UBC still stuck with geostatistics

Professor Dr Alastair J Sinclair has been teaching earth sciences at the University of British Columbia since 1964. It was but a dozen years after Matheron tried his hand at applied statistics. Young Georges Matheron in 1952 was an up-and-coming geologist in Algiers. He had a penchant for applied statistics in those early days. For example, he knew how to test for associative dependence between lead and silver grades in core samples of variable lengths. What he did not know was how to derive variances of length-weighted average lead and silver grades. Perhaps ironically, young Matheron in those days thought he was working with applied statistics. Yet he didn’t know how to test for spatial dependence in sample spaces or sampling units by applying Fisher’s F-test to the variance of a set and the first variance term of the ordered set.  He didn’t derive length-weighted average lead and silver grades for his data set. Young Matheron was not into reporting sets of primary data. Neither was Professor Dr Georges Matheron when he brought his creation to North America in June 1970!

Professor Dr Georges Matheron
Abuser of applied statistics
Creator of geostatistics
Founder of spatial statistics
Professor Dr Georges Matheron was not at all into sharing primary data with his students. Even for his PhD Thesis he saw fit to cook up a funny pair of primary data sets. So I decided to show how to test for spatial dependence between Matheron’s make-believe primary data sets in his 1965 PhD Thesis. What follows is Matheron’s minuscule data set for his thesis.

Test for spatial dependence have been applied to the variance of the set and the first variance term of the ordered sets. Fisher’s F-test shows that both data sets display a significant degree of spatial dependence. Matheron’s PhD thesis does not show how to test for spatial dependence between ordered data in either sample space. Yet Matheron has been called the Founder of Spatial Statistics.
Matheron’s 1965 PhD Thesis

Matheron’s magnum opus is posted on a massive website. Its webmaster has made a few minor changes to suggest that Matheron had applied geostatistics somewhat sooner than he had done in real time.

It is ironic to the extreme that geostatistics was hailed as a new science when Matheron and his disciples brought it to campus at the University of Kansas in June 1974. Matheron’s own tour de force at this colloquium was to invoke Brownian motion along a straight line. He did it to infer that his random functions are continuous between measured values. The study on Random kriging by A Marechal and J Serra at the Centre de Morphology Mathematique was successful under Matheron’s supervision. Figure 10 in this 1974 study metamorphosed in Figure 203 on page 286 in Chapter 10 The Practice of Kriging in Professor Dr Michel David’s 1977 Geostatistical Ore Reserve Estimation.

David’s 1977 textbook and Gy’s 1979 Sampling of Particulate Materials, Theory and Practice, stand side-by-side on a shelf in my office. One time soon I’ll use them to prove how the French sampling school has messed up statistical thinking. And all it really took was to ignore one-to-one correspondence between functions and variances, to assume spatial dependence between measured values in ordered sets, and to pay no attention to counting degrees of freedom.

Dr Alastair J Sinclair, PEng, PGeo
UBC Emeritus Professor

Professor Dr Alastair J Sinclair described in Applied Mineral Inventory Estimation how his “exciting and invigorating career” took off when he was exposed to Matheron’s ideas, and how he had “the good fortune to work with Journel, Huijbregts and Deraisme”. Good grief! Those were Matheron’s earliest students who took his musings for dogma, and who didn’t have a clue that the variance of the distance-weighted average cum kriged estimate had vanished into thin air on Matheron’s watch. Sinclair’s list of those who he was “fortunate to have worked with at various times” reads like a Who’s who in the world’s  geostatistical fraternity. Sinclair credits all of them to have contributed to his education. For once I do agree! I’m all in favor of giving credit where credit is due. But to give credit to everybody who has taught Professor Dr Alastair J Sinclair, PEng, PGeo how to apply a flawed variant of applied statistics is a bit over the top. Some geostatistocrats on Sinclair’s list know that each and every distance-weighted average cum kriged estimate does have its own variance. No ifs or buts! And whether Al likes it or not!

I wrote one more letter to Dr Martha C Piper, President, The University of British Columbia. I pointed out that H G Wells (1866-1946) had predicted, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”. I mentioned that statistical thinking served me well indeed as a consultant, a lecturer, an author and a publisher, and as a global citizen of sorts on IMO and ISO Technical Committees such as TC69-The application of statistical methods.

Professor Dr Nathan Divinsky was charged in 1949 with the teaching of mathematics to UBC students. He retired as a professor in the mathematics department in 1991. I met a few of his former students who enjoyed his teaching and appreciated the power of applied statistics. Once upon a time I called him to ask whether statistical inferences are possible without degrees of freedom. I’ll always remember what he said! Professor Dr Nathan Divinsky pointed out, “But without degrees of freedom statistical inferences are impossible”. Dr Nathan Divinsky passed away at 86. He was married for eleven years to former Prime Minister Kim Campbell. Who would dare doubt such a short, crisp and to the point response by a Professor of Mathematics? May he rest in peace!

McGill toils with Markov chains

McGill University claims to be at the cutting edge of defining ore deposits with Markov chains. The National Post on August 15, 2005 published an article with the caption `It`s mining by the numbers`. McGill`s Professor Dr Roussos Dimitrakopoulos pointed out that, `Uncertainty means probabilistic models, and there are a gazillion types of them`. He has yet to show how to select the least biased model. He has a $3.5 million budget to put Markov chains to work. I’ll call him Dr RD for short. I do respect his blatant chutzpah! Dr RD cited a study by the World Bank that alleged 73% of North American mines had failed. What he didn’t point out is that geostatistical software is to blame!

It is a bit of a mystery when, where and why Dr RD made up his mind to travel all the way back to Markov chains. Stringing Markov chains overnight on a fast computer seems to somehow pin down ore deposits. But Dr RD didn’t know that Markov chains cannot possibly give unbiased confidence limits for metal contents and grades of ore deposits! Markov and his chains may have made some sense before Fisher and Pearson feuded about degrees of freedom for the chi-square distribution. Why is it that counting degrees of freedom is still baffling the most gifted geostatistical gurus?

What’s more, Dr RD’s grasp of the properties of variances was already flawed in June 1993. At that time he was in a rush to get Geostatistics for the Next Century going. I had submitted by registered mail on March 10, 1993 an abstract for The Properties of Variances. I received an unsigned letter dated March 31, 1993. As luck would have it “a number of potential participants and their very interesting abstracts couldn’t be accommodated”. It so happened that I was one of those! All I wanted to do was show  how to derive unbiased confidence limits for metal contents and grades of ore reserves. We had shown how to do it in 1990. Professor Dr Michel David blew a fuse because we had applied “our own method”. Whose method had he expected? Given geostatistical peer review at CIM Bulletin in the 1990s I had asked JASA’s Editor for a courtesy review of The Properties of Variances. It passed JASA’s litmus test! A copy of The Properties of Variances is posted on my website. Peruse the properties of variances, count degrees of freedom, and derive confidence limits for mineral inventories. It is simple comme bon jour! I did it for Barrick Gold in 1998.

Professor Dr Michel David and his 1977 Geostatistical Ore Reserve Estimation were honored at Montreal, Quebec on June 3-7, 1993. Geostatistical scholars had come to praise the author of the very first textbook. It deals with Matheron’s new science in mind numbing detail. David brought up “the famous central limit theorem “ on page 33 in Chapter 2 Contribution of Distributions to Mineral Reserves Problems. Chapter 10 The Practice of Kriging shows how to derive sixteen (16) famous central limit theorems from the same nine (9) holes. David pointed out on page 286, “Writing all the necessary covariances for that system of equations is a good test to find out whether one really understands geostatistics!” Good grief! Counting degrees of freedom for his system of equations would have been a good test to find out whether David did grasp applied statistics. David’s Index does not refer to Markov chains. But who would have wanted to bring up Markov chains at David’s bash?

Lost : variance of kriged estimate
Found : zero kriging variance

It was none other than Stanford’s Professor Dr Andre G Journel who did! He had put forward a paper to shore up his own vision. It was called “Modeling Uncertainty, Some Conceptual Thoughts”. He had embellished his thoughts with prettified statements such as stochastic simulation, random models, Bayes’ updating, likelihood functions, sequential simulation and non-Gaussian models. That’s what preoccupied the mind of Matheron’s most gifted disciple in June 1993. It may well have turned off some of those who had come to praise David’s 1977 Geostatistical Ore Reserve Estimation!

Every Spring quarter at Stanford it is Emeritus Professor Dr A G Journel who teaches an advanced PhD level seminar. What he does not teach is that each and every distance-weighted average AKA kriged estimate does have its own variance in applied statistics. What he ought to study is Dr Isobel Clark’s 1979 Practical Geostatistics. She did derive the variance of a distance-weighted average AKA kriged estimate. Alas, Dr Clark didn’t test for spatial dependence between hypothetical uranium concentrations in her ordered set. Neither did she know that degrees of freedom for her set are positive irrationals rather than positive integers.

SAGD with Markov chains?

SAGD stands for Steam Assisted Gravity Drainage. It makes oil easier to recover. What has SAGD to do with Markov chains? That’s what I’ll discuss in this blog! I was into consulting at Fort McMurray long before Markov chains were strung together. I have worked with applied statistics since the 1960s. It would seem that geostatistocrats have forgotten that geostatistics converted Bre-X bogus grades and Busang’s barren rock into a massive phantom gold resource. I applied Fisher’s F-test to prove that the intrinsic variance of Bre-X’s gold was statistically identical to zero. No if or buts! The Ontario Securities Commission and the Toronto Stock Exchange set up a Mining Standards Task Force to protect mining investors. Canada’s most gifted geostatisticians got this task force to work without Fisher’s F-test. What boggles the mind is that the mining industry took to Stochastic Mine Planning with Markov Chains! It’s but one more fatally flawed flavor of geostatistics.  It was bred at Stanford University and put to work at McGill University. Geostatistocrats need no longer assume spatial dependence between measured values in ordered sets. CPUs crunch numbers overnight and stochastic mining plans pop up in the morning. It’s Markov’s gift to those who are not into counting degrees of freedom!

Here are a few notes on SAGD Reservoir Characterization Using Geostat: Application of the Athabasca Oil Sands, Alberta Canada. Its authors are Jason A McLennan and Clayton V Deutsch. The latter may well remember that once upon a time at some event we shook hands. What he does not remember is one-to-one correspondence between functions and variances. It is impossible to score a passing grade on Statistics 101 by stripping the variance off the distance-weighted average AKA kriged estimate! So I decided to look up what Clayton V Deutsch had been taught where, when, why and by whom. He earned a BSc in Mining Engineering at the University of Alberta in April 1985. Next, he got a Mac in Applied Earth Sciences (Geostatistics) at Stanford University in April 1987. Finally, he was granted his PhD in Applied Earth Sciences (Geostatistics) at Stanford University in June 1992. Now how’s that for kriging out loud!

I had mailed on November 14, 1990 a copy of Sampling and Weighing of Bulk Solids to Professor Dr R Ehrlich, Editor, Mathematical Geology. Here’s what he wrote on October 26, 1992: “Your feeling that geostatistics is invalid might be correct”. Attached to his letter was Professor Dr A G Journel’s response. Both the Editor’s letter and Journel’s response are posted on my website. Journel pointed out,”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”. Journel’s circular logic was a brazen tour de force. MG’s Editor has kept me posted after Dr D Merriam and Dr F Agterberg took over!

I want to show what McLennan and Deutsch didn’t do in this SAGD study before putting in plain words  who set the stage for Markov chains, when, where and why.

Top Surface and Bottom Surface: Realization 50

These figures show Northing and Easting coordinates and sets of measured values for top and bottom surfaces. What comes to mind when I look at such plots are door-to-door peddlers of days gone by. They would walk such that the shortest distance is covered when each and every door is called on but once. Today’s door-to-door peddlers are more into saving souls. And I’m into peddling on-line.  My eBook on Sampling and Weighing of Bulk Solids has been posted. Foremost on my mind is Metrology in Mining and Metallurgy. But I tend to slow down a bit whenever voodoo science drives me up a hanging wall!

SAGD Reservoir Characterization with Applied Statistics

A spreadsheet template with SAGD statistics will soon be posted on geostatscam.com. In due course I’ll show how to derive the mass of oil in each block and the variance of that mass. The same method can be applied not only to in-situ ores and oils but also to mined ores and oils. All it takes is to put the additive property of variances to work. Neither Markovian chains nor Matheronian geostatistics have any role to play in mineral exploration and mining.

David’s 1977 Geostatistical Ore Reserve Estimation shows in Figure 203 on page 286 a set of sixteen (16) points. Each point is a function of the same set of nine (9) holes. One-to-one correspondence between functions and variances dictates that each point does have its own variance. David on page 323 points to the infinite set of simulated values and ponders how to make it smaller. Journel and Huibregts 1978 Mining Geostatistics on page 308 points to a zero kriging variance. None of these geostatistocrats got into counting degrees of freedom!

Here’s what Dr Isobel Clark acknowledged in the Preface to her 1979 Practical Geostatistics“And finally to André Journel and others at Fontainebleau who taught me all I know about the theory of the Theory of Regionalized Variables”. It was Dr Clark who showed that each distance-weighted average AKA kriged estimate does indeed have its own variance. Stanford’s Journel didn’t know simply because Matheron didn’t know. It was Matheronian thinking that has messed up ore and oil reserve estimation all over the world. A few mining giants are sold on Markov chains. Canadian regulators do not know which end of a Markov chain is up! But that takes more than a few talks!

When to work with Markov chains

Once upon a time a keen geologist measured the degree of associative dependence between lead and silver in lead ore. Next, he put on paper Formule des minerais connexes and called it Note statistique No 1. He didn’t report his primary data but did correct an error. In time, he became famous. So much so that he set up the Centre de Géosciences/Géostatistique at Fontainebleau, France. Professor Dr G Matheron will be remembered either as the creator of geostatistics or as the founder of spatial statistics. As fate would have it; never in his life did the founder of spatial statistics apply Fisher’s F-test to verify spatial dependence between measured values in ordered sets.

Professor Dr George Matheron (1930-2000)
Creator of geostatistics
Founder of spatial statistics
Abuser of applied statistics

Matheron’s most gifted disciple was Dr A G Journel. He put forward on October 15, 1992, “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 was a prima facie case of circular logic. He did respond to a request from Professor Dr Robert Ehrlich, Editor, Journal, Mathematical Geology. Stanford’s Journel also deemed my reading too encumbered with classical “Fischerian” statistics. So the coauthor of Mining Geostatistics put forward, “In presence of dependence the classical notion of degrees of freedom vanishes: n spatially dependent data do not provide n degrees of freedom”. Good grief!

Now that’s where Professor Dr A G Journel and I didn’t see eye to eye! A set of n measured values gives df=n-1 degrees of freedom whereas an ordered set of n measured values gives dfo=2(n-1) degrees of freedom for the first variance term. Degrees of freedom are positive integers for sets of measured values with the same weight but positive irrationals for sets of measured values with variable weights. The concept of degrees of freedom left little space for ifs and buts!

Index A. Geostatistical Concepts in my copy of 1978 Mining Geostatistics does not refer to Degrees of freedom between Deconvolution and Discontinuity at the origin of a sampling variogram. What went missing on Matheron’s watch was the variance of the distance-weighted average AKA kriged estimate. Incredibly, Matheron’s students never told him too much was lost. On the contrary, the zero kriging variance of an infinite set of kriged estimates took on a silly life of its own. Neither does it list Markov chains above Massive deposits. Stanford’s Professor Dr A G Journel may not have been as hot on Markov chains as McGill’s Professor Dr R Dimitrakopoulos is on its role in stochastic mine planning. Unbiased confidence limits for metal contents and grades of mineral deposits can only be derived with applied statistics.

Andrey Markov (1856-1922)

A Markov chain is a mathematical system that transitions from one state to another between countable (finite) numbers of possible states. One ought to peruse the properties of variances before toiling with Markov chains. Study what McGill’s Dr RD didn’t want to know about the properties of variances when Geostatistics for the Next Century came about at the McGill Conference Office on June 3-5, 1993. What a pity that deriving unbiased confidence limits for metal grades and contents of ore reserves is still beyond Dr RD’s grasp.

Count Leo Tolstoy (1828-1910)

“I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives”.

Sir Ronald A Fisher (1890-1962) and Karl Pearson (1857-1936)

For quite a while these statisticians feuded about the chi-square distribution. Pearson worked with large data sets whereas Fisher worked with small data sets. Fisher was right! That’s why the chi-square distribution takes degrees of freedom into account. Take a long look at David’s 1977 Geostatistical Ore Reserve Estimation, Table 1.IV, Copper grade Prince Lyell. How about that? Why not reunite the distance-weighted average and its lost variance? Mining investors are bound to like it! In fact, Barrick Gold liked it before Bre-X’s boss salter passed away.

Geostatistocrats such as Professor Dr Michel David (1945-2000) and UBC Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo never got into counting degrees of freedom. Why is it that one-to-one correspondence between functions and variances is sine qua non in applied statistics but irrelevant in geostatistics. Dr Michel David was once listed as a Deceased Fellow with the Royal Society of Canada. He is no longer listed but I do not know why!

Some institutions of higher learning such as COSMO McGill Mining and Stanford University work with Markov chains to derive stochastic mining plans. What they cannot possibly derive are unbiased confidence limits for metal contents and grades of ore reserves. Geostatisticians stripped the variance off the distance-weighted average AKA kriged estimate. That’s how real functions got surreal variances!

A study on kriging small blocks

Dr Margaret Armstrong and Mr Normand Champigny had put this study on paper when they were toiling at the Centre de Géostatistique at Fontainebleau, France. Professor Dr Georges Matheron himself may have inspired them to compile their study in a paper. Be that as it may, this simple study has never been added to Matheron’s magnum opus. It was kriging small blocks that inspired Armstrong and Champigny to elaborate on what they had detected, namely “Mine planners tended to define ore/waste limits as finely as possible”.

How about that? Perfect people are hard to find. So, the average mine planner was often tempted to over-smooth small blocks. The central tenet of this study was that over-smoothed estimates should not be used to derive recoverable reserves. That sort of research may well be the reason why Normand Champigny was awarded a Diploma in Geostatistics.

And why was this study published in CIM Bulletin, March 1989? Here’s why! Professor Dr Michel David (1945-2000) and Professor Dr Alastair J Sinclair, PEng, PGeo, reviewed and approved each and every paper in which the term “kriging” popped up in those days. And Dr Frederik F Agterberg, Associate Editor with CIM Bulletin, would not have hesitated to approve Armstrong and Champigny’s study. Here are a few facts and figures that neither the authors nor the reviewers knew about.

Dr Isobel Clark, in Chapter 4 Estimation of her 1979 Practical Geostatistics, derives not only the distance-weighted average AKA kriged estimate but also its variance. What she didn’t do was test for spatial dependence in the sample space defined by her hypothetical uranium concentrations. She sets the stage on page 3 of Chapter 1 Introduction under Figure 1.1. Hypothetical sampling and estimation situation. On page 5 she puts forward “the convenient assumption that there is no trend within the scale in which we are interested…” On the same page she fiddled with the factor 2 for “mathematical convenience” and stumbled with her fickle “semi-variogram”. What went missing in her Index on page 127 above Disjunctive Kriging is Degrees of freedom. Dr Isobel Clark credits Professor Dr Andre Jounel and others at Fontainebleau who taught her all she knows “about the theory of the Theory of Regionalised Variables”. What a pity that she didn’t know how to test for spatial dependence within the sample space defined by her set of hypothetical uranium concentrations. But then neither did any geostatistical reviewer for CIM Bulletin know how to test for spatial dependence between measured values in ordered sets!


Dr Isobel Clark, author of Practical Geostatistics
BSc, MSc, DIC, PhD, FSS, FSAIMM, FIMMM, CEng

Bringing Matheron’s new science of geostatistics to the world was quite a tour de force. Scores of geologists thought it odd that so much could be done with so few boreholes. But too few knew applied statistics well enough to figure out what was wrong with geostatistics. What Matheron and his disciples had failed to grasp was not only that all functions do have variances but also that sets of measured values do give degrees of freedom. That’s about all it took to do so much with so few boreholes! CIMMP’s archive has what Matheron’s magnum opus does not have. And that’s an authentic copy of Armstrong and Champigny’s study for a mere C$20.00.

What was bad news for the mining industry  was that CIM Bulletin rejected Precision Estimates for Ore Reserves. I had mailed on September 28, 1989 four (4) copies to The Editor of CIM Publications. Not surprisingly, peer review of a paper that is at variance with the central tenets of geostatistical thinking turned out to be a blatantly biased and shamelessly self-serving sham. Our peers at CIM Bulletin were Professor Dr Michel David (1945-2000) and UBC Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo. What a shame that unbiased confidence limits for metal contents and grades of ore reserves remain as rare as hen’s teeth.

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 Bre-X’s 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 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 whenever UBC’s Emeritus Professor explains why the distance-weighted average lost its variance!

Professionals pine for public trust

Professional designations are powerful symbols. The public at large tends to trust those who 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 Alastair J Sinclair, PEng, PGeo
Emeritus Professor

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 still 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? Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo rejects 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.

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.”

Create spatial dependence where non exists

The Editor in Chief of the PEG 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 2006 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, PGeo 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 claims 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 posted this 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 irrational 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”.

The next 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. Shortly, I’ll post what I did, what I tried to do next, and what the Master of Ceremony didn’t do!

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 that 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 post on my website. What I want my readers to know most of all is the difference between sound statistics and goofy 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. In fact, ISO liked it so much that it became ISO 12745:2008. ISO has yet to pay a royalty. Nowadays my son 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 quoted too few references to the geostatistical literature. Professor Dr Alastair J Sinclair did find the variance of a general function a bit dated!

He frowned on other functions whose roots are traceable to applied statistics. He is Emeritus Professor at the University of British Columbia. He may still be teaching UBC’s students why working with variance-deprived distance weighted average point grades 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 is no longer a positive integers but becomes a positive irrational. 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 Professor Dr Georges Matheron hailed geostatistics 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. The Editor of 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 deemed necessary. And 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 had expected most of all were scores of references to the geostatistical literature. We did find what David himself had predicted statisticians would find. And he was right! Stripping the variance of the distance-weighted average point grade makes no scientific sense whatsoever! On the contrary, it’s a genuine scientific fraud ! David also felt we should have made reference to Gy’s 1979 Sampling of Particulate Materials, Theory and Practice. We should indeed have pointed out that Gy’s sampling constant ought to have its own variance. What a shame that far too few scientists and engineers grasp 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. A short while ago I 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 studied 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. But those who are against counting degrees of freedom are bound to score passing grades where 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.

Matheron got into his most creative thinking in 1958. It seems that “Problèmes de zéro et infini” took him by surprise. His deep thoughts have been archived as Note Statistique No 17. Yet it was Note Géostatistique No 28 that made an eponym of Krige’s name. Krige was the first to derive the distance-weighted average gold grade at the Witwatersrand complex. What he did not derive was the variance of the distance-weighted average AKA kriged estimate. D G Krige wrote a brief Preface to David’s 1977 Geostatistical Ore Reserve Estimation. David cautioned on the next page that ”…statisticians will find many unqualified statements…” Krige may not have studied Figure 203 on page 286. Even if he had done so he would not have detected that none of David’s distance-weighted averages had its own variance.

Confidence limits for variance estimates

 Table 1 gives assay results (g/t Au) for four (4) sets of subsamples. The variances in the first line would be obtained if infinite sets of test portions were selected and assayed. This sampling tree experiment was based on selecting and assaying but finite sets of thirty (30) test portions. Excel’s FINV function has been applied to derive lower and upper limits of 95% confidence ranges in (g/t)².

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