Tuesday, August 10, 2010

Geostatistics recast Statistics with upper-case S

Young Matheron in 1954 took a shine to what he then thought was statistics. Professor Dr Georges Matheron in the 1970s saw it at that time as his new science of geostatistics. Professor Dr Noel A C Cressie in 1993 saw it more as what he came to call Statistics with upper-case S. He is the brains behind that sort of stats stuff at the Ohio State University. He teaches Statistics with upper-case S at OSU’s Department of Statistics. But why teach Statistics with upper-case S? Here’s in plain prose how Cressie put it in his Preface: “Notice that Statistics is capitalized to distinguish it from its other meaning: a collection of numbers that summarize a complex phenomenon - such as baseball or cricket”. Good grief! Could that really be the reason why he brought Statistics with upper-case S to those who interpret statistics for spatial data? Has he paid any attention to the study of climate change? Didn’t it turn out to be a bit of a mess? Cressie cautioned elsewhere in his Preface, “We should not forget our roots”. How true! But why then did Cressie forget his own roots in mathematical statistics?

Dr Frederik P Agterberg, NRCan’s Emeritus Scientist, brought to my attention in November 2009 that Noel Cressie is a mathematical statistician. He suggested that I consult Cressie’s 1993 Revised Edition of Statistics for Spatial Data. He pointed out that it deals with “kriging variance and equivalent numbers of independent observations”. I was stunned to say the least. I do respect the properties of variances and the concept of degrees of freedom much more than do most scientists. Yet, I studied Cressie’s Statistics for Spatial Data with upper case S. In retrospect I should have studied his original work to find out how far he had already wandered away from the straight and narrow of mathematical statistics.

Why did Agterberg want me to study Cressie’s Statistics for spatial data? I do not have the faintest idea! I have asked Agterberg why he stripped the variance off his distance-weighted average in 1970 and in 1974. He has never told me why. French scholars such as A MarĂ©chal and J Serra worked with distance-weighted averages whose variances, too, had vanished in thin air. Matheron had taught MarĂ©chal and Serra everything he knew before they came to the USA in 1970 for the very first krige and smooth fest. Matheron and his disciples failed to grasp what Professor Dr Michel David called in 1977 the “famous” Central Limit Theorem. But then neither did David.

Geologic prediction problem in 1970
Typical kriging problem in 1974
Statistical fraud since 1954

Agterberg writes about the Central Limit Theorem in Chapter 6 Probability and Statistics of his 1974 Geomathematics. Yet, in Chapter 10 Stationary Random Variables and Kriging he paid no heed to the theorem that underpins sampling theory and sampling practice. That’s why NRCan should ask him to explain why his distance-weighted average does not have a variance.

At this stage I’ll go back in time some twenty years. That’s when I got to know Professor Dr Robert Ehrlich. He taught at the Department of Geological Science at the University of South Carolina. He was Editor-in-Chief of what was then known as the Journal for Mathematical Geology. I had mailed him on November 14, 1990 a paper called Precision Estimates for Ore Reserves. It was the same paper that our peers at CIM Bulletin saw fit to thrash. They had done so simply because we had ignored twenty years of geostatistical literature. We wrote it because geostatistics was then and is still today a scientific fraud. The Bre-X’s salting scam has not yet been used in a court of law to prove that geostatistics is a scientific fraud.

The point I want to make is that Professor Dr Robert Ehrlich is a scholar and an independent thinker. He was a perfect fit for the position of JMG’s Editor-in-Chief. Much to my delight he saw through much of the fluff that underpins Matheronian geostatistics. I had mailed him drafts of a few wicked papers and a copy of my 1984 Sampling and Weighing of Bulk Solids. And we did talk a few times about counting degrees of freedom and testing for spatial dependence. But that wasn’t to last alas!

All efforts to have our take on how to derive unbiased confidence limits for ore reserves reviewed by and published in the Journal for Mathematical Geology came to naught. What’s more, a paper titled The Properties of Variances went missing. What also went missing late in 1994 was Professor Dr Robert Ehrlich, JMG’s Editor-in-Chief. So, I asked Dr Daniel F Merriam, JMG’s new Editor-in-Chief, on January 13, 1995 why that paper had not yet been reviewed. He wrote a brief note on April 14, 1995 that it was rejected. So it was that JMG’s peer review process had thrashed the same paper just as thoroughly as did CIM Bulletin’s in November 1989. A few problems surfaced. Agterberg was CIM Bulletin’s Associate Editor and JMG’s Book Review Editor. He approved Abuse of Statistics for publication in CIM Bulletin. A copy of it was attached to The Properties of Variances. One of JMG’s reviewers pointed out that it “should never have appeared in print”. One cannot help but wonder who said so!