A smart student of sorts taught at TU Delft in 1958 a seminar on the skew frequency distribution of ore assay values. It was none other than young Agterberg. And did he teach real statistics in those days! Scores of students at the University of Utrecht did indeed grow up with real statistics! Agterberg was no exception. I only found out when I read his 2000 eulogy for Professor Dr Georges Matheron. He brought up that Professor H J de Wijs thought the ratio of element concentration values to be constant regardless of the volume of the block. Here’s ad verbatim Agterberg’s criticism of what Professor H J de Wijs taught at TU Delft in 1958, “…it would be better to apply the conventional method of serial correlation to series of assay values.” Now that was in 1958 Agterberg’s point of view on spatial dependence between measured values in ordered sets. Why then did he swallow Matheron’s assumed spatial statistics with hook, line, and sinker?

When ISO was set up in April 1947 at Paris, France, it was all about nuts and bolts. As a matter of fact, ISO/TC1 Screw heads came first and ISO/TC2 Fasteners was second. Ever since has ISO been setting up a broad range of standards while the world is putting its standards to the test. But I wonder why ISO did err on trueness. Here’s what ISO announced in its Technical Corrigendum 1 on 2005-08-15.

Accuracy (trueness and precision) of
measurement methods and results
Part 5: Alternative methods for the determination of
the precision of a standard measurement method

Every scientist and engineer ought to grasp the properties of variances. Those who don’t should not even try to apply a true t-test for bias. And nobody could do it without counting degrees of freedom. It is an irrefutable fact that a true t-test for bias cannot be applied without counting degrees of freedom. That’s why geologists ought to question the validity of geostatistics. The more so since the author of the very first textbook predicted that “…statisticians will find many unqualified statements…” What David didn’t predict was that he would blow a fuse if somebody did. By the way, keep your copy in a safe place. It may well become a collector’s treasure before this millennium is history. Counting degrees of freedom comes to mind as a topic that does not get the respect it so richly deserves. But I’m getting off my train of thought! Here’s a simple but true test for bias applied to an ancient set of paired data.

Testing for bias plays a key role in science and engineering. Student’s t-test is the par excellence test for bias. The t-test for paired data has always played a key role in my work. A bias between test results at loading and discharge is a constant cause of conflict between trading partners. The question is then whose test results are biased. A matter of concern in 1967 was dry ash contents of anthracite shipments from the mines in Pennsylvania to the port of Rotterdam. I went to the USA and determined that loss of dust during sample preparation was the most probable cause of bias between dry ash contents. I had done time at TUDelft. So, I knew that carbonaceous shale is softer than anthracite, and that hammer mills tend to crush and grind autogenously. That’s why I thought loss of fine dust during preparation of primary samples at loading would cause test samples to show lower dry ash contents at discharge in the Port of Rotterdam.

I know how to fingerprint boreholes. What’s more, Merks and Merks not only know how to fingerprint boreholes but how to derive unbiased confidence limits for metal contents and grades. We have known all of that since Professor Dr Michel David in February 1990 rejected Precision Estimates for Ore Reserves. He was but one of many similarly gifted geostatistical reviewers with CIM Bulletin. The same paper was praised by and published in Erzmetall, October 1991. Moreover, Borehole Statistics with Spreadsheet Software was approved by and published in SME Transactions 2000. I applied this technique to a large set of test results for a gold deposit in Kazakhstan. When I asked my contact at Barrick Gold what he thought of my report, his response was: “It’s worth its weight in gold”. I didn’t charge quite that much on February 9, 1998.

The First Coming of Professor Dr Roussos Dimitrakopoulos to McGill University came to pass in June 1993. He had come all the way from Down Under to chair Geostatistics for the Next Century. It was a bash where geostatistical thinkers of the world had flocked together. They had come to praise Professor Dr Michel David and his 1977 Geostatistical Ore Reserve Estimation. David wrote in his Introduction on page VII that “…statisticians will find many unqualified statements here”. Not a single thinker asked why David had done so. My son and I found some odd gaffes when we studied David’s stuff. That’s the very reason why we wrote Precision Estimates for Ore Reserves. My abstract for The Properties of Variances raised more eyebrows than interest. I have posted on my website both the paper and the review of CIM Bulletin.

Mrs Heather Monroe-Blum, Principal and Vice-Chancellor at McGill University, has not yet responded to my email of November 9, 2010. Neither did Dr Jacques Hurtubise, Chair, Department of Mathematics and Statistics, or Dr Christophe Pierre, Chair, Department of Engineering. I explained why geostatistics is an invalid variant of applied statistics. Here’s what I wrote ad verbatim:

On November 5, 2010 I perused Canada’s University Innovation Leaders. Something struck me as odd at McGill University. Stochastic mine planning is taught by Professor Dr Roussos Dimitrakopoulos at the Department of Mining and Materials Engineering. Stochastic mine planning with kriging variances is at odds with genuine variances in applied statistics as McGill students are taught at Mathematics and Statistics. Here’s what McGill students should know about applied statistics and geostatistics. Applied statistics morphed into geostatistics under the leadership of Professor Dr Georges Matheron, a French geologist-cum-probabilist and a self-made wizard of odd statistics. My 20-year campaign against the geostatocracy and its army of degrees of freedom fighters is chronicled on my blogs and my website.

The First Coming of Dr Roussos Dimitrakopoulos from Down Under all the way to McGill University came to pass in 1993. He had come to chair an International Forum on Geostatistics for the Next Century. The stage for this early forum was set at McGill’s Conference Office on June 3-5, 1993. Geostatistical scholars from far and wide had come to praise Professor Dr Michel David. For it was he who had crafted the very first textbook. His 1977 Geostatistical Ore Reserve Estimation does refer to “the famous central limit theorem”. Even degrees of freedom make a token appearance in Table 1.IV. His work did qualify for support from the National Research Council of Canada (Grant NRC7035). I do have my own copy of his book and have worried a lot about it. That’s why I mailed an abstract on “The Properties of Variances”. In fact, I did send it twice by registered mail. The first was lost and the second rejected. All I wanted to ask was why each and every distance-weighted average AKA kriged estimate did not have its own variance in his 1977 textbook. The more so since one-to-one correspondence between functions and variances is so sine qua non in my work!

My grandma taught me not to put all my eggs in one basket. She was a caring matriarch who told inspiring stories. She played card games but odds were beyond her grasp. She played for pennies but not with other people’s pennies. She didn’t have a PhD in anything. But I took her word and never put all my eggs in one basket.

Dr Pierre Gy (1924-…) and Professor Dr Georges Matheron (1930-2000) put the French sampling school on the world map. Matheron never put core samples from a single hole in one basket so to speak. But Gy did put a set of primary increments taken from a sampling unit in one basket. So he didn’t even get a single degree of freedom. The interleaved sampling protocol is described in several ISO Standard Methods. It is also described in Chapter 6 Spatial Dependence in Material Sampling of a textbook on Approaches in Material Sampling. Dr Bastiaan Geelhoed edited the text. IOS Press published the book in 2010.

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?