Dr Frederik P Agterberg tried to do so when he sang the praises of Professor Dr Georges Matheron and called him the Founder of Spatial Statistics. The keepers of Matheron`s magnum opus at his own Centre de Géostatistique didn`t quite see eye to eye with Agterberg`s rebranding. Matheron`s disciples were taught to hold him in the highest regard as the Creator of Geostatistics. It was Matheron himself who called geostatistics a new science in the early 1960s. Here`s in a nutshell what had inspired Matheron so much in his most creative of days. He taught that, “geologists stress structure and statisticians stress randomness”. I liked that a lot. I would have liked it even more had Matheron shown how to test for absence or presence of structure. All it would have taken is to apply Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set. He would have had to count the number of degrees of freedom for each set. That was a bit of a problem. Matheron and his following never got around to counting degrees of freedom.

CIM stands for Canadian Institute of Mining, Metallurgy and Petroleum. Once upon a time I was a proud CIM Member. Today I am the accidental CIM Life Member. My first message to CIM`s President was snail mailed on March 20, 1992. CIM`s President was William E Stanley of The Coopers & Lybrand Group in Vancouver. He was the first of many whom I had told why geostatistics is an invalid variant of applied statistics. We met, he listened to my story, and I wrote him a letter. CIM Bulletin of March 1989 had published Armstrong and Champigny’s A Study on kriging Small Blocks. Both authors were geostatistical scholars at the Centre de Géostatistique, France. They thought up the study since, “The kriging variance rises up to a maximum and then drops off.” What they found out is that “…mine planners are often tempted to kriging very small blocks.” How about that? Smoothing a little is good but smoothing very small blocks is bad. That sort of a pass-the-buck study did pass David’s peer review with red flags blazing.

The Bre-X fraud brought about an orgy of hand wringing but not even a token search for the truth, the whole truth, and nothing but the truth. The Ontario Securities Commission and the Toronto Stock Exchange set up a Mining Standards Task Force. Morley P Carscallen, OSC`s Commissioner, and John W Carson, TSE`s Senior Vice President, called on Canadian mining experts to set new standards. Of course, the old standards were dreadfully wrong. All it took was to assume gold between salted boreholes. That’s how Bre-X’s bogus grades and Busang’s barren rock added up to a phantom gold resource! So what did the Mining Standards Task Force do? It wrote a load of text but little else. Here’s why!

Not our world famous DSI Snake Sandwich High Angle Conveyor, but an overland conveyor this time.  I’ll just go ahead and cut to the chase.  Diamonds got me last time.  So what goes best with diamonds?  Well of course the precious metals that holds those gorgeous stones.  The stuff that’s going to diversify your portfolio because it’s worth so much now.  That’s right…GOLD!

So here’s what’s been going on.  Dos Santos International is currently finishing up the Los Filos Project that was awarded in cooperation with M3 Engineering of Tuscon, AZ.  Goldcorp’s Los Filos Project is in the Nukay mining district of central Guerrero State in southern Mexico.  It promises to be one of the largest open-pit mines in the country.  It reminds me of our diamond mine project in Canada.  Those systems are contributing to projects that are projected to overtake South Africa as the new primary source of diamonds for the world.  See, we like to do things bigger and better around here!

A world free of surreal geostatistics is long past due. Geostatistics was called a new science in the 1960s but turned out to be an insidious scientific fraud. Real statistics would have nipped the infamous Bre-X fraud in the bud but both CIM and IAMG ruled in favour of surreal geostatistics. Matheron’s so-called new science of geostatistics has already  made a mess of the study of climate change. That’s why our world ought to get rid of surreal geostatistics. And fast! Come frost bites or sun burns!
Thanks to all those who read my blogs. More than two million have done so. But I got fewer than ten comments. So, what’s the matter? Is it the way I write? All I do is put in plain words why geostatistics is a scientific fraud. Here’s what I have been writing for more than twenty years. Each weighted average has its own variance. Could I have put it any other way? It is a truism in real statistics. The Central Limit Theorem is bound to stand the test of time. Why then was the variance of the weighted average done away with in geostatistics? It was G Matheron in the early 1960s who called a weighted average a kriged estimate to honor D G Krige. Matheron never derived the variance of any kriged estimate. Neither did any of his devoted disciples.
What happened in the 1970s defies common sense and sound science. Was it Matheron himself or one of his disciples who thought that every one set of kriged estimates ought to have its own kriging variance? Stanford’s Journel was Matheron’s most astute student. He figured out that an infinite set of kriged estimates gives a zero kriging variance. Wow! Here’s what he taught Stanford’s neophytes in a nutshell. Assume spatial dependence between measured values in ordered sets, interpolate by kriging, smooth a little but not a lot. Stanford’s finest geostatistical mind never took to testing for spatial dependence, or to counting degrees of freedom.
Some readers may want to study the odd opus on geostatistics. I suggest a paper on kriging small blocks. It was put together by genuine geostatisticians from the Centre de Géostatistique in France. Professor Dr Margaret Armstrong and Normand Champigny were the first scholars who cautioned against reckless over-smoothing by careless mine planners.

Same time thirteen years ago some of Bre-X`s test results for gold landed on my desk. I had not asked for Bre-X’s data. But I had agreed to and signed a three-year confidentiality agreement with Barrick Gold Corporation. I did so on December 16, 1996. It was the very same confidentiality agreement Barrick Gold Corporation and Bre-X Minerals had signed a few days earlier. The first set of Bre-X data were transmitted by facsimile on December 17, 1996. I didn’t know then that my life would never be the same. Bre-X’s infamous phantom gold resource is but part of a tangled tale with as many twists and turns as Matheron took to create his new science of geostatistics. It’s a tale that taught me a lot more about the mining industry than I cared to know.
I sorted out the Bre-X fraud faster than Bre-X’s salting squad took to cook it up. I thought Barrick liked what I did. At least Barrick did when I applied statistics to prove that Bre-X was a salting scam.Barrick liked it so much that I signed on July 4, 1997 a Consulting Services Agreement with Barrick Goldstrike Mines Inc. I submitted on August 18, 1997 my report on Statistical Quality and Grade Control . Geostatisticians on Barrick’s staff didn’t think much of my report. I applied Fisher’s F-test to verify spatial dependence between gold grades of ordered core sections from a single borehole by applying Fisher’s F-test to the variance of the set and the first variance term of the ordered set. I had done the same thing with Bre-X’s salted boreholes. Stanford’s Journel would have assumed spatial dependence. But then, Matheron’s most gifted disciple never signed a Consulting Services Agreement with Barrick Goldstrike Mines Inc.When I was working with Bre-X’s test results my closest contact was a staff mining engineer at Barrick Gold Corporation in Toronto. We got along great because he knew plenty about sampling and assaying. And he knew why Bre-X’s bogus grades and Busang’s barren rock added up to a geostatistically engineered gold resource. He also knew how to test for spatial dependence, and why geostatistics should not be applied in reserve and resource estimation. He asked me whether I wanted to take a look at a large set of borehole data for a real gold deposit. Guess what? So, I did agree to and signed on October 22, 1997 a confidentiality agreement with Barrick Gold Corporation. I submitted my report on Confidence Limits for Gold Contents and Grades on February 9, 1998. When I called my contact to find out what he thought of my report he said, “It’s worth its weight in gold.” I didn’t ask him to put it in writing. His word was good enough for me.

Who wouldn’t! Debates beat apathy. The Munk Debates is cool. The more so since climate change was the theme for the Fourth Munk Debates. Climate change, just like continental drift, has been around for a few billion years. It took geologists from 1915 to 1950 to slow down to continental drift and call it plate tectonics. So, it’s about time to debate climate change. Why not call it weather dynamics? I work with metrology, the science of measurement. I took a crack at testing whether or not annual temperatures at several locations in Canada have changed significantly as a function of time. The average temperature of 6.57 centigrade in 2007 at Ottawa International Airport was significantly higher than the average temperature of 4.79 centigrade in 1939. Similarly, the average temperature of 8.30 centigrade in 2007 at Toronto International Airport was significantly higher than the average temperature of 6.04 centigrade in 1939. Average temperatures didn’t change at international airports in Calgary, Vancouver and Victoria. Neither did the average temperature in Coral Harbour and Iqaluit change significantly during the test period under examination.

Yes, you are reading this correctly.  There is no doubt that 2009 will go down in history as a year full of challenges and will always be thought of as the year of recession.  Personally, I could have lived without having to think about furloughs and workforce reductions.  But this year has also been fascinating to me because of the many businesses that I have come across, which managed to not only survival, but even thrived under the most difficult conditions.  They have figured out that superior core ethics and flexible strategic risk taking can bring you back into the middle of the business opportunities.

Dr Frits P Agterberg is Emeritus Scientist with Natural Resources Canada. He wrote a textbook on Geomathematics and scores of papers on a wide range of geological topics. He is the nimblest of geostatistical minds on this planet. His gift to assume spatial dependence between measured values in ordered sets is second to none but Stanford’s Journel. I called him on November 4, 2009, at NRCan in Ottawa but he was away from his Office. I caught him at home when I called his residence at 09:10 AM PDST. I asked him to explain why his zero- dimensional  distance-weighted average point grade does not have a variance.

Do you have just about three minutes worth of time? Then please read my essay on the topic of leadership. Today more than any time in history are we in need of ethical leaders: At work, on the Internet, in our social networks, at school and of course at home. And each and every one of us can make a start. Like my granddad always told me: “You have got to start with yourself and do not expect others to go first” Enjoy. Ralf