Teaching junk statistics at Stanford

Stanford University is Professor Dr Andre G Journel’s world. He has put down deep roots at Stanford since 1978. Journel teaches the same flaky stats that Professor Dr Georges Matheron taught him between 1969 and 1978. Journel was Matheron’s most gifted student. Matheron taught him all of the ins and outs of his novel science of geostatistics. Matheron may not have told Journel that he thought in 1954 he was a statistician. It took almost ten years to teach Journel how to assume, krige, and smooth with a lot of confidence and pride. Journel was Mining Project Engineer at the Centre de Morphology Mathematique from 1969 to 1973, and Maitre de Recherches at the Centre de Geostatistique from 1973 to 1978. Not surprisingly, he worked as profusely with symbols as Matheron did in his magnum opus. What Matheron failed to show his star disciple is how to test for spatial dependence between ordered sets of measured values in sample spaces and sampling units. Matheron and Journel never found the lost variance of Agterberg's distance-weighted average point grade.

Journel is the lead author of Mining Geostatistics. When the ink had dried in 1978 he took his book to Stanford’s students and taught them all about assuming, kriging and smoothing. My copy is a “1981 reprint with corrections.” Matheron’s Foreword makes a deeply dense read. In contrast, Dr Isobel Clark’s Preface to her 1979 Practical Geostatistics makes an easy read. Her cradle once rocked on the side of the Channel where Sir R A Fisher was knighted. Clark confessed it was Journel who taught her all she knows about the Theory of Regionalized Variables. Clark messed up degrees of freedom for ordered sets of measured values. She slashed for "mathematical convenience" the factor 2 in df₀=2(n-1) degrees of freedom for ordered sets, cooked up her silly semi- variogram, and scolded the poor souls who “sloppily call it a variogram”. Clearly, Clark and Journel disagreed about semi-variograms and variograms. Neither knew how to test for spatial dependence, how to chart sampling variograms, or how to count degrees of freedom.
Matheron’s 1978 Foreword to Mining Geostatistics went off on a tangent just as much as did his 1954 Note statistique No 1. He beat around the bush about geologists who “stress structure” and statisticians who “stress randomness.” Matheron’s point of view flies in the face of Visman’s sampling theory with its composition and distribution variances. Matheron predicted, “The user of Mining Geostatistics will come across nothing more than variances and covariances, vectors and matrices”. Matrices and vectors do indeed abound from cover to cover but so do pseudo variances and pseudo covariances. What all those so called “variances” and “covariances” in Mining Geostatistics do have in common with genuine variances and covariances are squared dimensions. The concept of degrees of freedom, too, failed to make the grade in Matheronian geostatistics. And that’s what will kill the kriging game!
I came across a genuine variance in a numerical example on page 63 of Mining Geostatistics. The authors divided a stope into four equal units, and assigned to each unit a grade equal to the outcome of a cast of “an unbiased six-sided die.” Now that does indeed give a genuine variance. Casting an unbiased die a large number of times gives a uniform probability distribution with a population mean of μ=3.5 and a population variance of σ²=2.917. The authors deserve praise for giving correct values, and for pointing out that the die ought to be unbiased. Surely, Stanford’s students ought to be taught how to measure the risk of playing all sorts of games of chance.

No real data in 1954 - Casting dice in 1978

The set of three (3) stopes is given on the same page. Each set of four units within its stope was put together with a six-sided unbiased die such that each unit has the same mean of 3.5. That sort of applied research is time-consuming but of critical importance when teaching all of the intricacies of geostatistics. A touch of classical statistics is required to test whether or not a given die is unbiased. The question of whether Journel's die was biased may have been solved by assuming it was unbiased. Fisher’s F-test shows that the variances of the sets and the first variance terms of ordered sets are statistically identical. Read what Journel said about “Fischerian (sic) statistics” in October 1992. How’s that for creative thinking and writing?
The zero kriging variance of σ²_k=0 is given on page 308, Chapter V The Estimation of in situ resources in Mining Geostatistics. Another unique feature of Matheronian geostatistics is one-to-one correspondence between zero kriging variances and infinite sets of kriged estimates. Even the OCS might find it a bit of a stretch to report a 95% confidence interval of zero ounces of gold for a mineral inventory with 9.9 million ounces.
Armstrong and Champigny solved this Catch-22 with a strict caution against over-smoothing. They did so in A Study on Kriging Small Blocks, CIM Bulletin, March 1989. The study implies that requirement of functional independence may be violated a little but not a lot All that geostatistical gobbledycook is cooked up because one-to-one correspondence between distance-weighted averages and variances became null and void in Agterberg's 1974 Geomathematics.
On a positive note, Dr John L Hennessy, Stanford’s President, is but one of the few leaders at institutes of higher learning who did bother to respond to my letters.

On August 23-28, 2009, IAMG’s Annual Conference will be held at Stanford University. What a wonderful opportunity for Stanford's President to peek around the corner and ask why the variance of Agterberg’s distance-weighted average point grade is still missing. Or he might ask Professor Dr Persi Diaconis to pose a few questions on his behalf. Diaconis is Stanford's Mary V Sunseri Professor of Statistics and Mathematics. He’ll know all about the Central Limit Theorem and its role in sampling theory and practice.