Professor Dr Margaret Armstrong and Professor Dr Roussos Dimitrakopoulos rank amongst the most gifted geostatistocrats on our little planet. What a shame that they smooth data sets beyond perfect fits! Dr RD is into stringing Markov chains between measured values! What he should not do is assume spatial dependence between measured values in ordered sets. What he ought to do is count degrees of freedom. Stringing Markov chains does not create spatial dependence anywhere in this universe!
Professor Dr Margaret Armstrong ranks high amongst geostatistical scholars. In contrast, Mr Normand Champigny has earned a Certificate of sorts and turned into a gifted CIM Member. CIM Bulletin published this small block study in March 1989. What the authors had discovered was that “kriged estimates for very small blocks are over-smoothed”, and that “mine planners often insist on kriging very small blocks!” Good grief! The problem is not so much that mine planners have not been taught how to test for spatial dependence between measured values in ordered sets. The real problem is that Professor Matheron did not know how to test for spatial dependence between measured values, and how to count degrees of freedom! So it was not at all surprising when Matheron flunked his PhD thesis in 1970! Yet, n 1974 Matheron was ready to teach “Brownian motion along straight lines!” He has been hailed as the Founder of Spatial Statistics! For crying out loud!
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.
That’s printed above the title page! Smaller print lower on the same page refers to A Sampling Manual and Reference Guide for Environment Canada Inspectors, First Edition. I perused its 231 pages and thought it ought to be revised. The more so since geostatistics is an invalid variant of applied statistics. Here’s why! A French scholar in the 1970s stripped the variance off the distance-weighted average, and called what was left a kriged estimate. Infinite sets of kriged estimates, zero kriging variances and zero degrees of freedom underpin Matheron’s science of geostatistics. Incredibly, geostatistics is an integral part of 2.0 Sampling in the Field and of 2.1 Site Selection and Documentation. The question is then why a stratified systematic sampling is an integral part of its very First Edition!
William Volk’s 1958 Applied Statistics for Engineers has put into plain words how to measure associative dependence between a function and its variance. Volk did so in Section 7.1.4 Variance of a General Function. He pointed out it was his only expansion into calculus! He had been awarded a Master’s degree in mathematical statistics at Rutgers University in 1951. Volk was familiar with the properties of functions and variances. He also knew how to count degrees of freedom and why!
Volk’s knowledge of the properties of variances showed that Sir R A Fisher (1890-1962) had inspired William Volk. It was Fisher who pioneered the concept of degrees of freedom for small data sets to counter Pearson’s χ²-distribution for large data sets. He had built a bridge between probability theory and homogeneous populations but also between applied statistics and finite sets of samples taken from all sorts of sampling units and sample spaces. Sir R A Fisher had given William Volk permission to include Table 7.8 in his 1958 Applied Statistics for Engineers.
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!
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!
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.