Professor Dr Roussos Dimitrakopoulos came up all the way from Down Under to chair a Forum on Geostatistics for the Next Century at McGill University on June 3-5, 1993. His task was to honor Professor Dr Michel David for writing the very first textbook on Matheron’s new science of geostatistics. David didn’t know how to test for spatial dependence and how to count degrees of freedom. He wrote his first textbook against all odds since he didn’t even know that functions do have variances. I have written quite a bit about the properties of variances. So, I send by registered mail an abstract to that futuristic forum at McGill University. Some person at McGill’s Conference Office encouraged me in an unsigned letter of March 31, 1993, to submit my abstract to another event. I'll have to dig up more bits and pieces about genuine variances.

Dimitrakopoulos likes McGill a lot. In fact, he settled down in La Belle Province after the Bre-X fraud was no longer on his mind. In a candid interview with the National Post on August 15, 2005, he clarified the intricacies behind his valuations of mining projects. Here’s what he said, “You drill a few holes, you think you understand something but what you know is very, very little. Uncertainty means probabilistic models, and there are a gazillion types of them.” How about that? Some mining investors might wonder how RD selects the least biased probabilistic model. Peter Ravenscroft, a senior executive with Rio Tinto and an expert at geostatistics, thinks what RD does is kind of cool and gave him a stack of dough.

Professor Dr Roussos Dimitrakopoulos was present at APCOM 2009 in Vancouver, British Columbia. The first line of his abstract reads, “Conventional approaches to estimating reserves and optimizing mine planning and production forecasting result in single, often biased forecasts.” I wonder what would have happened if Stochastic Mine Planning Optimization: New Concepts, Applications, and Monetary Value in an Ever Uncertain Market, had been applied to Bre-X’s exploration data. I also wonder why regulators and financial institutions do not insist the International Organization for Standardization set up a Technical Committee on Reserve and Resource Estimation. It's long past due! Matheron thought he was a statistician in 1954. Yet, his Note Statistique No 1 shows he didn't know how to test for spatial dependence between metal grades in ordered core samples. Neither did he know how to derive variances of length-weighted average lead and silver grades determined in core samples of variable lengths. So much for Matheron's new science of geostatistics!

Dr Frederik P Agterberg wrote in 2000 that Matheron was the Founder of Spatial Statistics. Matheron thought he was a statistician in 1954 when he wrote his Note Statistique No 1. He didn't write about spatial dependence between metal grades of ordered core sections with variable length. He did derive length-weighted average lead and silver grades but didn't derive the variances of these central values. In 1907 he stirred up "Brownian motion on a straight line." He did so because he liked Riemann integrals better than Riemann sums. He wrote in his 1978 Foreword to Mining Geostatistics why he proposed the name geostatistics in the 1960s. Professor Georges Matheron would have been shocked had he read in his obituary that he was the Founder of Spatial Statistics. Agterberg invited me on October 1, 2004, to present my views at the next IAMG annual meeting in Toronto. I happen to know a lot about IAMG events where geostatistocrats talk bafflegab. I would rather make my case against bogus stats at APCOM 2009.

Dr Michel David wrote a few words of caution in his 1977 Geostatistical Ore Reserve Estimation. First, he wrote, "...statisticians will find many unqualified statements..." Then, he blew the sales of his work by writing, "This is not a book for professional statisticians." But he was indeed right. David did prove it when he wrote his test for geostatistical proficiency. He took M&S's set of nine (9) measured values and "estimated" the same set of sixteen (16) what he came to call "...points..." He wrote on page 286 of his textbook, "Writing all the necessary covariances for that system of equations is a good test to find out whether one really understands geostatistics." Why did the author of the very first textbook on geostatistics fail to derive the variance of each of this sixteen (16) functionally dependent values? Why didn't he count degrees of freedom? If M&S's set of nine (9) measured values were evenly spaced, the set and the ordered set would give df=n-1=8 and dfo=2(n-1)=16 respectively. Why is the geostatocracy still asleep at the switch? Why is Bre-X's massive phantom gold resource all but forgotten?

A Marechal and J Serra wrote Random kriging in 1970 to celebrate the first krige and smooth bash in North America. M&S toiled under Matheron's tutelage at his Center de Morphology Mathematique, Fontainebleau, France. So, why did M&S set out to simplify Matheron's kriging equations with their own random kriging procedure? Under Punctual Kriging in Random kriging they show how to get a set of sixteen (16) functionally dependent values from a set of nine (9) measured values. M&S didn't show how to derive a variance of a functionally dependent value. Neither did they show 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. What Matheron never taught M&S was how to count degrees of freedom. In his own 1970 Random functions and their applications in geology Matheron wrote, "Let us denote a Brownian motion on a straight line." In Matheron's mind it somehow seemed to replace Riemann sums with Riemann integrals. Matheron never explained what Brownian motion and ore deposits have in common. M&S put Random kriging "within the geostatistical framework of the French school." Go figure why!

Dr Isobel Clark is the author of Practical Geostatistics. She wrote on the first page of Chapter 5 Kriging, "It would seem sensible to use a weighted average of the sample values, with the 'closer' sample values having more weight." On the same page she wrote, "The arithmetic mean is simply a special case where all the weights are identical." She wrote in her Preface that Journel and others at Fontainebleau taught her all she knows about the theory of the Theory of Regionalized Variables." She transposed for "mathematical convenience" the factor two (2) in dfo=2(n-1), the number of degrees of freedom for an ordered set of n measured values. That's how Clark's semi-variogram was born. Why did Fisher's F-test for spatial dependence between hypothetical uranium data fail to make Clark's grade in her 1979 Practical Geostatistics? And why does nobody care?

Statistically dysfunctional geoscientists write all sorts of things that are bound to hound them in time. Read what Stanford’s Journel wrote to the Editor of the Journal for Mathematical Geology. What he did was set the stage for conditional simulation on Stanford stationary. Take note of when he wrote it. And read what JMG’s Editor wrote to me. So, my feeling that geostatistics is invalid might be correct. How about that? He also wrote that different “flavors” of geostatistics may fail at different times. Now that’s kind of cool. I do know which flavor failed in the Bre-X fraud. It was the flavor of assuming continued gold mineralization between salted boreholes. The odd geostatistician might be taught how to test for spatial dependence and how to count degrees of freedom. Most are doomed to assume, krige, smooth, and rig the rules of statistics.

## Wednesday, September 09, 2009

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