Of tangled tales and geostatistics

Here are but a pair of my lingering questions. Why did Dr Frederik P Agterberg strip the variance off his distance-weighted average? Why did Professor Dr Noel A C Cressie dismiss degrees of freedom? I brought my concern to the attention of Minister Lisa Raitt on March 9, 2009, and of Minister Christian Paradis on March 6, 2010. NRCan’s technocrats were instructed to deal with my concern. Mark Corey, Assistant Deputy Minister, pointed out on June 4, 2009, “Geostatistics continues to evolve as a discipline, and we appreciate your contribution in this field.” Dr David Boerner, Acting Assistant Deputy Minister, declared on May 10, 2010, “Natural Resources Canada is a science-based organization and values the scientific rigor of the peer review process”. Now that’s a whole load of chutzpah! NRCan’s library is a treasure trove of works on geostatistics. Each and every one of them proves that geostatistics is but bogus geosciences. Look at Agterberg’s 1970 and 1974 works. He derived the distance-weighted average of a set of five (5) measured values determined at positions with variable coordinates in a sample space. He didn’t derive the variance of this distance-weighted average. He didn’t count the number of degrees of freedom for the set and for the ordered set. So much for Agterberg’s grasp of applied statistics. Of course, geostatistics couldn’t possibly get any worse, could it? But it did in 1970 when Matheron and his disciples came all the way to the USA!

Maréchal & Serra - Figure 10

Maréchal and Serra in 1970 derived a set of sixteen (16) distance-weighted averages on a 4 by 4 matrix. They did so from a set of nine (9) measured values determined at positions with variable coordinates. What M&S didn’t derive was the variance of any of those sixteen (16) distance-weighted averages. What Professor Dr Michel David didn’t do in 1977 was what M&S didn’t do in 1970, what Agterberg didn’t do in 1970 and in 1974, and what young Matheron didn’t do in 1954. David predicted that professional statisticians would find “unqualified statements” in his 1977 work. Now there’s one fact he got right. But once push came to shove he saw no wrong. Degrees of freedom did pop up on in his work but did so in a table others had put together. Little else made sense at all let alone statistical sense. M&S’s Figure 10 morphed into David’s Figure 203. He got into the nitty-gritty of geostatistics in Chapter 12 Orebody Modelling. That’s where he cooked up the tangled tale of conditional simulations and ran into infinite sets of simulated values. Finally, distance-weighted averages first morphed into kriged estimates and then into simulated values. Stanford’s Professor Dr Andre Journel was Matheron’s most gifted disciple. It is fitting then that he was the one who defined in 1978 the zero variance of the infinite set of distance-weighted averages-cum-kriged estimates. Voila, Matheron’s new science of geostatistics!


Why stop kriging when there are infinite sets of kriged estimates to play with? The problem is one-to-one correspondence between functions and variances. Have a function? Stuck with a variance! No ifs or buts! It is a fact that one-to-one correspondence between functions and variances is sine qua non in mathematical statistics. And don’t take my word for it. Read Volk’s Applied Statistics for Engineers. NRCan’s technocrats are blessed for they may borrow Volk’s 1980 book at NRCan’s library. Volk explains in exhaustive detail what geostatisticians love to hate. I already owned a 1958 copy when I was toiling in the Port of Rotterdam. It has fallen apart but my faith in Volk’s work never wavered. My second copy went missing when I traveled the world and taught sampling and statistics in all sort of settings. And I do have a 1980 copy. Chapter Seven is called Analysis of Variance and Section 7.1.4 is called Variance of a General Function.

Scientific rigor of the peer review process was shamelessly self-serving and blatantly biased already when NRCan was CANMET and Agterberg was Associate Editor with CIM Bulletin. He reviewed Abuse of Statistics but all he worried about was whether and when H G Wells praised statistical thinking. That’s how serious NRCan’s Emeritus Scientists took geostatistical peer review at CIM Bulletin in the 1990s.