Of tangled tales and geostatistics

Here are but a pair of my lingering questions. Why did Dr Frederik P Agterberg strip the variance off his distance-weighted average? Why did Professor Dr Noel A C Cressie dismiss degrees of freedom? I brought my concern to the attention of Minister Lisa Raitt on March 9, 2009, and of Minister Christian Paradis on March 6, 2010. NRCan’s technocrats were instructed to deal with my concern. Mark Corey, Assistant Deputy Minister, pointed out on June 4, 2009, “Geostatistics continues to evolve as a discipline, and we appreciate your contribution in this field.” Dr David Boerner, Acting Assistant Deputy Minister, declared on May 10, 2010, “Natural Resources Canada is a science-based organization and values the scientific rigor of the peer review process”. Now that’s a whole load of chutzpah! NRCan’s library is a treasure trove of works on geostatistics. Each and every one of them proves that geostatistics is but bogus geosciences. Look at Agterberg’s 1970 and 1974 works. He derived the distance-weighted average of a set of five (5) measured values determined at positions with variable coordinates in a sample space. He didn’t derive the variance of this distance-weighted average. He didn’t count the number of degrees of freedom for the set and for the ordered set. So much for Agterberg’s grasp of applied statistics. Of course, geostatistics couldn’t possibly get any worse, could it? But it did in 1970 when Matheron and his disciples came all the way to the USA!

Maréchal & Serra – Figure 10

Maréchal and Serra in 1970 derived a set of sixteen (16) distance-weighted averages on a 4 by 4 matrix. They did so from a set of nine (9) measured values determined at positions with variable coordinates. What M&S didn’t derive was the variance of any of those sixteen (16) distance-weighted averages. What Professor Dr Michel David didn’t do in 1977 was what M&S didn’t do in 1970, what Agterberg didn’t do in 1970 and in 1974, and what young Matheron didn’t do in 1954. David predicted that professional statisticians would find “unqualified statements” in his 1977 work. Now there’s one fact he got right. But once push came to shove he saw no wrong. Degrees of freedom did pop up on in his work but did so in a table others had put together. Little else made sense at all let alone statistical sense. M&S’s Figure 10 morphed into David’s Figure 203. He got into the nitty-gritty of geostatistics in Chapter 12 Orebody Modelling. That’s where he cooked up the tangled tale of conditional simulations and ran into infinite sets of simulated values. Finally, distance-weighted averages first morphed into kriged estimates and then into simulated values. Stanford’s Professor Dr Andre Journel was Matheron’s most gifted disciple. It is fitting then that he was the one who defined in 1978 the zero variance of the infinite set of distance-weighted averages-cum-kriged estimates. Voila, Matheron’s new science of geostatistics!

Why stop kriging when there are infinite sets of kriged estimates to play with? The problem is one-to-one correspondence between functions and variances. Have a function? Stuck with a variance! No ifs or buts! It is a fact that one-to-one correspondence between functions and variances is sine qua non in mathematical statistics. And don’t take my word for it. Read Volk’s Applied Statistics for Engineers. NRCan’s technocrats are blessed for they may borrow Volk’s 1980 book at NRCan’s library. Volk explains in exhaustive detail what geostatisticians love to hate. I already owned a 1958 copy when I was toiling in the Port of Rotterdam. It has fallen apart but my faith in Volk’s work never wavered. My second copy went missing when I traveled the world and taught sampling and statistics in all sort of settings. And I do have a 1980 copy. Chapter Seven is called Analysis of Variance and Section 7.1.4 is called Variance of a General Function.

Scientific rigor of the peer review process was shamelessly self-serving and blatantly biased already when NRCan was CANMET and Agterberg was Associate Editor with CIM Bulletin. He reviewed Abuse of Statistics but all he worried about was whether and when H G Wells praised statistical thinking. That’s how serious NRCan’s Emeritus Scientists took geostatistical peer review at CIM Bulletin in the 1990s.

Geostatistics recast Statistics with upper-case S

Young Matheron in 1954 took a shine to what he then thought was statistics. Professor Dr Georges Matheron in the 1970s saw it at that time as his new science of geostatistics. Professor Dr Noel A C Cressie in 1993 saw it more as what he came to call Statistics with upper-case S. He is the brains behind that sort of stats stuff at the Ohio State University. He teaches Statistics with upper-case S at OSU’s Department of Statistics. But why does he teach Statistics with upper-case S? Here’s in plain prose how Cressie put it in his Preface: “Notice that Statistics is capitalized to distinguish it from its other meaning: a collection of numbers that summarize a complex phenomenon – such as baseball or cricket”. Good grief! Could that really be the reason why he brought Statistics with a capitalized S to those who interpret statistics for spatial data? Has he paid any attention to the study of climate change? Turned out to be a bit of a mess, didn’t it? He cautioned elsewhere in his Preface, “We should not forget our roots”. But why then did Cressie forget his roots in mathematical statistics?

Dr Frederik P Agterberg, NRCan’s Emeritus Scientist, brought to my attention in November 2009 that Noel Cressie is a mathematical statistician. He suggested that I consult Cressie’s 1993 Revised Edition of Statistics for Spatial Data. He pointed out that it deals with “kriging variance and equivalent numbers of independent observations”. I was stunned to say the least. I do respect the properties of variances and the concept of degrees of freedom much more than do most scientists. Yet, I studied Cressie’s Statistics for Spatial Data with a capital S. In retrospect I should have studied his original work to find out how far he had already wandered away from the straight and narrow of mathematical statistics.

Why did Agterberg want me to study Cressie’s Statistics for spatial data? I do not have the faintest idea! I have asked Agterberg why he stripped the variance off his distance-weighted average in 1970 and in 1974. He has never told me why. French scholars such as A Maréchal and J Serra worked with distance-weighted averages whose variances, too, had vanished in thin air. Matheron had taught Maréchal and Serra everything he knew before they came to the USA in 1970 for the very first krige and smooth fest. Matheron and his disciples failed to grasp what Professor Dr Michel David called in 1977 the “famous” Central Limit Theorem. But then neither did David.

Geologic prediction problem in 1970
Typical kriging problem in 1974
Statistical fraud since 1954

Agterberg writes about the Central Limit Theorem in Chapter 6 Probability and Statistics of his 1974 Geomathematics. Yet, in Chapter 10 Stationary Random Variables and Kriging he paid no heed to the theorem that underpins sampling theory and sampling practice. That’s why NRCan should ask him to explain why his distance-weighted average does not have a variance.

At this stage I’ll go back in time some twenty years. That’s when I got to know Professor Dr Robert Ehrlich. He taught at the Department of Geological Science at the University of South Carolina. He was Editor-in-Chief of what was then known as the Journal for Mathematical Geology. I had mailed him on November 14, 1990 a paper called Precision Estimates for Ore Reserves. It was the same paper that our peers at CIM Bulletin saw fit to thrash. They had done so simply because we had ignored twenty years of geostatistical literature. We wrote it because geostatistics was then and is still today a scientific fraud. The Bre-X’s salting scam has not yet been used in a court of law to prove that geostatistics is a scientific fraud.

The point I want to make is that Professor Dr Robert Ehrlich is a scholar and an independent thinker. He was a perfect fit for the position of JMG’s Editor-in-Chief. Much to my delight he saw through much of the fluff that underpins Matheronian geostatistics. I had mailed him drafts of a few wicked papers and a copy of my 1984 Sampling and Weighing of Bulk Solids. And we did talk a few times about counting degrees of freedom and testing for spatial dependence. But that wasn’t to last alas!

All efforts to have our take on how to derive unbiased confidence limits for ore reserves reviewed by and published in the Journal for Mathematical Geology came to naught. What’s more, a paper titled The Properties of Variances went missing. What also went missing late in 1994 was Professor Dr Robert Ehrlich, JMG’s Editor-in-Chief. So, I asked Dr Daniel F Merriam, JMG’s new Editor-in-Chief, on January 13, 1995 why that paper had not yet been reviewed. He wrote a brief note on April 14, 1995 that it was rejected. So it was that JMG’s peer review process had thrashed the same paper just as thoroughly as did CIM Bulletin’s in November 1989. A few problems surfaced. Agterberg was CIM Bulletin’s Associate Editor and JMG’s Book Review Editor. Agterberg reviewed and approved  Abuse of Statistics. A copy was attached to The Properties of Variances. One of JMG’s reviewers pointed out that it “should never have appeared in print”. One cannot help but wonder who said so!

NRCan stuck with geostatistics

Dr Frederik P Agterberg went to work with geostatistics long before NRCan stood short for Natural Resources Canada. He is still Emeritus Scientist with NRCan`s Geological Survey of Canada. He is one of the most gifted geostatisticians in the world. As such, he has a soft spot for Professor Dr Georges Matheron and a penchant for his magnum opus. So much so that he called him the Founder of Spatial Statistics. He did so after Matheron had passed away in 2000. Matheron’s disciples didn’t agree with Agterberg’s view. Matheron taught them how to assume, krige and smooth with infinite confidence. So, they thought of him as the mastermind behind the Centre de Géostatistique and the Centre de Morphology Mathematique. What Matheron taught his disciples was inspired by one or other innovative theme that would call on his most creative thinking. That`s why they thought of him as the Creator of Geostatistics.

Professor Dr Georges Matheron (1930-2000)
Creator of Geostatistics
Founder of Spatial Statistics
Self-made Wizard of Odd Statistics

My son and I checked out what sort of new science Matheron had created. We found out in 1989 that his new science of geostatistics is an invalid variant of applied statistics. As a matter of fact, the author of the very first textbook on geostatistics couldn’t possibly have scored a passing grade on Statistics 101. He praised the “famous Central Limit Theorem” but failed to work with it when he should have. He never tested for spatial dependence between measured values in ordered sets. That’s why it didn’t take us long to get to the bottom of what was wrong. The author had seen fit to shelve degrees of freedom. But it took a long time to unravel what else was shelved, who did it, when, where and why. The power of the internet did make it possible to trace Matheron’s new science to its roots in the early 1950s. In those bygone days young Matheron was a budding geologist who went to work with what he then thought was applied statistics. As such he proved a tenuous grasp of applied statistics early on during his calling.

What struck me as a bad omen for Matheron’s new science of geostatistics was the fact that his grasp of the properties of variances can be traced to the French school of sampling in-situ ores and mined ores. What gets me hopping mad is sloppy sampling and statistics. That’s why I want to put in plain words what Matheron did in the early 1950s. In those days he was a novice geologist with the French Geological Survey (BRGM) in Algeria. His very first paper was called Formule des Minerais Connexes. It was dated November 25, 1954 and marked Note Statistique No 1 straight above its title. It would seem that Matheron saw himself as a statistician of sorts. All the same, CdG’s webmaster early in this century saw fit to mark his very first paper as Note Géostatistique No 1. Perhaps a dash of deception but too little and too late to fool anyone but the odd hardcore kriger.

Matheron’s Note Statistique No 1 was not reviewed by his peers. It took me quite a while to find out that Matheron was without peers. That was just as well since he didn’t quote literature on statistics. What was worse is that he didn’t report any primary data for l’Oued-Kebir. In fact, reporting primary data ranked just as low on his list of things to do as did counting degrees of freedom. Matheron derived population means of μ1=0.45% for lead and μ2=100 g/t for silver, and population variances of σ1=1.82%2 for lead and σ2=1.46 (g/t)² for silver. How he could have done so much with so little is a mystery. A finite set cannot possibly give population means and variances. But that’s what Matheron thought he got! He tested for associative dependence between lead and silver grades and got a correlation coefficient of ρ=0.85. He didn’t point out whether this correlation coefficient was statistically significant at 95%, 99% or 99.9% probability. What put a monkey wrench in Matheron’s first crack at statistics is that he didn’t test for spatial dependence. As luck would have it, Stanford’s Journel and Matheron’s most talented disciple put forward in 1992 that spatial dependence between measured values in ordered sets may be assumed. Testing for spatial dependence was just as trendy in 1992 as it was in 1954.

Matheron may have had a bit of an epiphany when it hit him that l’Oued-Kebir core samples did vary in length. That’s why on January 13, 1955 he tagged on a Rectificatif to his Note Statistique No 1. What he didn’t tag on were the lengths of his core samples. How he derived weighing factors was as clear as drill mud. The same weighting factors should have been applied when he tested for associative dependence between lead and silver. Weighting factors should also have been applied to test for spatial dependence between metal grades determined in ordered core samples of variable length from a single borehole. He didn’t know that degrees of freedom are positive irrationals when core samples vary in length. In other words, he didn’t even know how to fingerprint boreholes. What a shame that peerless Matheron kept on writing more of the same.

No matter what odd statistics Matheron did cook up it would smoothly pass his own peer review. It did make a mockery of statistics that his new science of geostatistics made it all the way to the USA in 1970. Tagged along on the trip were A Marechal and J Serra. They would assist Matheron in making a strong case for his novel science. The stage was set on campus at the University of Kansas for a geostatistics colloquium on 7-9 June 1970. In those days, Matheron, Marechal and Serra were geostatistical scholars at the Centre de Morphology Mathematique at Fontainebleau, France. Matheron himself had thought up Brownian motion along a straight line. It would set the stage for random functions to be continuous between measured values. He did so in his rambling Random Functions and their Application in Geology. What was still beyond Matheron’s grasp is how to verify 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. It did so since counting degrees of freedom had not yet made Matheron’s brief list of significant things to do.

Marechal and Serra in Figure 10 of Random Kriging show how to derive a set of sixteen distance-weighted averages from a set of nine measured values. What M&S didn’t derive was the variance of each and every distance-weighted average. David in 1977 took a long look at M&S’s data but didn’t derive the variance of each and every distance-weighted average either. What David did run into were infinite sets of distance-weighted averages. Journal in 1978 was so taken with David’s infinite set of distance-weighted averages that he took the zero variance with hook, line and sinker. Matheron in 1960 found out about D G Krige’s work at the Witwatersrand gold complex in South Africa and came up all sorts of krige-inspired adjectives and verbs. That’s in a nutshell why Matheron’s new science of geostatistics took on a life of its own for no reason whatsoever.

Agterberg’s 1970 Autocorrelation Functions in Geology was about what he then called “a geologic prediction problem”. He defined a set of measured values at unevenly distributed positions in a sample space. His problem was not so much how to derive the value of the stochastic variable at the selected position. His real problem was that he didn’t derive the variance of his distance-weighted value at the selected position. On a positive note, he didn’t make a point of the fact that his set of measured values didn’t define an infinite set of variance-deprived distance-weighted average values. He didn’t test for spatial dependence by taking a systematic walk that visits each measured value but once, and that covers the shortest possible distance between all positions. Agterberg’s 1970 geologic prediction problem popped up as “a typical kriging problem” in his 1974 Geomathematics.

A geologic prediction problem in 1970! A typical kriging problem in 1974! The eulogy for Matheron in 2000! The silence of NRCan’s Emeritus Scientist in 2010! What’s the matter with NRCan’s brass? When will Dr Frederik P Agterberg be asked to explain why his distance-weighted average doesn’t have a variance?

Back when NRCan was Canmet I knew several of its scientists. Most of all I remember Dr Jan Visman, a Dutch mining engineer with a keen interest in coal processing. He was an accidental sampling expert of sorts because of his need to understand coal processing. We were members of ASTM D05 on sampling and analysis of coal. He headed the Western Regional Laboratories of the Department of Mines and Technical Survey until his retirement in 1976. I owe him a debt of gratitude. His 1947 PhD thesis made it clear that the variance of the primary sample selection stage is the sum of composition and distribution components. That’s why I’m keeping his memory alive on Wikipedia.

Dr Robert Sutarno was a true expert on applied statistics in general and interlaboratory test programs in particular. He taught me a lot about statistical analysis of interlaboratory test programs, and about preparation and certification of reference samples. I met him when we were members of the Canadian Advisory Committee to ISO Technical Committee 102 on iron ore. We traveled to Japan in 1974. The fact that Bob spoke Dutch was a bonus for me. I was more conversant with German and French than with English when we came to Canada in 1969. But that’s not the end of my case against geostatistics!

The Age of Statistics is upon us

How I wish it were true! But that`s what W J Reichmann thought in 1961. It’s the very title of Chapter 1 in his delightful Use and abuse of statistics. The first line of its Preface points out: `Very few people nowadays can progress very far without at some point coming in contact with statistics`. Now that’s what I have been trying to tell the geostatistocracy since the early 1990s. So I pointed to Reichmann’s work in Abuse of Statistics. I own several scores of books on sampling and statistics. Applied statistics underpins sampling practice just as much as probability theory does sampling theory. As such, degrees of freedom play a key role in sampling practice but none at all in sampling theory. No ifs or buts! Except in CIM Bulletin. In Matheron’s tour de force of course. And in Cressie’s Statistics with upper-case S.

The Editor of CIM Bulletin wrote on September 21, 1992 that “articles of a controversial nature” may be published under the heading Forum. It’s hard to believe that applied statistics was controversial in those days. Of course, The Geological Society of CIM has got to be vigilant when deciding what GEOSOC members get to read. So I was pleased that Abuse of Statistics was approved for publication with the proviso that the source of my most favorite quote be disclosed. That’s what Dr Frits P Agterberg wanted. In those days, Agterberg was Associate Editor with CIM Bulletin. In due course, he would wish not only geologists but geoscientists at large to work with geostatistics. Here’s what H G Wells (1866-1946) once said, “Statistical thinking will one day be as necessary for efficient citizenship and the ability to read and write.” How about that? I do not know when or even if Wells said it and to whom. But Darrell Huff thought Wells had said so. Surely, the author of How to lie with statistics would not tell a lie. So I put Huff’s book on my short list of references. And I put Wells’ thought on statistical thinking on top of my brief but somehow controversial article.

Peer review at The Geological Society of CIM in those days was a sham. Not only was it blatantly biased but it was also shamelessly self-serving. Why did it see fit to reject Precision Estimates for Ore Reserves? It did so because we didn’t refer to twenty years of geostatistical literature! And why didn’t we do that? We didn’t because Professor Dr Michel David’s 1977 Geostatistical Ore Reserve Estimation didn’t show how to derive unbiased confidence limits for metal grades and contents of in-situ ores. As a matter of fact, geostatisticians still do not know how to derive unbiased confidence limits for metal contents and grades of ore reserves. All the same, The Geological Society of CIM rejected Dependencies and degrees of freedom and The properties of variances just as brazenly as did the Journal for Mathematical Geology.

CIM’s GEOSOC failed to grasp in 1992 why the properties of variances and the concept of degrees of freedom cannot be ignored with impunity. That’s when Bre-X Minerals was getting ready to explore for gold in Kalimantan, Indonesia. I’m sick and tired thinking of Bre-X’s salting scam. The more so because Bre-X’s massive phantom gold resource was cooked up by assuming the same gold grades between step-out lines of boreholes as within lines of boreholes. It’s the doctrine of Stanford’s Journel. Agterberg argued in 2009 that Bre-X’s test results for gold are “no real data”. The problem was that the Ontario Securities Commission thought they were. And many Bre-X investors thought likewise!

I’m still tickled orange that applied statistics played a key role in unraveling the Bre-X fraud. I have large sets of bogus gold assays determined by cyanide leaching 250 g test portions taken from crushed and salted drill core sections. I’ll show why it makes sense to test for rather than assume spatial dependence between measured values in ordered sets.

The first step was to insert three (3) lines of kriged boreholes between two lines of (2) salted boreholes in Busang’s South-East Zone. The second step was to derive statistics for two (2) lines of salted boreholes and three (3) lines of kriged boreholes. A little applied statistics was enough to show that geostatistics creates spatial dependence where it does not exist.

Neither line of salted boreholes displays a significant degree of spatial dependence. In contrast, all lines of kriged boreholes display a significant degree of spatial dependence. What a shame it’s all bogus gold. What’s real is that even test results for gold in salted boreholes do give degrees of freedom. In contrast, functionally dependent values such as kriged estimates are never blessed with degrees of freedom. All of that is old hat in applied statistics! The age of applied statistics may still not be upon us but the age of the internet is. The worldwide net has made it easy to find out who messed up what, when, where and why. Geostatistics is about to look a lot worse.

Stanford’s Journel shed light on geostatistics

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

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

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

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

In a footnote on the very same page Journel & Huijbregts 1978 Mining Geostatistics mentioned J Serra and A Maréchal. David’s 1977 Geostatistical Ore Reserve Estimation, too, mentioned J Serra and A Maréchal. In fact, David took this example from Serra and Maréchal’s 1970 Random Kriging. Matheron’s 1970 Random Functions and their application in Geology, too, was presented at the 1970 Geostatistics colloquium on campus at The University of Kansas in June 1970. And so was Agterberg’s 1970 Autocorrelation Functions in Geology.

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

Time is money: Another case of pay-me-now-or-pay-me-later

This one is for you Mr. Plant Manager or CEO.? Especially if your company is publicly traded company you are very familiar with how tight money appears to be when it comes to funding projects that involve machinery and condition monitoring, which do not have a ? to a 1 year ROI it is virtually impossible to bring them alive.? I have seen projects not make it even though they would have saved the company tenths of thousands of Dollars in power savings, cooling water elimination, repair reduction etc.  You also know that little expense is spared when production is down because a machine broke that sometimes does not even need to have been a critical piece of equipment.? Bunches of money are then spent trying to expedite the repair or replacement.? Ironic, is it not?

I have lost track of how many maintenance managers I have spoken to that wanted to buy a much more reliable and efficient machine that had an average ROI of around 2 years in most cases.? Much like local anglers the manager is casted his line out into the big yearly budget pond in hope that his request would finally be granted.? Yet he gets few nibbles? and thus he is reduced to repeating the same spiel in the following year.?

Now I am not saying that every project is worth pursuing, however, I would implore plant managers and CFOs to look twice before sending your maintenance managers back to the pond:? The money that they could be saving you over time would pay great dividends in less than 2 years.  Imagine what you could do with that money then!? You would need to have faith and not get tied up in the 90 day turn thinking for a little while.? Or you could kick it up a notch and let your CFO run the number that you are currently spending in unnecessary downtime and repairs.? Do not trust existing numbers.? Go speak with you maintenance people that do the actual work and see if your impression now matched what your balance sheet is trying to tell you.? Do not be surprised finding out that your company has become complacent by accepting the current state of affairs as something that cannot change.? If you still cannot go through with the project it may be time sharing this blog with the main company board.? They also should go out and walk the plant floor sometime soon and see what short term thinking does to their folks, morale and most of all their cherished profits.? Perhaps the maintenance managers can finally go home with a big catch from the pond.?

Have an awesome day,

Ralf Weiser

Voodoo statistics at IAMG

Acronyms serve to make long tags short. Ranking high among the world’s most famous acronyms are USA and IBM. Laser and taser are well-known objects that have but rhyme in common. EMF stands for Eclipse Modeling Framework. ASTM, DIN and ISO are familiar to those who develop and work with national and international standard methods. IAMG stood for International Association for Mathematical Geology from 1968 to 2007. IAMG’s Council in January 2008 resolved to call it the International Association for Mathematical Geosciences. What IAMG’s Council never did was set up an ISO Technical Committee on Reserve and Resource Estimation.

Professor Dr Georges Matheron may well have thought that he was peerless. In way too many ways he was indeed without peers. It was a blessing of sorts in disguise. All of his work is so richly embellished with symbols that tallied up to a tangle of formulas. All of it fell far short of a clear and concise text. He made up all sort of terms if and when required. But what he didn’t do was provide primary data sets. So, his work does not make an easy read even in French let alone in English. What does matter is that CdG’s website has made Matheron’s work accessible to the world.

So it came about in 1970 that Matheron’s new science of geostatistics was all geared up to do more with less. That was the very year it made its way to the University of Kansas, Lawrence. D F Merriam, Chief of Geologic Research, Kansas Geological Research, and IAMG Historian, called it a colloquium. It was a thoughtful touch that he dedicated the proceedings to ‘all geostatisticians and statistical geologists’. Matheron had come all the way from his Centre de Morphologie Mathematique to talk about Random Functions and their Application in Geology. His tour de force was to somehow force Brownian motion along a straight line. He didn’t spell out what Brownian motion and ore deposits could possibly have in common. What did matter most was that Matheron’s so-called random functions are continuous along intervals between ordered sets of measured values.

Matheron was not the only geostatistical scholar from his Centre de Morphologie Mathematique. A Marechal and J Serra had come along to talk about Random Kriging. What captured my attention was M&S’s Figure 10. It turned out to be a dead ringer for Figure 203 in David’s 1977 work. Both figures show how to derive a set of sixteen (16) distance-weighted averages from a set of nine (9) holes. It may look like the miracle at the wedding of Cana in Galileo. But that’s what geostatistics is all about. Agterberg derived but a single distant-weighted average point grade from a set of five (5) measured values. Marechal, Serra, and David derived a set of sixteen (16) distance-weighted averages. Each and every so-called kriged estimate is a zero-dimensional and variance-deprived weighted average point grade. It turned into the heart and soul of Matheronian geostatistics.

Infinite set of distance-weighted averages

When Matheron’s new science struck the University of Kansas, Lawrence in June 1970 it didn’t hit raw nerves. At that time, IAMG stood for International Association for Mathematical Geology. And Matheronian geostatistics kept coming along by hook and by crook.

Assume, krige, smooth, be happy!

IAMG’s News Letter No 38 reported that all members of its discipline belong to one of three schools of thought: Those who practice and strongly advocate geostatistics, those who are violently (and vocally) opposed to geostatistics, and the silent majority, who wonder what all of the shouting is about. The same newsletter shows Michel David accept the Krumbein Medal from IAMG’s President John Davis. News Letter No 38 had put into perspective why our paper on Precision Estimates for Ore Reserves troubled David as much as it did. He didn’t show how to derive unbiased confidence limits for the mass of metal in a volume of in-situ ore. Why then did David expect Merks & Merks to refer to twenty years of geostatistical literature? Many questions and but few answers. Stay tuned for sound statistics!

You can turn teamwork into success: Plan…Do…Review

Planning and Doing (Implementation) come natural to us. However, setting time aside and reviewing what has been done or implemented is not common practice. Always stick with the process step that you are at the time. When you are planning stage, do not do any of the other two things. The same goes for the Doing and Reviewing part. You will save on nerves, effort and money if you do the well.

The most vital component to a successful team task is the review process. It is the most frequent overlooked task in any project you need to undertake. Some projects may make great progress at first and then later fail because along the course of anything you do in business there will always be some tweaking along the way and no one ever took the time to include this in a review phase. The “tweaking” changes the dynamics of a project and if no one takes time to record what, why and how it happened you will not be able to capture why the results were different than expected. This is extremely frustrating for everyone and wastes resources with a direct impact on the net bottom line because you will never know why you failed, or worse why you had success.

Think of how many team based projects you may have been involved in that did not provide the desired results. I venture saying that the vast majority of them failed because no one thought of drawing the line at the beginning of the project and ask that there be a time line, a set of criteria for the results be reviewed and measurements. This normally leads to so called open ended projects. This is one of the biggest morale busters as the involved people will not be able to conclude anything. Something that was supposed to be only a temporary or experimental measure now has become the permanent solution without openly and officially saying so. One of the most important items any employee is looking for in an organization is that his or her contributions are “worth” the effort and make a difference. How is the employee ever going to figure this out if you never conclude the project? A winning company turns the knowledge from a finished project into common practice. Working for a winning company is equally important to an employee.

Another such waste comes from not paying attention to what phase you are in. What I mean by that is that most teams get so far ahead of themselves and start doing without thoroughly finishing the planning session. Did you ever paint a room in your house or apartment? Well, then you know what I am talking about. It takes so much more effort and mostly time to prepare for the painting, than it does to do the actual painting. Make sure that you have covered the must-have items of a successful endeavor such as mission, goal, strategy, tactics, responsibilities, authority, timeline and the most important one: measurements. Take this into account when you form a team for a specific task. Make sure to allow ample time for the team to plan the course of the project and only then start thinking about the implementation part. Do not mix up the project phases. When you plan – plan; when you do – do; do not forget to review – just review and do not start revising your plan in the midst of it. Finish it well by recognizing the contributions made and that the project either did or did not turn into common practice.

A plan is only a plan as long as you stick to your plan. Otherwise it is a new one. Do not get me wrong here. I am not advocating that you go through with a project when a team recognizes that it makes no sense. But I am saying that you need to adhere to the distinctly different process phases of your project once you have all bought into the course of action. Otherwise you will diminish your success rate of any project.

Ralf Weiser

Rebranding Professor Dr Georges Matheron

Dr Frederik P Agterberg tried to do so when he sang the praises of Professor Dr Georges Matheron and called him the Founder of Spatial Statistics. The keepers of Matheron`s magnum opus at his own Centre de Géostatistique didn`t quite see eye to eye with Agterberg`s rebranding. Matheron`s disciples were taught to hold him in the highest regard as the Creator of Geostatistics. It was Matheron himself who called geostatistics a new science in the early 1960s. Here`s in a nutshell what had inspired Matheron so much in his most creative of days. He taught that, “geologists stress structure and statisticians stress randomness”. I liked that a lot. I would have liked it even more had Matheron shown how to test for absence or presence of structure. All it would have taken is to apply Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set. He would have had to count the number of degrees of freedom for each set. That was a bit of a problem. Matheron and his following never got around to counting degrees of freedom.

On a positive note, Matheron did test for associative dependence between lead and silver grades of drill core samples. This test may well have been the very reason why Matheron thought he was a statistician. His 1954 Formule des Minerais Connexes is indeed marked Note Statistique No 1. In his Rectificatif à la Note Statistique No 1, Matheron derived weighted average lead and silver grades. What he failed to derive were variances of weighted average lead and silver grades. So, I am quite pleased that the  Centre de Géostatistique has posted so much of Matheron’s work. On the negative side, its webmaster saw fit to predate the evolution of Matheron’s new science of geostatistics. That’s why his very first paper did end up as Note Géostatistique No 1. Providentially, his 1954 Formule des Minerais Connexes and its Rectificatif are still marked Note Statistique No 1.

So it was that Matheron didn’t take to working with the Central Limit Theorem. David did recall the famous Central Limit Theorem in his 1977 Geostatistical Ore Reserve Estimation. He didn’t much work with it either. A critical subject that failed to make Matheron’s list of things to teach is one-to-one correspondence between functions and variances. Yet, it is a condition sine qua non in mathematical statistics. It is no wonder then that the properties of variances are beyond the grasp of the geostatistical fraternity. I have never thought much of Professor Dr Georges Matheron’s thinking. Whenever I do think of Matheron, I remember him as a self-made wizard of odd statistics.

Professor Dr Michel David took a shine to Matheron’s new science of geostatistics. David did so while he was teaching at l’École Polytechnique, University de Montréal, Québec, Canada. And he did predict that ‘statisticians would find many unqualified statements’ in his 1977 Geostatistical Ore Reserve Estimation. He didn’t predict he couldn’t care less if someone pointed out what was wrong and why. Some twenty years ago I did but few cared. So, I’ll just keep doing it again and again! Chapter 10 The Practice of Kriging shows how to do more with fewer boreholes by paying no attention at all to the rules of mathematical statistics.

Fig. 203. Pattern showing all the points within B,
which are estimated from the same nine holes.

David borrowed the above figure from Maréchal and Serra’s 1970 Random Kriging. Both were scholars at Matheron’s Centre de Morphology Mathématique. Here’s word for word what I have come to call David’s test for geostatistical acuity. “Writing all the necessary covariances for that system of equations is a good test to find out whether one really understands geostatistics”. I have pointed out that a good test to find out whether one really understands mathematical statistics is to count the number of degrees of freedom for David’s system of equations. The correct count is zero! That’s how Matheron and his timid minions took reserve and resource estimation into a dead-end street.

But even more bad science pops up in Chapter 12 Orebody Modelling. In Section 12.2 Conditional Simulation, David wrote about the infinite set of simulated values. He wonders how to make infinite sets smaller and get models closer to reality. In Section 12.2.1 Using a Simulated Model, he wrote about some pudding proof and a posteriori proved simulations. But nobody cries out loud in the face of such blatant nonsense. What are the odds to win when playing 649?

So, why then did Agterberg try to rebrand Matheron the Founder of Spatial Statistics after he had passed away? Now that’s a long story. The short of it is that there are many more geoscientists than geologists on our little planet. Remember global warming? And how to assume spatial dependence between measured values in ordered sets? That’s what way too many geoscientists are taught. Stay tuned for real statistics. And tune out to surreal geostatistics.

One more message to CIM’s President

CIM stands for Canadian Institute of Mining, Metallurgy and Petroleum. Once upon a time I was a proud CIM Member. Today I am the accidental CIM Life Member. My first message to CIM`s President was snail mailed on March 20, 1992. CIM`s President was William E Stanley of The Coopers & Lybrand Group in Vancouver. He was the first of many whom I had told why geostatistics is an invalid variant of applied statistics. We met, he listened to my story, and I wrote him a letter. CIM Bulletin of March 1989 had published Armstrong and Champigny’s A Study on kriging Small Blocks. Both authors were at that time geostatistical scholars at the Centre de Géostatistique, France. They thought up the study since, “The kriging variance rises up to a maximum and then drops off.” What they found out is that “…mine planners are often tempted to kriging very small blocks.” How about that? Smoothing a little is good but smoothing very small blocks is bad. That sort of a pass-the-buck study did pass David’s peer review with red flags blazing.

Early in 1990 we found out that Precision Estimates for Ore Reserves was rejected. Our paper showed how to test for spatial dependence between gold grades of ordered rounds in a drift. David’s 1977 textbook didn’t show how to test for spatial dependence, or how to count degrees of freedom. Neither did his work show how to derive unbiased confidence limits for metal contents and grades of in-situ ores. So, I put Geostatistics or Voodoo Science on paper, and The Northern Miner printed it on March 20, 1992. Champigny was no longer a geostatistical scholar at the Centre de Géostatistique in France but a Senior Consultant with The Coopers & Lybrand Group in Toronto. He never lost his passion for kriging and smoothing. As a matter of fact, he rounded up a team of anonymous ore reserve practitioners to stand on guard against the rise and fall of kriging variances. What he and his team did prove was that the properties of variances were far beyond their grasp. The Northern Miner put Champigny’s rambling tale in print on May 18, 1992. Armstrong went beyond the pale and lectured on scientific integrity in De Geostatisticis of July 1992.

Following is the text of my emessage of January 13, 2010, to Michael J Allen, CIM’s President, Vice President, Engineering, with Teck Corporation, Member of APEGBC and SME, and a CIM Fellow:

About twenty years ago I reported to CIM that geostatistics is an invalid variant of applied statistics. Geostatistocrats with CIM Bulletin promptly put up a spirited battle to salvage the new science of geostatistics. And a fine job they did! Matheron’s madness of surreal geostatistics even survived the Bre-X fraud. Statistics turned into geostatistics under the guidance of Professor Dr Georges Matheron, a French probabilist who became a self-made wizard of odd statistics in the 1950s. A brief history of my 20-year campaign against the geostatocracy and its army of degrees of freedom fighters is chronicled on my website.

Dr Frederik P Agterberg, Past President, International Association for Mathematical Geosciences formerly know as International Association for Mathematical Geology, called Matheron (1930-2000) the Founder of Spatial Statistics. Agterberg ranked Matheron on a par with giants of real statistics such as Sir Ronald A Fisher (1890-1962) and Professor Dr J W Tukey (1915-2000). Agterberg was wrong! Matheron fumbled the variance of the length-weighted average in 1954. Agterberg himself fumbled the variance of the distance-weighted average first in his 1970 Autocorrelation Functions in Geology and once more in his 1974 Geomathematics. Agterberg is Emeritus Scientist with Natural Resources Canada. He ought to but has yet to explain why his distance-weighted average point grade does not have a variance. After all, Gemcom‘s geostatistical software converted Bre-X’s 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 phantom gold resource was statistically identical to zero. Duplicate test results for gold by cyanide leaching determined in a few boreholes would have been enough to unravel the Bre-X fraud in a timely manner.

I make a clear and concise case for real statistics. Test 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. Chart a sampling variogram to show where spatial dependence in a sample space (or in a sampling unit) dissipates into randomness. We applied Fisher’s F-test in Precision Estimates for Ore Reserves. And we did it again in our APCOM 2009 paper entitled Metrology in Mineral Exploration.

Geostatisticians assume spatial dependence between measured values in ordered sets, interpolate by kriging, smooth some kind of least biased subset of an infinite set of Agterberg’s zero-dimensional and variance-deprived distance-weighted average point grades AKA kriged estimates or kriged estimators, and rig the rules of real statistics with reckless abandon. I urge CIM to investigate whether or not geostatistics is a scientific fraud. I do so as a CIM Life Member. Please do not assume that CIM need not resolve this matter.

To strip or not to strip?

CIM Bulletin approved Abuse of Statistics for publication. Dr Frits Agterberg wanted to know when and where Wells spoke so highly about statistical thinking. I wasn’t about when Wells said what he did. What I do know is that Darrell Huff said Wells did. That’s good enough for me. Huff did so in his 1954 How to Lie with Statistics. It was the very same year that young Matheron didn’t know how to test for spatial dependence between metal grades of ordered core samples, how to derive the variance of the set of metal grades, and how to derive the variance of the central value of the set. Huff never found out what Matheron did wrong. But then, neither did Matheron himself! And Agterberg, Armstrong, David, Journel and scores of geostatistocrats never broke rank with Matheron.

I want to move fast forward to the present. Michael J Allan, CIM President in 2010, writes under President’s Notes about A time of renewal. Let’s read what else he wrote. “Our work in providing standard reserve and resource definitions that are used by the country’s securities regulators is an example of the ongoing technical contributions CIM makes to the industry at large”. For heaven’s sake! Geostatistics is as alive and flawed as it was in the 1970s. So it seems that CIM is not about to kill the incredible kriging machine. For infinite sets of kriged estimates and zero kriging variances set the stage for boundless krige and smooth fests. APEGBC ‘s Code of Ethics is not written to rule against scientific fraud. What will kill the kriging machine is the study of climate dynamics on our little planet. No ifs and buts!

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