Thursday, March 14, 2013

Flunking his PhD Thesis

Put it on paper; call it a PhD thesis; get it approved! Simple comme bonjour, n’est-ce pas! But his PhD supervisors at Université de Paris Sorbonne did not approve Professor Georges Matheron’s PhD thesis. On the contrary, they wanted to know what I had wanted to know since the Bre-X fraud! The title of Matheron’s thesis was “Les variables régionalisées et leur estimation: une application de la theory des fonctions aléatoires aux sciences de la nature”. How about that? Thank goodness French was my very first foreign language!

How did Matheron test for spatial dependence in sample spaces and sampling units? He never did! That is why Matheron got stuck on the very first page of his PhD thesis. He didn’t know in 1965 how to test for spatial dependence between measured values. His PhD supervisors had posted on his thesis two (2) sets of whole numbers with the same central value. One set was ordered and the other was randomly distributed.  Matheron’s PhD thesis added up to 301 pages of dense text and scores of symbols. But his PhD supervisors deemed it not enough to merit a PhD in his novel science of geostatistics! It’s rather silly that the Creator of Geostatistics and the Founder of Spatial Statistics did not know how to test for spatial dependence between sets of integers. But why didn’t he know?  Applying Fisher’s F-test and counting degrees of freedom have never been part and parcel of his novel science. His failure to test for spatial dependence was part and parcel of what he fondly called his new science of geostatistics when he took it to North America in June 1970.

Professor Georges Matheron came with his most gifted disciples. Neither knew how to test for spatial dependence by applying Fisher’s F-test to the variance of a set and the first variance term of the ordered set. His disciples believed Matheron was teaching a new science. His PhD supervisors were aware that his new science was an invalid variant of applied statistics. Matheron’s thinking was alive in the eyes of his disciples. He had always taught that a distance-weighted average AKA a kriged estimate does not have a variance. How about that? Strip the variance off the distance-weighted average and call what’s left “a kriged estimate”. Good grief! Distance-weighted averages have variances but kriged estimates no longer do! D G Krige had not come all the way to Lawrence, Kansas. M David and A G Journel were busy writing textbooks about Matheron’s novel science.

A colloquium took place on campus at the University of Kansas, Lawrence in June 1970. D F Merriam, Chief of Geologic Research, Kansas Geological Survey, kept a record and Plenum Press put it in print. No list of visitors was kept. The event was useful to those who do work with applied statistics. Koch and Link, the authors of Statistical Analysis of Geological Data, talked about their work. Part I was published in 1970 and Part II came along in 1971. Both the famous Central Limit Theorem and the concept of Degrees of Freedom are still alive in Koch and Link’s work. I have had copies of both parts since the 1970s. I have used a data set in Sampling and Weighing of Bulk Solids. Tukey’s WSD test has also played a role in my work. Some Further Inputs describes what Professor Dr J W Tukey had seen in real time at Lawrence, Kansas. He wondered what would happen in two-dimensional sample spaces. Good grief! I was already working with three- dimensional sampling units and sample spaces. 

Marechal and Serra’s Random kriging and Matheron’s Random Functions and their Application in Geology had both been cooked up either at the Centre de Géostatistique or at Centre de Morphologie Mathématique. The variance had been stripped off the distance-weighted average and the concept of degrees of freedom was dismissed. Why did the geostatistical mind have distance-weighted averages morph into kriged estimates? The odd geostatistocrat may still remember the “famous Central Limit Theorem”.  All it would have taken is a passing grade in Statistics 101.

Matheron talked about Random Functions and their Application in Geology. He set the stage with a bizarre paradigm of Brownian motion along a straight line in deep time. It made counting degrees of freedom an exercise in extreme futility. Those who would have been tempted to count them would have scored a failing grade on Geostatistictics 101. Ranked high among vagaries in Matheron’s take on spatial dependence was his reference to the “quasistationarity” condition! Good grief!

Marechal and Serra talked about Random Kriging. Terms such as punctual kriging put into perspective what this new science of geostatistics was all about. Figure 10 did as little for Matheron’s new science as it would do for David’s 1977 Geostatistical Ore Reserve Estimation.   

Figure 10 – Grades of n samples belonging to
nine rectangles P of pattern surrounding x

A facsimile of Marechal and Serra’s Figure 10 is given in David’s first textbook as Fig. 203 on page 286 in Chapter 10 The Practice of Kriging. The National Research Council of Canada has given generous support to David’s imperfect thinking. It did so with its Grant NRC7035. NRC did not engage in statistical quality control in those days. NRC has changed its name and approves Markov chains. So much for SQC!

No comments:

Post a Comment