Wednesday, January 18, 2012

Bamboozled by French sampling gurus

The original brains behind the French sampling school were those of Dr Pierre Gy and of Professor Dr Georges Matheron. Gy’s L’Échantillonage des Minerais en Vrac is deeply troubling. Matheron’s Synopsis to Gy’s opus is dated January 15, 1967. It was translated into English, Spanish, and German. Gy’s work consists of Volume 1 with but 168 pages of dense text, and Volume 2 with a whopping 470 pages.

Gy did refer to a pair of articles by G Gould and a set of eight (8) by Dr J Visman. Both of them were true experts who did grasp the properties of variances. Gy and Matheron have never grasped why degrees of freedom play a key role in sampling practice. In fact, confidence limits for metal contents and grades of in-situ ores and mined ores demand that degrees of freedom be taken into account. The question is then why French sampling gurus did not count degrees of freedom.

SGS Geneva had asked me on February 17, 1978 to peruse Gy’s paper on Unbiased Sampling from a Falling Stream of Particulate Material. I was to “possibly correct any English wording which may seem inappropriate”. Gy’s terminology was unusual to say the least. So what I decided to do was jot down handwritten notes in Gy’s draft. My scribbles were mailed on March 1, 1978. SGS Geneva had supported Gy’s test program to derive the optimum width and speed of linear cutters. What Gy had not done is cover coarse particles with fines. A coarse particle that impacts the leading edge of a cutter has a higher probability to become part of the primary sample than a similar particle that bounces off its trailing edge. That’s but one of several reasons why cross belt samplers have become so popular.

Gy’s Sampling of Particulate Materials, Theory and Practice ended up on my desk at SGS Vancouver. It did so close to Christmas 1979. Gy had graced my copy with his compliments, his signature, and his invoice. It was Volume 4 in Developments in Geomathematics. Three volumes had already been released by Elsevier Scientific Publishing Company. David’s 1977 Geostatistical Ore Reserve Estimation was the second volume. Our assay lab had just unscrambled the Tapin Copper salting scam. I wanted to know how to test for spatial dependence between gold grades of ordered core samples. But David did not know how to test for spatial dependence.

I scrutinized Gy’s work from cover to cover. Elsevier had not typeset Gy’s first take on sampling theory and practice. So Gy had had to paste corrections on a number of pages. Scores of his literary gems boggled my mind. Stunning terms are bi-univocal relationship, degenerate splitting process, durationless instant, increment reunion, maximum maximorum, punctual sample and zero-dimensional lot. It was a good omen that the Central Limit Theorem was mentioned twice in his Index. I couldn’t find it on one of those pages but did find it on the other. The term “degrees of freedom” was missing between “degenerate splitting processes” and “degree of representativeness”. Surprisingly, it did surface under “variogram”. Gy rambled on about, “Statistical analysis of a sequence of data by means of the Student-Fisher (SF) test”. Sir R A Fisher and W S Gosset would have found it uncool!

I need to digress before unscrambling Gy’s sampling constant. I spoke German and French a bit better than English when we came to Canada in 1969. So I decided to take survey sampling at Simon Fraser University. Later on my son really studied at SFU. Ed Merks completed his BSc (Honours) in 1986 and his MSc in 1987. He obtained his PhD in Computing Science. He was awarded the Graduate Dean’s Medal from the Faculty of Applied Science in 1986 and 1992. My son knows at least as much as I do about applied statistics. And he knows a lot more about computing science! It was a while before Precision Estimates for Ore Reserves got under David’s skin and was rejected by CIM Bulletin. And that was a scientific fraud! The variance of Gy’s sampling constant is another scientific fraud. The French sampling school still does not know that each and every function does have its own variance. Quelle domage!

I’ll move fast forward to the 1990s. My work with Cominco left me mesmerized by confidence limits for metal grades and contents of in-situ ores and mined ores. So I had thought that David’s 1977 Geostatistical Ore Reserve Estimation and Clark’s 1997 Practical Geostatistics would come in handy. A friend gave me Journel and Huijbregts’s 1978 Mining Geostatistics. That’s when Merks and Merks found out why Professor Dr Georges Matheron, Dr Pierre M Gy and Professor Dr Michel David were birds of a feather. I work with applied statistics simply because I have studied Volk’s Applied Statistics for Engineers. It taught me all I needed to know about one-to-one correspondence between functions and variances.

Stay tuned for more about the first sampling gurus who ignored the properties of variances, and who assumed, kriged, smoothed, and rigged the rules of applied statistics with impunity!