Tag Archives: gold

Rail-Veyor now hauling all Deep 1 Production Material at Agnico Eagle’s Goldex Mine

Sudbury (ON), Canada – Rail-Veyor Technologies Global announced that it’s Rail-Veyor system is now hauling all of the production material at Agnico Eagle Mines Limited’s Goldex Mine in Val-d’Or, Quebec, Canada for their Deep 1 project. Installation of the energy-efficient 3 km underground system began as part of Goldex’s new Deep 1 project which was started up in July 2017.

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Martin Engineering: Conveyor Technology helps Gold Rush Team compete

Neponset (IL), USA – Martin Engineering has supplied belt conveyor technology to 316 Mining Company to maximize the output of their gold mining operations. 316 Mining is well known from “Gold Rush”, the most popular show on the Discovery channel. The show follows the exploits of three competing mining teams as they seek to extract the most placer gold from their operations.

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Oversmoothing small blocks?

Why did Dr Roussos Dimitrakopoulos get into stringing Markov chains between measured values? He may have done so because he did not want his disciples to know how to test for spatial dependence between measured values in ordered sets! Neither did Dr RD want his disciples to know how to count degrees of freedom. Sir R A Fisher has been teaching in Australia why degrees of freedom ought to be counted. Dr RD has studied in Australia but does not teach his disciples that degrees of freedom ought to be counted! Even NSERC/CRSNG does not care that Dr RD ignores degrees of freedom while stringing Markov chains between too few measured values.

It is an irrefutable fact that degrees of freedom have been relevant in applied statistics ever since Sir R A Fisher has been counting degrees of freedom in Australia. In contrast, Dr R Dimitrakopoulos may have told NSERC/CRSNG that stringing Markov chains between measured values in ordered sets generates ore reserves where none exist. Good grief!  Why has NSERC/CRSNG not responded to my request for support. The more so since it is so simple to derive unbiased confidence limits for metal contents and grades of in-situ mineral inventories. I found it simple to prove that Bre-X was a fraud. In fact, the intrinsic variance of  Bre-X’s glory borehole turned out to be statistically identical to zero! In those days, Dr RD’s string of Markov chains would have created a massive phantom gold reserve!

Chairman Peter Munk retired?

Who knows? Munk has always been driven to mine gold! So his offspring may be driven too! Do Barrick’s investors worry? Who cares? Here are some facts and figures! Once upon a time I had asked Barrick Gold Corporation to invest C$100,000 in applied statistics. What I had been given was a massive set of gold grades in drill core samples. I converted gold grades into masses of in-situ gold. Next, I derived 95% confidence limits for gold grades and contents. I have not yet described in detail how I unscrambled the Bre-X salting fraud! Dr Roussos Dimitrakopoulos is sticking to stringing Markov chains rather than applying a simple test for spatial  dependence between measured values in ordered sets and counting degrees of freedom. Who could possibly be behind stringing Markov chains? Stay tuned to find out why truth is stranger than fiction.

Barrick Gold has awarded C$1million to Dr Roussos Dimitrakopoulos. Dr RD prefers to ignore degrees of freedom and to dismiss real variances. He prefers to string Markov chains between measured values in ordered sets. He cannot possibly derive unbiased confidence limits for gold grades and contents. But Dr RD keeps happily stringing along! McGill’s students have not yet been taught how  to count degrees of freedom and why! Of course, it makes no sense whatsoever to string functionally dependent values between measured values in ordered sets. What makes sense is testing for spatial dependence between gold grades within boreholes! Stuffing strings of Markov chains between measured values makes no sense whatsoever!

My memo on Statistical Evaluation of Test Results was sent to Mr Alan R Hill, Executive President, on December 17, 1996. I was pleased to have so many test results for gold. What lingers in my mind is a visit to Barrick’s office in Toronto. I had been invited to come by on December 17, 1996 at 10:00AM. We were talking about tasks I thought ought to be done. That’s when the meeting room door opened ajar. It was Chairman Munk! All he did was ask President Carrington to come and see him after we were finished.

I had been talking about a test program at Bre-X’s site in the Kalimantan jungle. I was given 2,200 test results in crushed core samples each with a length of 2.9 m. Lakefield Research had measured gold by atomic absorption in what was called 0.1 m library core. I wondered what could have been added to 2.9 m of crushed core samples! Filings of a gold/silver alloy?

Several books have been written about Bre-X and its turbulent existence. I have a copy of each. Gold Today, Gone Tomorrow squeezed more facts between its covers than others did. Who  keeps track of those who strip variances off distance-weighted averages AKA kriged estimates?  Wikipedia published goofy science under Geostatistics. All it took was to strip the variance off the distance-weighted average and call what’s left a kriged estimate. Geostatistocrats like to play kriging games with infinite sets of kriged estimates and zero kriging variances. Good grief!

It’s mining by the numbers

It’s the title of an article in the National Post of August 15, 2005. Drew Hasselback had put it on paper in his clear and concise manner. He had figured that assessing deposits looked a little like hedge-fund traders weighing options. It was Professor Dr Roussos Dimitrakopoulos (Dr RD) who told him that mining is a numbers game and that he is about to change the rules. Dr RD could afford to do so because Natural Sciences and Engineering Research Council of Canada had given him $3.5 million to study how to value mining projects. So he was driven to put on paper his take on mining projects. Here’s what turned him on: “You drill a few holes, you think you understand something, but what you know is very little.” Good grief! Was Dr RD ever inspired to test for spatial dependence between test results for ordered core sections from a single borehole? Did he ever count degrees of freedom? What’s his cutting-edge stuff made off! What had he been taught in Australia? How did he get McGill stuck with stochastic modeling? Why did McGill lobby so hard to recruit Dr RD of the University Of Queensland in Australia? Nowadays he’s cooking up new rules for the mining game at Montreal’s McGill University!

Professor Dr Roussos Dimitrakopoulos had already chaired at McGill University in 1993 an “International Forum in honour of Michel David’s contribution to geostatistics”. I’m glad to own a copy of Professor Dr M David’s 1977 Geostatistical Ore Reserve Estimation. Figure 203 on page 286 shows a set of sixteen (16) points each of which is derived from the same set of nine (9) holes. Maréchal and Serra (1970) used the same set in Random Kriging at a 1970 Geostatistics Colloquium at the University of Kansas on 709 June 1970.  Professor George Matheron lectured on the topic of Random Functions and their Application in Geology, and was inspired to invoke Brownian motion along a straight line.

That’s why I was inspired to put forward The Properties of Variances. In fact, I had submitted a copy by registered mail on February 3, 1993 and on March 10, 1993. Here’s the text of an unsigned letter dated March 31, 1993: “Thank you for your interest in the Forum organized in honour of Michel David’s contribution to geostatistics. Due to the remarkable response to the Forum, we regret that we are unable to accommodate a number of potential participants and their very interesting abstracts. We appreciate your efforts and would encourage you to submit your abstract to another event. Thank you again and may we wish you the best with your work.”

Dr RD’s innovative take on assessing ore deposits makes no sense whatsoever. Here’s why! He is but one of several scores of geostatistocrats who have stripped the variance off the distance-weighted average AKA kriged estimate. Infinite sets of kriged estimates and zero kriging variances are bound to get ore reserve practitioners into deep trouble. I wonder what DR RD would have done if he were told to count degrees of freedom. I have counted degrees of freedom to derive 95% confidence limits for grades and contents of gold deposits and to derive the intrinsic variance of gold.

Applied statistics proved the intrinsic variance of Bre-X gold to be statistically identical to zero. It is straightforward to derive unbiased confidence limits for metal contents and grades of ore deposits.  I have done so long before Bre-X’s test samples were salted on the pool table in the Kalimantan jungle. All I want to do is show how to!

Geostatistics for the Next Century?

An International Forum to honour Professor Dr Michel David for his contribution to geostatistics? What’s this world coming to! I read David’s 1977 Geostatistical Ore Reserve Estimation after Elsevier had published it. David’s work has never been a part of any ISO Standard. Yet, ISO Standards have been my bread and butter since I joined ISO/TC102 – Iron Ore in 1974. ASTM’s Board of Directors has awarded me in 1995 for continuous membership of Section 5 Petroleum Products, Lubricants and Fossil Fuels.

Tracing geostatistics to its roots in applied statistics is simple comme bonjour. It’s about as simple as to create spatial dependence where it does not exist! What a pity that interpolation between measured values does not give unbiased precision estimates for grades and contents! Stripping variances off distance-weighted averages AKA kriged estimates has made no sense at all in my work. Professor Matheron in 1970 put in place Brownian motion along a straight line! Good grief! Professor Dr Michel David showed in Fig. 203 on page 286 a set of measured values with df=8 degrees of freedom. He pointed out that his 1977 textbook is not for professional statisticians. I do agree!

Dr R A Blais and Dr G Perrault were not surprised that distance-weighted averages had metamorphosed into kriged estimates. The National Research Council of Canada kept Grant NRC7035 coming in convenient increments. Professor Dr Michel David’s 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation added another 216 rambling pages.

Geostatistics converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Applied statistics proved the intrinsic variance of Bre-X’s gold to be statistically identical to zero. Are geostatistocrats still marching in place? It would have made sense to unravel what was wrong with Bre-X in 1993 rather than stringing Markov chains in 2014!

All events at Montreal, Quebec, Canada took place on June 3-5, 1993. Practitioners of geostatistics had flocked from far and wide to praise Professor Dr Michel David. He had completed in 1977 what was called Geostatistical Ore Reserve Estimation. Scores of geostatisticians were driven to assume spatial dependence between measured values in ordered sets. The more so since a few samples selected at different positions in a finite sample space do give infinite sets of distance-weighted averages AKA kriged estimates.

Professor Matheron’s new science of geostatistics was based on selecting a subset of any infinite set of kriged estimates, and on smoothing pseudo kriging variances to perfection. Assume spatial dependence between measured values, interpolate by kriging, smooth a lot, think a little, and rig the rules of mathematical statistics with impunity. Common sense dictates that testing for spatial dependence between measured values in ordered sets ought to precede interpolation by kriging. The more so since the variance has been stripped off each and every distance-weighted average AKA kriged estimate. Why work with an ordered set of kriged estimates and derive a semi-variogram? Why not work with an ordered set of measured values and derive a true sampling variogram? David’s 1977 Geostatistical Ore Reserve Estimation is the worst textbook on this planet. Until David’s 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation came along and made it worse!

It’s simple to create spatial dependence where it does not exist. What a pity that interpolation between measured values does not give unbiased precision estimates! Stripping variances off distance-weighted averages AKA kriged estimates made no sense at all in my work. Professor Matheron in 1970 put in place Brownian motion along a straight line! Good grief! Professor Dr Michel David showed in Fig. 203 on page 286 a set of measured values with df=8 degrees of freedom. He pointed out that his 1977 textbook is not for professional statisticians. I do agree!

Dr R A Blais and Dr G Perrault were not at all surprised that distance-weighted averages had metamorphosed into kriged estimates. The National Research Council of Canada kept Grant NRC7035 coming in convenient increments. Professor Dr Michel David’s 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation added another 216 rambling pages.

Here’s a take on his 1988 Handbook of Advanced Geostatistical Ore Reserve Estimation. It was geostatistics that converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Applied statistics proved the intrinsic variance of Bre-X’s gold to be statistically identical to zero. How many geostatistocrats are still marching in place? It would have made more sense to unravel what was wrong with Bre-X in 1993 than stringing Markov chains in 2014!

All events at Montreal, Quebec, Canada took place on June 3-5, 1993. Practitioners of geostatistics had flocked from far and wide to praise Professor Dr Michel David. He had completed in 1977 what was called Geostatistical Ore Reserve Estimation. Scores of geostatisticians were driven to assume spatial dependence between measured values in ordered sets. The more so since a few samples selected at different positions in a finite sample space do give infinite sets of distance-weighted averages AKA kriged estimates.

Professor Matheron’s new science of geostatistics was based on selecting a subset of some infinite set of kriged estimates, and on smoothing pseudo kriging variances to perfection. Assume spatial dependence between measured values, interpolate by kriging, smooth a lot, think a little, and rig the rules of mathematical statistics with impunity. Common sense dictates that testing for spatial dependence between measured values in an ordered set ought to precede interpolation by kriging. The more so since the variance has been stripped off each and every distance-weighted average AKA kriged estimate. Why work with ordered sets of kriged estimates and derive semi-variograms? Why not work with ordered sets of measured values and derive real sampling variograms? Why not count degrees of freedom of ordered sets? David’s 1977 Geostatistical Ore Reserve Estimation was the worst textbook on this planet. Until his 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation came along and made a worse read!

Sampling and Ore Reserves

The Prospectors and Developers Association of Canada (PDAC) approved the above title in the 1990s. It did so to set the stage for a seminar at the Royal York Hotel, Toronto, Ontario for Saturday, March 23, 1991. I was tickled pink to be the first speaker. My textbook on Sampling and Weighing of Bulk Solids had been translated into Mandarin. I had asked for a royalty but ended up with a cup of green tea! The interleaved sampling protocol had been tested and was incorporated in several ISO Standard Methods. Professor Dr Michel David took a seat close to where I stood behind a lectern. He may have listened but posed no questions. He had studied how Matheron’s new science of geostatistics should be put into practice! Matheron and his disciples had done so by stripping the variance off the distance-weighted average and calling what was left a kriged estimate. Infinite sets of distance-weighted averages AKA kriged estimates and zero kriging variances metamorphosed into the heart and soul of Matheron’s new science of geostatistics. So much so that the world’s mining industry embraced his novel science with reckless abandon. All I did was prove the intrinsic variance of gold at Bre-X’s property to be statistically identical to zero. But it did take a sound grasp of the properties of variances!

I have kept David’s 1977 Geostatistical Ore Reserve Estimation and Volk’s 1958 Applied Statistics for Engineers side-by-side on a bookshelf. Dr David didn’t know how to derive unbiased confidence limits for contents and grades of reserves and resources. What’s more, David did not know how to test for spatial dependence between ordered sets of measured values by applying Fisher’s F-test to the variance of the set and the first variance term of the ordered set. In Table 1.IV on page 25 Dr David pointed to the chi-square distribution for copper grades at Prince Lyell. David’s Index should have but did not refer to degrees of freedom on page 358. He should have listed degrees of freedom between deflected holes and density. Neither Professor Matheron nor any disciple such as Professor Dr David grasped how to test for spatial dependence between measured values in ordered sets.

Elsevier Scientific Publishing Company printed the First Edition of Geostatistical Ore Reserve Estimation in The Netherlands in 1977. Reprints were distributed in 1978, 1979 and 1982. None showed how to test for spatial dependence between ordered sets, or how to derive unbiased confidence limits for metal contents and grades of ore reserves. David cautioned that “… statisticians will find many unqualified statements…” and that “… it is not a book is not for professional statisticians…” Did he ask professional statisticians to show him how to test for spatial dependence and how to count degrees of freedom? Did David know how to derive unbiased confidence intervals and ranges for metal contents and grades of reserves and resources?    

 Here’s what Professor Dr Michel David revealed in his Introduction: “The financial help of the National Research Council of Canada (Grant NRC7035) is gratefully acknowledged as well as the opportunity to use the drafting facilities of the department of Mineral Engineering at Ecole Polytechnique.” One more contribution of Professor Dr Michel David to the evolution of Professor Georges Matheron’s science of geostatistics surfaced in his 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation. The author explicates: “This work was produced at Ecole Polytechnique de Montréal and its services are greatly appreciated. Many of the results presented were obtained in the course of research funded by the Natural Science and Engineering Research Council of Canada (grant 7035)”. Dr Roger A Blais, CC, OQ, MSRC, played a pivotal in keeping grant 7035 coming. I was left to unscramble the Bre-X fraud after geostatistical software had converted Bre-X’s bogus gold grades and Busang’s barren rock into a massive phantom gold resource.  And I did!

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

A study on kriging small blocks

Margaret Armstrong and Normand Champigny called on but a few facts to get their small block study going in the 1980s. Following are two (2) facts that underpin their study:

Mine planners often insist on kriging very small blocks
Kriged estimates of very small blocks are over-smoothed

These geostatistical scholars had found out that kriged block grade estimates and measured grades no longer display associative dependence when variogram ranges are less than half the spacing between samples. Good grief! I couldn’t have thought that up even if I were a crafty kriger or a cunning smoother! Surely, geologists and mining engineers didn’t expect kriging to create random numbers! Yet, CIM Bulletin put in print what the authors thought about the rise and fall of kriging variances. Who were the peers who reviewed Armstrong and Champigny’s study? Didn’t they know why the kriging variance rises up to a maximum and then drops off? Who was the Editor of CIM Bulletin in 1989? What did she or he think of the rise and fall of kriging variances? But why did P I Brooker think in 1986 that kriging variances are robust?

Armstrong_Figure_2

Figure 2. Kriging variance as a function of the variogram range

After CIM Bulletin of March 1989 had landed on my desk it took but little time to figure out what was wrong with Armstrong and Champigny’s study. I didn’t find out that Matheron had flunked his PhD thesis in 1965 until his magnum opus was posted on a massive website. His disciples in 1970 stripped the variance off the distance-weighted average, and called what was left a kriged estimate! Infinite sets of kriged estimates and zero kriging variances made no sense in any scientific discipline but Matheron’s new science of geostatistics. Geostatistocrats kept kriging and smoothing simply because blatantly biased and shamelessly self-serving peer reviews made Matheron’s new science go too far. CIM Bulletin should have never approved and published A study on kriging small blocks. One-to-one correspondence between functions and variances is sine qua non in mathematical statistics! It would be a walk in the park to prove in a court of law that Matheron’s new science of geostatistics is an invalid variant of mathematical statistics.

Armstrong and Champigny studied kriging small blocks at the Centre de Géostatistique, Fontainebleau, France. Armstrong got what Matheron had failed to get in 1965. She was awarded a PhD in geostatistics at Matheron’s centre early in this century. She had already been awarded a Master’s degree in mathematical statistics at the University of Queensland, Australia. Why then didn’t she know how to test for spatial dependence between measured values in ordered sets by applying Fisher’s F-test to the variance of the set and the first variance term of the ordered set? Why hadn’t she mastered how to count degrees of freedom? Why did she allude to the fact that mine planners are often tempted to krige very small blocks. Does she deserve credit for asking how small is “too small”? I was pleased to note that Normand Champigny had been awarded a Diploma of Geostatistics. What a pity he didn’t know how to test for spatial dependence, and why degrees of freedom ought to be counted.

CIM Bulletin reviewed A study on kriging small blocks and published it under Ore Reserve Estimation in March 1989. All I want to know who approved this study for CIM Bulletin. Geostatistical peer review at CIM Bulletin was a blatantly biased and shamelessly self-serving sham. It got a lot worse after the Bre-X fraud. What has made peer review at CIM Bulletin a farce is the fact that Markov chains are strung to define stochastic mining plans!

Scores of geostatistocrats have been taught how to krige and smooth at the Centre de Géostatistique in Fontainebleau, France. Yet, Matheron himself did not know how to test for spatial dependence in 1965. What he did do in 1970 was think up Brownian motion along a straight line. He talked about his vision at The University of Kansas, Lawrence in June 1970.  Maréchal and Serra, in turn, had thought up Random Kriging. They derived sixteen (16) distance-weighted averages AKA kriged estimates from the same set of nine (9) measured values. David’s 1977 Geostatistical Ore Reserve Estimation on page 286 in Chapter 10 The Practice of Kriging shows the very same set that Maréchal and Serra’s Random Kriging had worked with in 1970.

MS_Fig10

Michel David’s 1977 M&S picture

Geostatistical software converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Applied statistics proved the intrinsic variance of Bre-X’s gold to be statistically identical to zero. It did so several months before Bre-X’s boss salter passed away, and before Munk’s Golden Phoenix was put in print.

What’s wrong with Matheron’s 1965 PhD Thesis

Once upon a time a young geologist in Algiers derived the degree of associative dependence between lead and silver grades of drill core samples. What he didn’t derive were length-weighted average lead and silver grades. Neither did he test for spatial dependence between metal grades of ordered core samples. This geologist did do it with a bit of applied statistics so he called his article Note statistique No1! In time, one of several scores of dedicated disciples decided to change it to Note géostatistique No1. Somebody do so after the Internet was born! The same disciple is still the custodian of Matheron’s magnum opus. He may well want to play with Matheron’s new science of geostatistics from the 1950s to eternity. Good grief! That’s long time! And it’s a headache already! The more so since Note géostatistique No28 shows “krigeage” in its title. Did Matheron ever ask Krige whether he wanted his name to become a genuine eponym?

Matheron was a master at working with mathematical symbols. He couldn’t possibly have taught his disciples how to test for spatial dependence between mathematical symbols. What’s more, he didn’t even know in the 1950s how to test for spatial dependence between measured values in ordered sets. Neither did he know how to test for spatial dependence in his 1965 PhD thesis! As a matter of fact, Matheron has never tested for spatial dependence between measured values in ordered sets. 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. Degrees of freedom for both sets ought to be counted and taken into account. Matheron is remembered either as the Founder of Spatial Statistics or as the Creator of Geostatistics. I don’t care what his disciples called him. What I care about is that he didn’t know how to test for spatial dependence by applying Fisher’s F-test! Why did Matheron strip the variances off distance-weighted averages cum kriged estimates? And why did he assume spatial dependence between measured values in ordered sets?

Those who were to judge Matheron’s PhD Thesis on November 10, 1965 may well have asked him to put in plain words the nitty-gritty of his thesis.  Matheron had called it “LES VARIABLES RÉGIONALISÉES ET LEUR ESTIMATION”. His PhD supervisors were Professor Dr Swartz, President, Professor Dr Fortet and Professor Dr Caileux, Examinators. This team proposed a second thesis with the title “PROPOSITIONS DONNÉES PAR LA FACULTÉ”. Did Matheron’s supervisors ask him to jump hoops? And how far would Matheron jump to defend variance-deprived distance-weighted averages cum kriged estimates? The very first page of a whopping 301 pages of Matheron’s 1965 thesis mesmerized me. Why had Matheron cooked up a pair of prime data sets? Why were both inserted under INTRODUCTION on the very first page? Why didn’t he show how to test for spatial dependence? Why didn’t PhD candidate George Matheron know how to test for spatial dependence and count degrees of freedom?

Matheron_Thesis_data
All it takes to test for spatial dependence is to compare observed F-values with tabulated F-values. Of course, degrees of freedom ought to counted and be taken into account. I have applied Fisher’s F-test to verify spatial dependence in sample spaces and sampling units alike. I have done so ever since I worked on ASTM and ISO Standards. Geostatistical software converted Bre-X’s bogus grade and Busang’s barren rock into a massive phantom gold resource.  I unscrambled the Bre-X salting scam by proving that the intrinsic variance of gold was statistically identical to zero. Of course, it is of critical importance to grasp the properties of variances.

Matheron_Stats
It became Matheron’s new science of geostatistics when the variance was stripped off the distance-weighted average and what was left was called it a kriged estimate. Did Matheron really think had created a new science. Geostatistocrats thought he really  did! Good grief!