Thursday, November 11, 2010

Different times but same fools

Travelling back in time was what H G Wells made nightmares off. I have read the latest biography about his life and time. Michael Sherborne called it Another Kind of Life. Here’s what I learned. Wells did not praise statistical thinking because Ronald A Fisher won the case for degrees of freedom. Sherborne pointed out that the quotation which Darryl Huff did attribute to H G Wells came from Samuel S Wilks. When Wilks gave his 1954 presidential address to the members of the American Statistical Association, he said: ”The great body of physical science, a great deal of the essential fact of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood for complete initiation as an efficient citizen of one of the great new complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima, as it now to be able to read and write.” Sherborn tracked that rather rambling sentence down to Chapter 6 of Wells’s Mankind in the Making. It was Wells himself who brought it down to, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” Wells had a way with words and women. But who would not want Wells’s way with words?

Samuel S Wilks in 1954 praised statistical thinking in the USA. Meanwhile in Algeria Georges Matheron thought he was working with applied statistics. He called his first paper Formule de Minerais Connexes and marked it Note Statistique No1. CdG’s webmaster has posted it as Note géostatistique No 1. Matheron tested for associative dependence between lead and silver grades determined in drill core samples of variable length. He didn’t show his set of primary data nor did he give references. He deemed himself without peers. And that’s just as well. Matheron in a Rectificatif to his paper derived length-weighted average lead and silver grades for core samples of variable length. Here’s where he failed. His degree of associative dependence between lead and silver didn’t take into account the variable length of core samples. He didn’t derive the variances of lead and silver grades. Neither did he derive the variances of length-weighted average lead and silver grades. Matheron, too, lost David's "famous Central Limit Theorem".

Lost and never found

He didn’t even try to test for spatial dependence between ordered sets of metal grades. Young Matheron had a long way to go. Yet, he kept marching in place to the din of kriging drums.

the founder of Spatial Statistics

So it was that he never did what he had failed to do in 1954. It was Dr Frederik P Agterberg in his eulogy who called Professor Dr Georges Matheron (1930-2000) the founder of Spatial Statistics. Here’s what may baffle many a mind! Matheron and his minions would rather assume spatial dependence between measured values than apply Fisher’s F-test to the variance of the set and the first variance term of the ordered set. To assume spatial dependence where it doesn’t exist is the very reason why the study of climate dynamics is such a mess.

CIM Bulletin has been my core source of fickle stats since the 1990s. A few of my papers were published in CIM Bulletin and may be downloaded from CIM’s website. Life Members, too, do pay for downloads. In contrast, Matheron’s work may be downloaded from CdG’s website free of charge. A paper for which no download fee ought to be charged is Armstrong and Champigny’s A Study on Kriging Small Blocks. David must have been pleased that mine planners were to blame for over-smoothed estimates. But he was not at all pleased that Precision Estimates for Ore Reserves was short of references to geostatistics. So, I submitted the same paper on November 14, 1990 to the Journal for Mathematical Geology. JMG’s reviews turned out to be a toss-up. That’s why JMG’s Editor had asked his Associate Editor to review our paper. JMG’s Associate Editor was the same Margaret Armstrong who studied kriging of small blocks. Of course, she saw fit to reject a paper that was praised by and published in Erzmetall.

Professor Dr Margaret Armstrong

Armstrong’s up-to-date list of publications does not refer to the study on over-smoothed small blocks. She doesn’t even mention her stirring Freedom of Speech? She wrote it as Editor of De Geostatisticis. It was a little leaflet with a few pages of text about the blessings of geostatistics. From time to time one more leaflet would be published to praise Matheron’s gift to the mining industry. Mark Twain knew a bit about mining. He may never have claimed that a mine is a hole in the ground with a liar on top. What I would do if I were a mining investor is question the validity of mineral inventories in annual reports. I would do so until the mining industry sets up an ISO Technical Committee on reserve and resource estimation. That would have made the 31st President of the United States proud!

Friday, November 05, 2010

BHP Billiton fell for stochastic sham

Assume that I have invested in BHP Billiton. Surely, I would want to know where my mining giant is going. And most of all I would want to know whether or not Chairman Marcus Kloppers knows what he is doing. Does he have a buddy on his Board who knows a bit about applied statistics? Would she or he know that functions do have variances, and that only measured values do give degrees of freedom? Take a long look at my short story. Assume, krige, smooth, and rig the rules of applied statistics. The roots of geostatistics rest in the archives of CIM Bulletin. What I have done for more than twenty years is keep my story alive. It’s about an invalid variant of applied statistics. It was geostatistics that converted Bre-X’s bogus grades and Busang’s barren rock so smoothly and effortlessly into a massive inferred gold resource. Just the same, Fisher’s F-test proved that the intrinsic variance of gold at Busang was statistically identical to zero. I do not know where Kloppers was when Bre-X Minerals blew up. What I do know is that BHP Billiton was not the only one who put up plenty of play dough to do more with fewer boreholes. So let’s go forward to the play!

McGill Professor Dr Roussos Dimitrakopoulos is Canada Research Chair and BHP Billiton Chair in Mine Planning Optimization at the Department of Mining, Metals and Materials Engineering. He came all the way from Down under in June 1993 to celebrate at McGill University a forum called Geostatistics for the Next Century. When I read about this forum I thought it somewhat premature. That’s why I put together The Properties of Variances and submitted the abstract by registered mail on January 4, 1992. My son and I had studied David’s 1977 Geostatistical Ore Reserve Estimation. The author did not know how to derive unbiased confidence limits for metal contents and grades of volumes of in-situ ore. That’s why we derived confidence limits in Precision Estimates for Ore Reserves. But Dr RD was not at all interested in properties of variances in 1993. And he’s still not interested in 2010!

Professor Dr Roussos Dimitrakopoulos is a Member of IAMG. Once upon a time, IAMG stood for International Association for Mathematical Geology. Nowadays, it stands for International Association for Mathematical Geosciences. The novel tag does make sense. More geoscientists than geologists study this little planet. Dr RD is Editor-in-Chief, the Journal for Mathematical Geosciences.


As such, he approves what meets his requirements and rejects what is at variance with stochastic mine planning with kriging variances. Much of Behind Bre-X, The Whistleblower’s Story, reviews the works of Matheron, Agterberg, David, Dimitrakopoulos, Journel, and scores of likeminded geostatistical thinkers.

Here’s what I wrote on April 19, 2010 to Dr Marius Kloppers, Chief Executive Officer,
BHP Billiton Plc, London, United Kingdom.
A great deal of my experience was put together in Sampling and Weighing of Bulk Solids. I did so after I had been Assistant to the Chairman of Cominco Ltd. For example, I derived unbiased confidence limits for the mass of metal contained in a mass of mineral concentrate or mined ore. ISO/TC 183 checked and approved this method. ISO published it as ISO 13543:1996 Determination of mass of contained metal in a lot.
Attached is a copy of my letter of November 30, 1994, to the Chairman, CIM Ad Hoc Reserve Definitions Committee. I pointed out that the mass of contained metal in a volume of in-situ ore is a function of volume, in-situ density, and a grade factor. This function, too, does have its own variance. In fact, one-to-one correspondence between functions and variances is a condition sine qua non in mathematical statistics. In geostatistics, however, not all functions do have variances. The variance of the distance-weighted average aka kriged estimate went missing. Drill core sections were crushed and salted at Bre-X’s Busang site when I wrote the enclosed letter in November 1994. Geostatistics converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Mathematical statistics proved the intrinsic variance of gold to be statistically identical to zero.
The purpose of my letter is to suggest that the mining industry should set up and support an ISO Technical Committee on reserve and resource estimation. It is simple to derive confidence limits for masses of metals in reserves, and to derive confidence limits for proved masses of metals in resources. My son and I did set the stage in 1992.

Dr Marius Kloppers, Chairman, BHP Billiton, has not yet replied to my letter.