Rebranding Professor Dr Georges Matheron

Dr Frederik P Agterberg tried to do so when he sang the praises of Professor Dr Georges Matheron and called him the Founder of Spatial Statistics. The keepers of Matheron’s magnum opus at his own Centre de Géostatistique didn’t quite see eye to eye with Agterberg’s rebranding. Matheron’s disciples were taught to hold him in the highest regard as the Creator of Geostatistics. It was Matheron himself who called geostatistics a new science in the early 1960s. Here’s in a nutshell what had inspired Matheron so much in his most creative of days. He taught that, “geologists stress structure and statisticians stress randomness”. I liked that a lot. I would have liked it even more had Matheron shown how to test for absence or presence of structure. All it would have taken is to apply Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set. He would have had to count the number of degrees of freedom for each set. That was a bit of a problem. Matheron and his following never got around to counting degrees of freedom.

On a positive note, Matheron did test for associative dependence between lead and silver grades of drill core samples. This test may well have been the very reason why Matheron thought he was a statistician. His 1954 Formule des Minerais Connexes is indeed marked Note Statistique No 1. In his Rectificatif à la Note Statistique No 1, Matheron derived weighted average lead and silver grades. What he failed to derive were variances of weighted average lead and silver grades. So, I am quite pleased that the Centre de Géostatistique has posted so much of Matheron’s work. On the negative side, its webmaster saw fit to predate the evolution of Matheron’s new science of geostatistics. That’s why his very first paper did end up as Note Géostatistique No 1. Providentially, his 1954 Formule des Minerais Connexes and its Rectificatif are still marked Note Statistique No 1.

So it was that Matheron didn’t take to working with the Central Limit Theorem. David did recall the famous Central Limit Theorem in his 1977 Geostatistical Ore Reserve Estimation. He didn’t much work with it either. A critical subject that failed to make Matheron’s list of things to teach is one-to-one correspondence between functions and variances. Yet, it is a condition sine qua non in mathematical statistics. It is no wonder then that the properties of variances are beyond the grasp of the geostatistical fraternity. I have never thought much of Professor Dr Georges Matheron’s thinking. Whenever I do think of Matheron, I remember him as a self-made wizard of odd statistics.

Professor Dr Michel David took a shine to Matheron’s new science of geostatistics. David did so while he was teaching at l’École Polytechnique, University de Montréal, Québec, Canada. And he did predict that ‘statisticians would find many unqualified statements’ in his 1977 Geostatistical Ore Reserve Estimation. He didn’t predict he couldn’t care less if someone pointed out what was wrong and why. Some twenty years ago I did but few cared. So, I’ll just keep doing it again and again! Chapter 10 The Practice of Kriging shows how to do more with fewer boreholes by paying no attention at all to the rules of mathematical statistics.

Fig. 203. Pattern showing all the points within B,

which are estimated from the same nine holes.

David borrowed the above figure from Maréchal and Serra’s 1970 Random Kriging. Both were scholars at Matheron’s Centre de Morphology Mathématique. Here’s word for word what I have come to call David’s test for geostatistical acuity. “Writing all the necessary covariances for that system of equations is a good test to find out whether one really understands geostatistics”. I have pointed out that a good test to find out whether one really understands mathematical statistics is to count the number of degrees of freedom for David’s system of equations. The correct count is zero! That’s how Matheron and his timid minions took reserve and resource estimation into a dead-end street.

But even more bad science pops up in Chapter 12 Orebody Modelling. In Section 12.2 Conditional Simulation, David wrote about the infinite set of simulated values. He wonders how to make infinite sets smaller and get models closer to reality. In Section 12.2.1 Using a Simulated Model, he wrote about some pudding proof and a posteriori proved simulations. But nobody cries out loud in the face of such blatant nonsense. What are the odds to win when playing 649?

So, why then did Agterberg try to rebrand Matheron the Founder of Spatial Statistics after he had passed away? Now that’s a long story. The short of it is that there are many more geoscientists than geologists on our little planet. Remember global warming? And how to assume spatial dependence between measured values in ordered sets? That’s what way too many geoscientists are taught. Stay tuned for real statistics. And tune out to surreal geostatistics.