Freedom of speech?

Once upon a time Dr Margaret Armstrong was entrusted with the review of opinions deemed at variance with Matheron’s new science of geostatistics. She was keen on talking about Matheron’s gift to mankind. She did so in De Geostatisticis! In N°14 she was beating around the bush about Freedom of Speech? From time to time she would dream up another and mail it to subscribers. I didn’t mind at all to be on her mailing list! On the contrary, it was a convenient way to keep track of thinkers who were into praising Matheron’s new science of geostatistics without thinking about counting degrees of freedom!

Let me explain what Marechal and Serra talked about at a Colloquium on geostatistics at The University of Kansas in 1970. They showed how to strip the variance off the distance-weighted average and call what was left a kriged estimate. Infinite sets of kriged estimates and zero kriging variances morphed into the heart and soul of Matheron’s novel science of geostatistics. Thank goodness, the Editor of De Geostatisticis didn’t really call it Matheron’s gift to mankind. On the contrary, it made me think of Mark Twain and his postulate that a mine is a hole in the ground with a liar on top. Nowadays it is still a hole in the ground but the liar on top is stringing Markov chains. Mining investors should be aware that stringing Markov chains does not give unbiased confidence limits for metal contents and grades of mineral inventories. The TSE and the OSC have not yet taken a close look at stochastic mine planning with Markov chains.

Margaret Armstrong had been awarded a Master’s degree in mathematical statistics at the University of Queensland. After migrating to France she was awarded a doctorate in geostatistics. What she does is called “stochastic modeling in the earth sciences”. Professor Georges Matheron had flunked his PhD in 1965 simply because didn’t know how to test for spatial dependence by applying Fisher’s F-test. Yet, it was Dr F P Agterberg who praised him as the Creator of Spatial Statistics upon his passing in 2000. It made me wonder when, where and why Professor Dr A G Journel had been awarded PhD. The more so since he only teaches those who do have a PhD in geostatistics!

Following is ad verbatim the text of Armstrong’s review of Precision Estimates for Ore Reserves. It was put together by Merks and Merks and praised by and published in Erzmetall. I’m proud that my son was the coauthor. He has a PhD in Computing Science, and was awarded the Graduate Dean’s Medal from the Faculty of Applied Science in 1986 and 1992. His interests include programming language design, software engineering and parallel algorithms.

Here’s what Dr Margaret Armstrong wrote about our approved and published paper:

“The text presents no equation, no development except for the trivial relative variance of a product of independent factors (p. 3-4). Variance of errors are mistaken for spatial variance, F-tests are called for forgetting the condition of independent samples, kriging variances are said to “violate the requirement of independence” when they were developed precisely to handle the case of (spatial) dependence, the central limit theorem is invoked for the trivial σ²/n variance of estimation of the mean of n independent sample values, the list could go on and on….. Definitive statements such as “Only the variances for ordered or randomized sets of measured grades generate reliable and realistic precision estimates….” are put without even a definition of what an ordered set is, less any proof. The individual has some understanding of sampling of particulate materials, and believes he can transfer such notions, as is, to problems involving spatial distributions.”

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Als VdS-zertifizierter Errichter für Funkenlöschanlagen führt GreCon neben der Anlagenkonzeption auf Wunsch alle für die Inbetriebnahme einer solchen Anlage erforderlichen Installationsleistungen wie z. B. Elektroverkabelungen, die Verlegung der Löschrohrleitung sowie deren Isolierung durch. „Wir bieten unseren Kunden ein „Rundum-Sorglos-Paket“ und nehmen ihnen das Sich-kümmern und Koordinieren ab“, so Dirk Saschenbrecker, der die für eine Installation erforderlichen Gewerke betreut.

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Volk’s Applied Statistics for Engineers

It was William Volk who has written my favorite textbook! I have kept a copy of its 1958 edition on my desk when I was making a living in the Port of Rotterdam. What I like most of all in Applied Statistics for Engineers is that Volk explains the properties of variances in such rich detail. My first copy is falling apart but I’m still as smitten with its contents as I was in 1958. Volk pointed out in his Preface that he was indebted to Professor Sir Ronald A Fisher (1890-1962). It didn’t take long to figure out why Section 7.1.4 Variance of a General Function in Volk’s 1958 textbook proved that each function does have its own variance. Stripping the variance off the weighted average cum kriged estimate set the stage for Matheron’s new science of geostatistics. This fact became of critical importance when my grasp of the properties of variances made it possible to prove that the intrinsic variance of Bre-X’s gold was statistically identical to zero. So I’m pleased that the properties of variances did indeed stand the test of time in Volk’s Applied Statistics for Engineers.

What did not stand the test of time are degrees of freedom.  The concept of degrees of freedom is relevant in applied statistics but irrelevant in geostatistics. Degrees of freedom would have vanished without a trace if it were not for Table1.IV. Copper grade Prince Lyell in David’s 1977 Geostatistical Ore Reserve Estimation. Grant NRC7035 made it possible to put so much junk stats on paper. I have always applied Fisher’s F-test to prove spatial dependence between measured values in ordered sets. I did so with test results for ordered core sections from single boreholes but also with test results for ordered sets of on-stream measurements in mineral processing plants. Should Matheronian geostatistics be an integral part of geosciences? Or should it be rejected as a scientific fraud? Of course, it should be rejected! If only because geostatistics is messing up the study of climate dynamics!

 Sir Ronald A Fisher (1890-1962) was knighted since he counted degrees of freedom for small data sets.  Karl Pearson (1857-1936) devised the chi-squared distribution in terms of observed and expected ratios. He did so in his Galton Laboratory. Sir Ronald A Fisher went to Australia and worked for a while at CSIRO (Commonwealth Scientific and Industrial Research Organization). He passed away in 1962 and was put to rest in Adelaide. He has never been awarded a Nobel price. My confidence in Sir Ronald A Fisher and his famous F-test is bound to last far beyond my time.  

 Margaret Armstrong migrated to France after she had completed her Master’s degree in mathematical statistics at the University of Queensland in the 1990s. Between Australia and CERNA, Mines Paris Tech, France, she may have paid too little attention Matheron’s new science of geostatistics. Or Matheron may not have told her that he had flunked his PhD thesis in 1965. But surely, Armstrong should have known all about Fisher’s F-test and about counting degrees of freedom. She could have told Professor Georges Matheron all about counting degrees of freedom. Why did Matheron confer on Armstrong a PhD in geostatistics s0 shortly after she had left Down Under and made landfall in the City of Lights

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SME approved applied statistics

SME did so at the turn of the century. Its acronym stands for The Society for Mining, Metallurgy, and Exploration, Inc. Not only did it approve Process simulation with spreadsheet software and put it in print in Minerals & Metallurgical Processing, Vol 16, No 2, May 1999. It also approved Borehole statistics with spreadsheet software and published it in Volume 308 of Transactions 2000. I was tickled pink that SME’s reviewers approved applied statistics. The more so since SME’s reviewers thought my work would stir up a hornet’s nest! But not a single hornet stirred! As a matter of fact, Stanford’s Professor Dr A J Journel didn’t put up opposition against applied statistics! He may well remember what he wrote on October 15, 1992 to the Editor of the Journal of Mathematical Geology? Here are but a few paragraphs of Professor Journel’s musings!

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.

It is not correct to state categorically that kriging, or for that matter any other interpolation algorithm, does not add any information to the system. It does through the implicit or explicit model of correlation. Indeed, change the variogram model yet keep the same data, the kriging estimates change. This correlation/covariance/variogram model can be borrowed from another field or outcrop, it is then genuine new information. Or, it can be inferred from the same data used for kriging. In the latter case, new information is introduced through aspects of the sample bivariate (two-point) distribution. The important question is, of course, how representative of the unsampled area is that bivariate information, i.e., how appropriate is the prior “decision” of stationarity.

 What a world of difference between SME’s reviews and Professor Dr A J Journel’s shamelessly self-serving drivel. Merks and Merks 1991 Precision estimates for ore reserves was praised by and published in Erzmetall 44 (1991) Nr 10. David, the author of 1977 Geostatistical Ore Reserve Estimation, deemed our paper deficient in references to the geostatistical literature. Professor Dr A J Sinclair, PEng, PGeo, was the second reviewer. He objected to scores of equations incorporated in several ISO Standards after I had been active on several ISO Committees since 1974. Sinclair was thinking in the 1970s that Professor G Matheron was onto something! He didn’t notice that the variance had been stripped off the distance-weighted average AKA kriged estimate. UBC’s President didn’t notice either. Yet, I have delivered to the Office of Dr Martha Piper a pair copies of Sampling and Weighing of Bulk Solids

Geostatisticians always praise geostatistical theory and practice. Stripping the variance off the distance-weighted average and calling what’s left a kriged estimate are the heart and soul of Matheron’s new science. I saw an opportunity to talk about applied statistics come along when Geostatistics for the Next Century made an early landing at McGill University. The stage was set at McGill’s Conference Centre in August 1993. I had submitted by registered mail my view on Properties of Variances. I was told on behalf of the Chair, that all seats were taken. Somebody did wish me success with my research!

Professor Dr A G Journel, Geology and Environmental Sciences, Stanford University, talked about stochastic simulation and Bayes’ Theorem but didn’t yet drift into Markov chains. He didn’t talk about confidence limits for contents and grades of mineral resources. Meanwhile, Bre-X Minerals was drilling and salting in the Kalimantan jungle. Stanford’s Dr A G Journel got into teaching more of the same. Stanford’s Journel taught only those with a PhD in geostatistics! For teaching out loud!

From stripping variances to stringing Markov chains

Did Professor Georges Matheron (1930-2000) make fundamental contributions to science? That’s what Dr F P Agterberg wrote  in Matheron’s eulogy! Here’s what Professor Matheron ought to have known but didn’t! He did not know how to apply Fisher’s F-test to the variance of a set and the first variance term of the ordered set. He did not know how to count degrees of freedom! He did not apply Fisher’s F-test when his PhD supervisors asked him to show how to test for spatial dependence. He didn’t test for spatial dependence by applying Fisher’s F-test to the variance of a set and the first variance term of the ordered set! He did not compare his observed F-value with tabulated F-values at 95%, 99% and 99.9% probability. He did not take degrees of degrees of freedom into account.  Study http://www.geostatscam.com/ to find out why Matheron’s work did not include Fisher’s F-test!

 Geostatistocrats remember Matheron either as the Creator of Geostatistics or as the Founder of Spatial Statistics. Yet Matheron didn’t grasp in 1965 how to test for spatial dependence! He didn’t even know how to test for spatial dependence when his PhD supervisors had given him trivial data sets. One was a perfectly ordered set and the other was shuffled into randomness. Matheron’s PhD thesis rambled on for a whopping 301 pages of dense text and countless symbols. Yet, Matheron flunked his PhD thesis. The problem was not so much that he didn’t know how to test for spatial dependence. The real problem was that Matheron taught his disciples that spatial dependence between measured values in ordered sets may be assumed. Good grief! What made matters worse is that Matheron didn’t count degrees of freedom the same way as did Sir R A Fisher. So how did Matheron and his disciples study the dynamics of spatial dependence? They assumed spatial dependence.  Of course, it was doomed to fail without Fishers’ F-test!  

Matheron and a few of his students visited the University of Kansas, Lawrence on June 7-9, 1970. They had come to represent the Centre de Morphologie Mathematique, Paris, France. Matheron talked about Random functions and their application in geology. He invoked Brownian motion along a straight line to solve a few estimation problems.  Marechal and Serra spoke about Random Kriging. The caption under Figure 10 explicates:  Grades of n samples belonging to nine rectangles P of pattern surrounding x.  This figure was reborn as Figure 203 on page 286 of David’s 1977 Geostatistical Ore Reserve Estimation. Its author prevaricated about “an infinite set of simulated values”. Stanford’s Journel in his 1978 Mining Geostatistics derived the zero kriging variance

Professor Dr Michel David refers in Chapter 2 to what he called the famous central limit theorem. Yet, he didn’t refer to this theorem in his Index. In Figure 203 on page 286 David shows M&S’s set of sixteen (16) Central Limit Theorems each of which is a function of the same set of nine (9) measured values! Surely, stripping variances off functions does not make any sense whatsoever. Why does the geostatocracy work with kriging variances that tend towards zero? Why call geostatistics a new science when all that has been done is strip the variance off the distance-weighted average AKA kriged estimate? Why string Markov chains between measured values when ordered sets do not display a significant degree of spatial dependence? Why strip the variance off the distance-weighted average grade? Why not report unbiased confidence limits for metal contents and grades of mineral inventories? Surely, stringing Markov chains cannot possibly give unbiased confidence limits for metal contents and grades of mineral inventories!

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Mit Wirkung zum 1. Oktober 2013 firmiert K-Tron, ein weltweit führender Anbieter von Dosiergeräten, pneumatischen Förderungen und kompletten Materialfördersystemen, unter dem Markennamen Coperion K-Tron. Coperion wurde im Dezember 2012 von der US-amerikanischen Hillenbrand, Inc., übernommen. K-Tron gehört seit 2010 zur Process Equipment Group (PEG) von Hillenbrand.

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