Vale Malaysia Minerals (VMM), eine Tochtergesellschaft des brasilianischen Bergbaukonzerns Vale SA mit Sitz in Rio de Janeiro, hat die BEUMER Group mit der Lieferung von 16 Muldengurtförderern beauftragt.
Bei der Herstellung von Wurst- Fleisch-und Fischwaren sowie anderen Lebensmitteln werden große Mengen Gewürze und Gewürzmischungen eingesetzt. Die Gewürze sollen im industriellen Produktionsprozess möglichst keimfrei in die Lebensmittel gelangen. Längeres Erhitzen kommt nicht in Frage: das würde zwar die Keime abtöten, aber auch die Geruchs- und Geschmackstoffe zerstören oder austreiben.
The caption on my website reads: “Geostatistics: From human error to scientific fraud.” Much of it is still the way it was when I posted it in August 2005. Those who wish to grasp geosciences ought to take a close look at what it took Professor G Matheron to cook up his new science of geostatistics. Here’s what he did do in a nutshell! He stripped the variance off the distance-weighted average and called what was left a kriged estimate. Infinite set of kriged estimates and zero kriging variances became the heart and soul of Matheronian geostatistics. Matheron’s disciples quickly went to work with infinite sets of kriged estimates and zero kriging variances. It was not so much a shame that Matheron goofed! What was a shame is that so many of his disciples goofed along! Fisher’s F-test and degrees of freedom never played a role in Matheron’s novel science of geostatistics. It is simple comme bon jour to find out that geostatistocrats neither took to testing for spatial dependence nor to counting degrees of freedom!
Professor G Matheron defied his PhD supervisors and flunked
What made Matheron’s new science of geostatistics click? Who knows! Stripping the variance off the distance-weighted average and calling what’s left “a kriged estimate” made no sense at all. All the same, infinite sets of kriged estimates and zero kriging variances became the heart and soul of geostatistics. So what did young Matheron do with applied statistics in 1954? He tested for associative dependence between lead and silver grades of drill core samples. The degree of associative dependence between lead and silver grades turned out to be ρ=0.85. What he didn’t do was test for spatial dependence between grades of ordered core samples. Neither did he derive weighting factors to take into account that core samples varied in density and length. Matheron marked it Note Statistique No 1 but made a correction. Sets of primary data were not as prominent in Matheron’s work as were his superstrings of symbols. The custodian of Matheron’s magnum opus thought it fitting to change Note Statistique No 1 to Note Geostatistique No 1. Perhaps a touch of deception but Matheron’s novel science was not going anywhere fast in deep time. Are all of Matheron’s sets of measured data archived? Was D C Krige tickled pink when his name turned into a genuine eponym? Many questions have yet to be answered!
It took chutzpa to go the USA in June 1970 and peddle geostatistics as a new science. The more so since Professor Matheron would rather flunk his PhD thesis than reunite the distance-weighted average and its variance! So here’s how he flunked! His PhD supervisors had asked him to show how to test for spatial dependence between sets of randomized and ordered whole numbers. Yet, Matheron saw fit to ignore this request! His PhD thesis was called Regionalized variables and their estimation”. It added up to 301 pages of dense text with two (2) sets of whole numbers on the first page followed by scores of symbols on the next 300. What his PhD supervisors had asked him to do is to test both sets for spatial dependence. Since nobody had been inspired to do so I took to testing each set for spatial dependence.
M&S derive 16 kriged estimates
Matheron brought along a pair of his disciples. Matheron talked about Brownian motion along a straight line. Marechal and Serra talked about Random Kriging and showed how to derive 16 kriged estimates from 9 measured grades. David pointed to M&S’s Figure 10 on page 286 in his 1977 . David wondered how to make infinite sets of simulated values smaller. Good grief! Matheron’s new science was a gift to those who ignore the power of Fisher’s F-test and the concept of degrees of freedom. So he got the world stuck with infinite sets of variance-deprived kriged estimates and zero kriging variances! That’s what Matheron’s gift to mankind has been in a nutshell. Incredibly, he was hailed not only as the Founder of Geostatistics but also as the Creator of Spatial Statistics. Professor G Matheron passed away the 7th of August 2000.
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?
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.
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.
William Volk in his Preface pointed out that his take of applied statistics is traceable to a course he had taught in 1951. The McGraw-Hill Book Company published the first print in 1958. Its frontispiece reads: “for Dorothy whose confidence is without limits”. What a touching view on confidence without limits! I bought my first copy in the 1960s when I was working in the Port of Rotterdam. I have placed Jan Visman’s 1947 PhD thesis on coal sampling and William Volk’s Applied Statistics for Engineers side-by-side on the same bookshelf. I have tried to find out more about Volk after we had come to Canada in 1969 but to no avail. I wanted to write a Wiki page about Volk, his textbook, and his grasp of variances as displayed in Section 7.1.4 Variance of a General Function and in Section 7.3 Confidence Range of Variances. I still wonder whether or not Volk was of Dutch decent.
It was fortunate to have met Jan Visman and Greg Gould on ASTM Coal and Coke. I found out the hard way that TUDelft did not teach Visman’s take on coal sampling. I have learned most about Visman and his sampling theory after he went from Ottawa to Edmonton. I wrote a Wiki page about Dr Jan Visman and his work. His sampling theory underpins the interleaved sampling protocol. It was readily accepted for mineral concentrates simply because it gives a single degree of freedom for each sampling unit. ASTM recognized me for 25 years of continuous membership in 1995. Good grief! All I really did was do what I like to do! The more so since Matheron’s curse of his novel science of geostatistics had not yet impacted my work. On a trip to Australia I lost a copy of Volk’s Applied Statistics for Engineers. What’s more, Australian customs confiscated my bag with red and white beans. I knew a bit about toads and rabbits but never thought red and white beans were as bad. I used my beans to prove that large increments give a higher degree of precision than small increments. Simple comme bonjour! Testing for spatial dependence between measured values in ordered sets was straightforward with on-stream analyzers. When Volk wrote about the power of Student’s t-test to detect a bias, he showed how to derive Type I errors and Type II errors. I have taken to talking about Type I risks and Type II risks.
Gy’s 1979 Sampling of Particulate Materials and Volk’s 1980 Applied Statistics for Engineers still stand side-by-side on the same shelf. Gy had mailed me a copy with his compliments and his invoice on Christmas 1979. Elsevier Scientific Publishing Company has released it as Part 4 in Developments in Geomathematics. Part 1 is Agterberg’s 1974 Geomathematics and Part 4 is David’s 1977 Geostatistical Ore Reserve Estimation. Missing in Gy’s textbook between degenerate splitting processes and degree of representativeness are degrees of freedom. Gy points in Section 31.3 on page 381 to “a Student-Fisher’s t distribution with ν=N-1 degrees of freedom (DF)”. Gy was almost on the mark. His wordy gems struck me as Gy’ologisms! His references to Matheron’s new science of geostatistics are beyond the pale. Next to Gy’s 1979 Sampling of Particulate Materials, Theory and Practice on the same shelf stands David’s 1977 Geostatistical Ore Reserve Estimation, Journel & Huijbregts 1978 Mining Geostatistics, Clark’s 1979s Practical Geostatistics, and Mandel’s 1964 The Statistical Analysis of Experimental Data.
What Matheron and his disciples cooked up at a geostatistics colloquium on campus of The University of Kansas, Lawrence on 7-9, 1970 will not stand the test of time. Matheron conjured up Brownian motion along a straight line. His disciples stripped the variance off the distance-weighted average and called what was left a kriged estimate. Infinite sets of variance-deprived kriged estimates and zero kriging variances added up to the genuine scientific fraud of geostatistics.
“Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.”
H G Wells (1866-1946)
Wells was a prolific writer with a keen sense of rights and wrongs in his life and time. What had inspired him to praise statistical thinking were the works of Karl Pearson (1857-1936), and of Sir Ronald Aylmer Fisher (1890-1962). Pearson worked with large data sets whereas Fisher worked with small data sets. That was what inspired Fisher to add degrees of freedom to Pearson’s chi-square distribution. Thus was born a feud between giants of statistics. Degrees of freedom converted probability theory into applied statistics, and sampling theory into sampling practice. Fisher and Pearson were both outstanding statisticians. They inspired H G Wells and scores of statisticians. Applied statistics shall stand the test of time until our sun bloats into a red giant and Van Gogh’s Sun Flowers are bound to burn to a crisp.
Why did geoscientists get into geostatistical thinking? All it took was a young French geologist who went to work at a mine in Algeria in 1954. He measured associative dependence between lead and silver grades of drill-core samples. But he did not count degrees of freedom. So, he did not know whether his correlation coefficient was significant at 95%, 99% or 99.9% probability. What is more, his drill-core samples varied in length. As a result, the number of degrees of freedom is a positive irrational rather than a positive integer. He did not know how to test for spatial dependence by applying Fisher’s F-test to the variance of the set of measured values and the first variance term of the ordered set. His first paper was not peer reviewed. Nobody asked him to report primary data and give references. As luck would have it, he was without peers. Professor Dr Georges Matheron and his magnum opus were accepted on face value. His students thought of him as “creator of geostatistics”. Dr Frederik P Agterberg in his eulogy called him “founder of spatial statistics”. Yet, between 1954 and 2000 Professor Dr Georges Matheron did not teach his disciples how to test for spatial dependence and how to count degrees of freedom.
My son and I wrote Precision Estimates for Ore Reserves. It was based on applied statistics as it had been developed by Fisher and Pearson and was praised by Wells. We did 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. We had studied David’s 1977 Geostatistical Ore Reserve Estimation. Professor Dr Michel David did not show how to test for spatial dependence and how to count degrees of freedom. Our paper was submitted to CIM Bulletin on September 28, 1989. We did not criticize geostatistics nor did we refer to it. CIM Bulletin rejected it but Erzmetall praised and published it in October 1991.
Bre-X Minerals was selling stock and getting ready to drill at Busang. The internet would not be ready for a while. The mining industry liked unbiased confidence limits for masses of metals contained in mined ores and mineral concentrates. What it did not like in the 1990s and still does not like in 2010 are unbiased confidence limits for masses of metals contained in reserves. I had sent to CIM Bulletin on September 21, 1992, an article on Abuse of Statistics. The Editor advised that articles of a controversial nature can be published in CIM Forum. I was asked to cite a specific reference for the quotation in which H G Wells spoke so highly about statistical thinking. I had found it long ago in Darrell Huff’s How to lie with statistics. Penguin Books published the first edition in 1954 when young Matheron worked in Algeria. Matheron and Agterberg would have been pleased had Wells praised geostatistical thinking.
Geostatistics messed up the study of climate change. Spatial dependence in our sample space of time may or may not dissipate into randomness. Sampling variogram shows whether, where and when it does. High school students ought to be taught how to construct sampling variograms. It would have made H G Wells smile.
Professor G Matheron didn’t grasp in 1965 how to test for spatial dependence in sample spaces. What he did in 1970 is evoke Brownian motion along straight lines. He was scheduled to speak about it at the University of Kansas, Lawrence, Kentucky. He had taught A Marechal and J Serra all about kriging and smoothing at the Centre de Morphology Mathematique, Fontainebleau, France. Matheron has never explained why he stripped the variance off the distance-weighted average and called what was left a kriged estimate. Neither did The Founder of Spatial Statistics put in plain words why the distance-weighted average had metamorphosed into a kriged estimate. It was not D G Krige who called it a kriged estimate but Matheron! That’s in a nutshell why Professor Matheron could do so much with so little!!
Professor George Matheron had decided to talk about Random Functions and their Application in Geology. That’s when he talked about Brownian motion along straight lines. But a global estimation problem surfaced. Marechal and Serra did in Random Kriging in 1970 what M David would do in his 1977 Geostatistical Ore Reserve Estimation. In fact, M&S’s Figure 10 showed in 1970 what David’s Figure 203 did on page 286 of Chapter 10 The Practice of Kriging. One cannot possibly trust geostatistocrats who reject the Central Limit Theorem, the concept of degrees of freedom, and the power of Fisher’s F-test.
Dr F P Agterberg and his Autocorrelation Functions in Geology caught my attention when I perused his article. He was in those days no longer with the Kansas Geological Survey but with the Geological Survey of Canada. Figure 1 shows what Agterberg in 1970 had called:
Figure 1. Geologic prediction problem: values are known for five irregularly spaced points P1-P5. Value at P0 is unknown and to be estimated from five known values.
Fig. 64 Typical kriging problem; values are known at five points. Problem is to estimate value at point P0 from the known values at P1-P5.
This figure is also a take on Agterberg’s work. He is the author of Geomathematics, Mathematical Background and Geo-Science Applications. It was published in 1974 by Elsevier Scientific Publishing Company, Amsterdam New York. Dr F P Agterberg, in his 2000 tribute to Professor Dr G Matheron, remembered him as the Founder of Spatial Statistics. Yet, Matheron had never tested for spatial dependence between measured values in ordered sets. On the contrary, he was a master at assuming spatial dependence where it didn’t exist. Matheron could not have tested for spatial dependence at his Center de Morphology Mathematique. Why teach Fisher’s F-test if students are taught to assume spatial dependence? Agterberg’s tribute to Matheron taught me a lot about his thinking. When he was a graduate student at the University of Utrecht young Agterberg presented at the Technical University of Delft (TUDelft) a seminar on the skew frequency distribution of ore assay values. But that’s another part of my narrative!
Put it on paper; call it a PhD thesis; get it approved! Simple comme bonjour, n’est-ce pas! But the PhD supervisors at Université de Paris Sorbonne did not approve Professor Georges Matheron’s PhD thesis. On the contrary, they wanted to know what I have wanted to know for a long time! The title of Matheron’s thesis was “Les variables régionalisées et leur estimation: une application de la theory des fonctions aléatoires aux sciences de la nature”. How about that? Thank goodness French was my very first foreign language!
How did Matheron test for spatial dependence in sample spaces and sampling units? He never did! That is why Matheron got stuck on the very first page of his PhD thesis. He didn’t know in 1965 how to test for spatial dependence between measured values. His PhD supervisors had posted on his thesis two (2) sets of whole numbers with the same central value. One set was ordered and the other was randomly distributed. Matheron’s PhD thesis added up to 301 pages of dense text and scores of symbols. But his PhD supervisors deemed it not enough to merit a PhD in his novel science of geostatistics! It’s rather silly that the Creator of Geostatistics and the Founder of Spatial Statistics did not know how to test for spatial dependence between sets of integers. But why didn’t he know? Applying Fisher’s F-test and counting degrees of freedom have never been part and parcel of his novel science. His failure to test for spatial dependence was part and parcel of what he fondly called his new science of geostatistics when he took it to North America in June 1970.
Professor Georges Matheron came with his most gifted disciples. Neither knew how to 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. His disciples believed Matheron was teaching a new science. His PhD supervisors were aware that his new science was an invalid variant of applied statistics. Matheron’s thinking was alive in the eyes of his disciples. He had always taught that a distance-weighted average AKA a kriged estimate does not have a variance. How about that? Strip the variance off the distance-weighted average and call what’s left “a kriged estimate”. Good grief! Distance-weighted averages have variances but kriged estimates no longer do! D G Krige had not come all the way to Lawrence, Kansas. M David and A G Journel were busy writing textbooks about Matheron’s novel science.
A colloquium took place on campus at the University of Kansas, Lawrence in June 1970. D F Merriam, Chief of Geologic Research, Kansas Geological Survey, kept a record and Plenum Press put it in print. No list of visitors was kept. The event was useful to those who do work with applied statistics. Koch and Link, the authors of Statistical Analysis of Geological Data, talked about their work. Part I was published in 1970 and Part II came along in 1971. Both the famous Central Limit Theorem and the concept of Degrees of Freedom are still alive in Koch and Link’s work. I have had copies of both parts since the 1970s. I have used a data set in Sampling and Weighing of Bulk Solids. Tukey’s WSD test has also played a role in my work. Some Further Inputs describes what Professor Dr J W Tukey had seen in real time at Lawrence, Kansas. He wondered what would happen in two-dimensional sample spaces. Good grief! I was already working with three- dimensional sampling units and sample spaces.
Marechal and Serra’s Random kriging and Matheron’s Random Functions and their Application in Geology had both been cooked up either at the Centre de Géostatistique or at Centre de Morphologie Mathématique. The variance had been stripped off the distance-weighted average and the concept of degrees of freedom was dismissed. Why did the geostatistical mind have distance-weighted averages morph into kriged estimates? The odd geostatistocrat may still remember the “famous Central Limit Theorem”. All it would have taken is a passing grade in Statistics 101.
Matheron talked about Random Functions and their Application in Geology. He set the stage with a bizarre paradigm of Brownian motion along a straight line in deep time. It made counting degrees of freedom an exercise in extreme futility. Those who would have been tempted to count them would have scored a failing grade on Geostatistictics 101. Ranked high among vagaries in Matheron’s take on spatial dependence was his reference to the “quasistationarity” condition! Good grief!
Marechal and Serra talked about Random Kriging. Terms such as punctual kriging put into perspective what this new science of geostatistics was all about. Figure 10 did as little for Matheron’s new science as it would do for David’s 1977 Geostatistical Ore Reserve Estimation. David refers to the same infinite sets of distance-weighted averages cum kriged estimates in his textbook
Figure 10 – Grades of n samples belonging to
nine rectangles P of pattern surrounding x
A facsimile of Marechal and Serra’s Figure 10 is given in David’s first textbook as Fig. 203 on page 286 in Chapter 10 The Practice of Kriging. The National Research Council of Canada has given generous support to David’s imperfect thinking. It did so with its Grant NRC7035. NRC did not engage in statistical quality control in those days. NRC has a new name but approves Markov chains. So much for SQC!
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?
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.
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!