What’s wrong with Matheron’s 1965 PhD Thesis

Once upon a time a young geologist in Algiers derived the degree of associative dependence between lead and silver grades of drill core samples. What he didn’t derive were length-weighted average lead and silver grades. Neither did he test for spatial dependence between metal grades of ordered core samples. This geologist did do it with a bit of applied statistics so he called his article Note statistique No1! In time, one of several scores of dedicated disciples decided to change it to Note géostatistique No1. Somebody do so after the Internet was born! The same disciple is still the custodian of Matheron’s magnum opus. He may well want to play with Matheron’s new science of geostatistics from the 1950s to eternity. Good grief! That’s long time! And it’s a headache already! The more so since Note géostatistique No28 shows “krigeage” in its title. Did Matheron ever ask Krige whether he wanted his name to become a genuine eponym?

Matheron was a master at working with mathematical symbols. He couldn’t possibly have taught his disciples how to test for spatial dependence between mathematical symbols. What’s more, he didn’t even know in the 1950s how to test for spatial dependence between measured values in ordered sets. Neither did he know how to test for spatial dependence in his 1965 PhD thesis! As a matter of fact, Matheron has never tested for spatial dependence between measured values in ordered sets. 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. Degrees of freedom for both sets ought to be counted and taken into account. Matheron is remembered either as the Founder of Spatial Statistics or as the Creator of Geostatistics. I don’t care what his disciples called him. What I care about is that he didn’t know how to test for spatial dependence by applying Fisher’s F-test! Why did Matheron strip the variances off distance-weighted averages cum kriged estimates? And why did he assume spatial dependence between measured values in ordered sets?

Those who were to judge Matheron’s PhD Thesis on November 10, 1965 may well have asked him to put in plain words the nitty-gritty of his thesis.  Matheron had called it “LES VARIABLES RÉGIONALISÉES ET LEUR ESTIMATION”. His PhD supervisors were Professor Dr Swartz, President, Professor Dr Fortet and Professor Dr Caileux, Examinators. This team proposed a second thesis with the title “PROPOSITIONS DONNÉES PAR LA FACULTÉ”. Did Matheron’s supervisors ask him to jump hoops? And how far would Matheron jump to defend variance-deprived distance-weighted averages cum kriged estimates? The very first page of a whopping 301 pages of Matheron’s 1965 thesis mesmerized me. Why had Matheron cooked up a pair of prime data sets? Why were both inserted under INTRODUCTION on the very first page? Why didn’t he show how to test for spatial dependence? Why didn’t PhD candidate George Matheron know how to test for spatial dependence and count degrees of freedom?

Matheron_Thesis_data
All it takes to test for spatial dependence is to compare observed F-values with tabulated F-values. Of course, degrees of freedom ought to counted and be taken into account. I have applied Fisher’s F-test to verify spatial dependence in sample spaces and sampling units alike. I have done so ever since I worked on ASTM and ISO Standards. Geostatistical software converted Bre-X’s bogus grade and Busang’s barren rock into a massive phantom gold resource.  I unscrambled the Bre-X salting scam by proving that the intrinsic variance of gold was statistically identical to zero. Of course, it is of critical importance to grasp the properties of variances.

Matheron_Stats
It became Matheron’s new science of geostatistics when the variance was stripped off the distance-weighted average and what was left was called it a kriged estimate. Did Matheron really think had created a new science. Geostatistocrats thought he really  did! Good grief!

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