Thursday, June 28, 2012

UBC still stuck with geostatistics

 Professor Dr Alastair J Sinclair has been teaching earth sciences at the University of British Columbia since 1964. It was but a dozen years after Matheron tried his hand at applied statistics. Young Georges Matheron in 1952 was an up-and-coming geologist in Algiers. He had a penchant for applied statistics in those days. For example, he knew how to test for associative dependence between lead and silver grades in drill core samples of variable lengths. What he did not know was how to derive variances of length-weighted average lead and silver grades. Perhaps ironically, young Matheron at that time thought he was working with applied statistics. Yet he didn’t know how to test for spatial dependence in sample spaces and sampling units by applying Fisher’s F-test to the variance of the set and the first variance term of the ordered set.  Neither did he derive length-weighted average lead and silver grades for his data set.

Professor Dr Georges Matheron
Abuser of applied statistics

Creator of geostatistics
Founder of spatial statistics

Professor Dr Georges Matheron was not at all into sharing primary data with his students. Even for his 1965 PhD Thesis he saw fit to cook up a funny pair of minuscule primary data sets.

 Matheron's primary data sets for 1965 PhD Thesis

So I have decided to show how to test for spatial dependence between Matheron’s make-believe primary data. All I did was apply Fisher's F-test to the variance of the set and the first variance terms of the ordered set and compare the observed F-values with tabulated F-values.

Stats for Matheron's 1965 PhD Thesis

Matheron’s magnum opus is posted on a massive website. Its webmaster made a few minor changes to suggest that Matheron had applied geostatistics somewhat sooner than he had done in real time.

It is ironic to the extreme that geostatistics was hailed as a new science when Matheron and his disciples brought it to campus at the University of Kansas in June 1970. Matheron’s own tour-de-force at this colloquium was to invoke Brownian motion along a straight line. He did so to infer that his random functions are continuous between measured values. The study on Random kriging by A Marechal and J Serra at the Centre de Morphology Mathematique seemed successful under Matheron’s supervision. Figure 10 in this 1970 study metamorphosed in Figure 203 on page 286 in Chapter 10 The Practice of Kriging in Professor Dr Michel David’s 1977 Geostatistical Ore Reserve Estimation.

David’s 1977 textbook and Gy’s 1979 Sampling of Particulate Materials, Theory and Practice, stand side-by-side on a shelf in my office. One time soon I’ll use them to prove how the French sampling school has messed up statistical thinking. And all it really took was to ignore one-to-one correspondence between functions and variances, to assume spatial dependence between measured values in ordered sets, and to pay no attention to counting degrees of freedom.

Dr Alastair J Sinclair, PEng, PGeo
UBC Emeritus Professor

Professor Dr Alastair J Sinclair described in Applied Mineral Inventory Estimation how his “exciting and invigorating career” took off when he was exposed to Matheron’s ideas, and how he had “the good fortune to work with Journel, Huijbregts and Deraisme”. Good grief! Those were Matheron’s earliest students who took his musings for dogma, and who didn’t have a clue that the variance of the distance-weighted average cum kriged estimate had vanished into thin air on Matheron’s watch. Sinclair’s list of those who he was “fortunate to have worked with at various times” reads like a Who’s who in the world's  geostatistical fraternity. Sinclair credits all of them to have contributed to his education. For once I do agree! I’m all in favor of giving credit where credit is due. But to give credit to everybody who has taught Professor Dr Alastair j Sinclair, PEng, PGeo how to apply a flawed variant of applied statistics is a bit over the top. Some geostatistocrats on Sinclair’s list know that each and every distance-weighted average cum kriged estimate does have its own variance. No ifs or buts! Whether Al likes it or not!

I wrote one more letter to Dr Martha C Piper, President, The University of British Columbia. I pointed out that H G Wells (1866-1946) had predicted, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”. I mentioned that statistical thinking served me well indeed as a consultant, a lecturer, an author and a publisher, and as a global citizen of sorts on IMO and ISO Technical Committees such as TC69-The application of statistical methods.

Professor Dr Nathan Divinsky was charged in 1949 with the teaching of mathematics to UBC students. He retired as a professor in the mathematics department in 1991. I met a few of his former students who enjoyed his teaching and appreciated the power of applied statistics. Once upon a time I called him to ask whether statistical inferences are possible without degrees of freedom. I’ll always remember that he said, “But without degrees of freedom statistical inferences are impossible”. Dr Nathan Divinsky passed away at 86. He was married for eleven years to former Prime Minister Kim Campbell. Who would dare doubt such a short, crisp and to the point response by a Professor of Mathematics? May he rest in peace!

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