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 the federal government 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!
An International Forum in honour of Professor Dr Michel David’s contribution to geostatistics? What’s this world coming to! I had resolved to read David’s 1977 Geostatistical Ore Reserve Estimation after Elsevier had published it. David’s work is not a part of any ISO Standard but ISO standards have been my bread and butter since I joined ISO/TC102 – Iron Ore in 1974. The ASTM Board of Directors in 1995 awarded me 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!
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!
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!
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.
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
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!
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!
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?
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.