958 work. I have lost two copies while I was teaching sampling and statistics around the world. Initially, I taught coal sampling for the McGraw-Hill Seminar Center. After Trans Tech Publications had published Sampling and Weighing of Bulk Solids in 1985 I drifted into mineral exploration and mining. Showing why geostatistics is a scientific fraud ranks high on my list of things to do on this planet. Volk’s tattered 1958 textbook remains my favorite. I would have written a Wiki page about William Volk and his work if I had known him as well as I did Dr Jan Visman. But Wiki is not what it used to be when those who assume, krige and smooth, do rig the rules of applied statistics.

The above table gives arithmetic mean assay results (g/t Au) for each of four (4) sets of samples. The variances in the second line would be obtained if infinite sets of test portions were selected and assayed. However, this sampling tree experiment was based on selecting and assaying finite sets of thirty (30) test portions which give 29 degrees of freedom. Excel’s FINV function has been applied to derive lower and upper limits of 95% confidence ranges in (g/t)².

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.

ASTM ought to shred geostats standards

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.

Founder of Geostatistics
Founder of Spatial Statistics

ASTM Committee D18 was set up after Geostatistics for the Next Century came about somewhat early in 1993. That’s when geostatisticians from far and wide had flocked together at Montreal, Canada. They had come to praise David’s 1977 Geostatistical Ore Reserve Estimation. Nobody asked David why he had not derived the variance of the distance-weighted average. The more so since Dr Isobel Clark did derive this variance in her 1979 Practical Geostatistics. Sadly, she wasn’t present at McGill. All I had wanted to do was point out that functions do have variances. Alas, my view was as unpopular at Geostatistics for the Next Century as it was when Professor Dr Michel David was the chief enforcer of geostatistics with CIM Bulletin.

David’s peers had come not only to praise his 1977 textbook but also to peddle their own geostat stuff. For example, Journel peddled Modeling Uncertainty: Some Conceptual Thoughts. What David had done in this textbook was derive sixteen (16) distance-weighted averages from nine (9) boreholes. He didn’t derive the variance of each distance-weighted average. He didn’t test for spatial dependence between ordered boreholes. Neither did he count degrees of freedom. David did come up an infinite set of what he then called “simulated values”. Journel derived the zero kriging variance of David’s infinite set of simulated values AKA kriged estimates. Here’s in a nutshell what Professor Dr Georges Matheron has taught all of his disciples. Assume spatial dependence between measured values in ordered sets, interpolate between measured values, smooth the least biased subset of some infinite set of kriged estimates, and rig the rules of applied statistics with impunity. He did all of his thinking about Brownian motion along a straight line in this gloomy edifice.

Centre de Géostatistique
Centre de Morphology Mathématique

Matheron invoked it on this continent in June 1970. Brownian motion set the stage to assume spatial dependence between measured values in ordered sets rather than test for it by applying Fisher’s F-test. One of Matheron’s most gifted disciples was Stanford’s Journel. Not surprisingly, Journel never did what Matheron had not taught him to do. But surely, Journel knew a bit of spatial stuff!

Merks and Merks Precision Estimates for Ore Reserves was praised by and published in Erzmetall. All we did was test for spatial dependence between gold grades of an ordered set of twelve (12) rounds in a drift. Here’s what Stanford’s Journel wrote on October 15, 1992 to Professor Dr Robert Ehrlich, JMG’s Editor, “…Mr. Merks’ anger arises fro [sic!] a misreading of geostatistical theory, or a reading too encumbered by classical “Fischerian” [sic!] statistics.” Journel beat a bit more around the bush when he wrote, “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.” He ponders on page 6 of his clarification, “I’ll leave it to you to decide whether this letter should be sent to J. W. Merks; however, I strongly feel that Math Geology has had more than its share of detracting invectives.” Professor Dr Robert Ehrlich, JMG’s Editor, wrote on October 26, 1992, “Your feeling that geostatistics is invalid might be correct.” JMG's Editor did attach a copy of Journel’s 6-page letter. Distracting invectives? I’ll say!

How many Stanford students did he teach about Brownian motion along a straight line? What a silly notion when measuring mineral inventories. What’s more, Fisher’s F-test is forbidden where spatial dependence is deemed to exist a priori. That’s why ASTM ought to shred all standard methods cooked up by ASTM Committee D18 on Soil and Rock. These letters and many others are or will soon be posted on my website under Correspondence. Of course, ASTM Committee D18 ought to be dismissed. Soon I’ll post where we were before we met Dr Ricardo R Stone and his partner. He passed away shortly after we met. Ricardo was an IBM Fellow and a Member of ASTM E11 on Quality and Statistics.

ASTM got stuck with geostatistics

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

ASTM has yet to sort out when and why geostatistocrats have made such a mess of applied statistics. Matheron and his disciples brought geostatistics all the way to North America in the 1970s. The problem is not that distance-weighted average point grades morphed into kriged estimates to honor D G Krige. The real problem is that variances of distance-weighted average point grades AKA kriged estimates didn’t morph along but got lost. Kriged estimates and kriging variances are the heart and soul of geostatistics. David’s 1977 Geostatistical Ore Reserve Estimation and Journel’s 1978 Mining Geostatistics reject the fact that every kriged estimate has its own variance. Clark’s 1979 Practical Geostatistics, unlike David in 1977 and Journel in 1978, derived not only the distance-weighted average point grade but also its true variance. But here’s the cinch!

Having a PhD in geostatistics seems a must when assuming spatial dependence between measured values in ordered sets. Yet, it’s so simple to apply Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set. It puts on view whether or not orderliness in sampling units or sample spaces dissipates into randomness. Who wouldn’t want to know? Geostatisticians would have known if they ever got around to counting degrees of freedom. Those who scored a passing grade on Statistics 101 are bound to grasp the properties of variances. Some may even know that one-to-one correspondence between functions and variances is sine qua non in applied statistics.

ASTM itself got on track so to speak in 1898. At that time engineers and chemists of the Pennsylvania Railroad needed standard methods. It made me nostalgic to read such an account of courage and vision. At that time there were no degrees of freedom to count. Geostatistocrats have never stooped to count stuff what can neither be seen nor touched. Once upon a time I was in charge with sampling shipments of Pennsylvania anthracite in the Port of Rotterdam. ASTM Standard Methods for coal were specified in contracts between trading partners. It would be a long while before ISO Standards for coal caught up with ASTM Standard Methods. Now I wish ISO will never catch up. Greg Gould asked me a long while ago what I thought about interpolation between bias test data. Good grief! That looked too much like real kriging! That’s why I put together a false test for bias in a previous blog. I wouldn’t want ASTM Committee D05 to dictate how ISO TC27 is to test for bias. But it may well do so!

Those who had master minded ASTM Standard Methods for Soil and Rock must have been smitten silly with geostatistics. My son and I had found out in 1989 why geostatistics is an invalid variant of applied statistics. My work for Barrick Gold in 1997 proved that geostatistical software converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Student’s t-test proved that crushed core samples had been salted with placer gold. Bre-X’s duplicates for every tenth test sample proved the intrinsic variance of gold at Busang to be statistically identical to zero. That’s the very reason why I’ll always work with applied statistics.

Here’s what I did point out in April 1994. Either fundamental requirements of probability theory and applied statistics are no longer valid or geostatistical theory and practice are fatally flawed. ASTM’s President wrote on May 13, 1994 that he had asked Mr Bob Morgan, Director of Technical Committee Operations, about the role of Committee E11 Quality and Statistics. What I wanted to study but never got was a copy of D5549-94e1 Standard Guide for Reporting Geostatistical Site Investigations. Robert J Morgan, ASTM’s Director Technical Operations, asked me in February 1995 to direct my input to R Mohan Srivastava.

Geological statistician
AKA geostatistician

Teaching Mo all I know about sampling and statistics tops my list of things to never do. It would take more than a few blogs to show what Mohan could have done had he grasped in June 1993 what was wrong with David’s 1977 textbook. That’s when Mo and his coauthor went to McGill University. As a matter of fact, that’s where the united geostatocracy went to praise David’s 1977 Geostatistical Ore Reserve Estimation. For crying out loud!