SAGD stands for Steam Assisted Gravity Drainage. It makes oil easier to recover. What has SAGD to do with Markov chains? That’s what I’ll discuss in this blog! I was into consulting at Fort McMurray long before Markov chains were strung together. I have worked with applied statistics since the 1960s. It would seem that geostatistocrats have forgotten that geostatistics converted Bre-X bogus grades and Busang’s barren rock into a massive phantom gold resource. I applied Fisher’s F-test to prove that the intrinsic variance of Bre-X’s gold was statistically identical to zero. No if or buts! The Ontario Securities Commission and the Toronto Stock Exchange set up a Mining Standards Task Force to protect mining investors. Canada’s most gifted geostatisticians got this task force to work without Fisher’s F-test. What boggles the mind is that the mining industry took to Stochastic Mine Planning with Markov Chains! It’s but one more flavor of geostatistics.  It was bred at Stanford University and put to work at McGill University. Geostatistocrats need no longer assume spatial dependence between measured values in ordered sets. CPUs crunch numbers overnight and stochastic mining plans pop up in the morning. It’s Markov’s gift to those who are not into counting degrees of freedom!

Once upon a time a keen geologist measured the degree of associative dependence between lead and silver in lead ore. Next, he put on paper Formule des minerais connexes and called it Note statistique No 1. He didn’t report his primary data but did correct an error. In time, he became famous. So much so that he set up the Centre de Géosciences/Géostatistique at Fontainebleau, France. Professor Dr G Matheron will be remembered either as the creator of geostatistics or as the founder of spatial statistics. As fate would have it; never in his life did he test for spatial dependence between measured values in ordered sets by applying Fisher’s F-test.

Professor Dr George Matheron (1930-2000)
Creator of Geostatistics
Founder of Spatial Statistics

Dr Margaret Armstrong and Mr Normand Champigny had put this study on paper when they were toiling at the Centre de Géostatistique at Fontainebleau, France. Professor Dr Georges Matheron himself may have inspired them to compile their study in a paper. Be that as it may, this simple study has never been added to Matheron’s magnum opus. It was kriging small blocks that inspired Armstrong and Champigny to elaborate on what they had detected, namely “Mine planners tended to define ore/waste limits as finely as possible”.

How about that? Perfect people are hard to find. So, the average mine planner was often tempted to over-smooth small blocks. The central tenet of this study was that over-smoothed estimates should not be used to derive recoverable reserves. That sort of research may well be the reason why Normand Champigny was awarded a Diploma in Geostatistics.

The methane gas explosion at the Westray Mine in Plymouth, Nova Scotia, Canada on May 9, 1992 caused the death of 26 miners. Mine managers Gerald Philips and Roger Parry were charged with manslaughter and criminal negligence causing death. The mills of justice ground to a halt when the Crown had failed to give full disclosure of all of its exhibits by November 15, 1994.

Mr Duncan R Beveridge, QC, with Beveridge, Lambert & Duncan, called during the summer of 1999 to find out what I knew about sampling and statistics. I pointed to Sampling and Weighing of Bulk Solids, my activities on ISO Technical Committees, and my savvy in solving scams such as the Bre-X fraud. I transmitted a facsimile of my curriculum vitae which was similar to the one currently posted on my website.

Professional designations are powerful symbols. The public at large tends to trust those who qualify. Noblesse oblige, bien sur! Here’s what the public ought to know! The current code of ethics does not always protect the public at large. I was aware of this code long before I read the Vancouver Sun of March 1, 2012. Much of it is posted under Correspondence on my website. The National Engineering and Geoscience Month (NEGM) was this year held in Vancouver, BC. Its members have as strong a need to be appreciated and understood as I do! But far too few of its members remember as well as I do how geostatistics converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Kilborn Engineering Pacific Ltd cooked up Bre-X’s phantom gold resource here in Vancouver, BC. I had given my short course on sampling and statistics at Kilborn’s Office long before Bre-X Minerals got into drilling holes at its gold property in Borneo, Indonesia. It bothered but few professionals that geostatistics as Kilborn knew it in the 1990s morphed into stochastic mine planning at McGill University in 2010s. Among those who couldn’t care less whether or not functions have variances is UBC Emeritus Professor Dr Alastair J Sinclair, PEng. He took a liking to Matheron’s thinking in the 1970s. He has been teaching Matheronian geostatistics to scores of students at the University of British Columbia.

It took a while to post on my website much of what I know about sampling and applied statistics in mineral exploration, mining, mineral processing, smelting and refining. My webmaster and I have done so in the format of downloadable PDF files. Cash flow is used to derive unbiased confidence limits for content and grade of a reserve, and of the proven part of a resource.

The Canadian Institute of Mining, Metallurgy and Petroleum in 2006 made me a Life Member. I am the most irate Life Member of that iconic institution. Every year CIMMP asks its Life Members for donations. It wants to teach students all about mineral exploration, mining, mineral processing, smelting and refining. Sounds familiar, doesn’t it! But I have never donated a penny. Not as long as UBC’s Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo is teaching students to assume spatial dependence between measured values in ordered sets. Why doesn’t he grasp that each distance-weighted average does have its own variance? Did he ever peruse Clark’s 1979 Practical Geostatistics? She derived the variance of her distance-weighted average hypothetical uranium concentration. Alas, what she didn’t do was test for spatial dependence between measured values in her wacky sample space. So it seems that Clark’s take on applied statistics is imperfect.

CIM Bulletin approved and published in 1991 a paper called Simulation models for mineral processing plants. In contrast, CIM Bulletin did reject in 1990 what Merks and Merks had called Precision estimates for ore reserves. Professor Dr Michel David (1945-2000) decided to reject our paper because we had applied our own method and had quoted too few references to the geostatistical literature. Professor Dr Alastair J Sinclair did find the variance of a general function a bit dated!

He frowned on other functions whose roots are traceable to applied statistics. He is Emeritus Professor at the University of British Columbia. He may still be teaching UBC’s students that working with variance-deprived distance weighted average point grades AKA kriged estimates does make sense in Matheronian geostatistics.

Searching for sound sampling practices always deserves praise. Sampling experts in South Africa have tried to put into plain words what sound sampling practices are all about. What a shame that they took a shine to Pierre Gy’s sampling errors. So much so that they have decided to put together a study of Gy’s sampling errors. Gy had grasped but little of what he had come to call “sampling errors”. What a pity that sampling experts in South Africa, too, have failed to come to grips with Gy’s sampling errors as much as had Gy himself.

The original brains behind the French sampling school were those of Dr Pierre Gy and of Professor Dr Georges Matheron. Gy’s L’Échantillonage des Minerais en Vrac is deeply troubling. Matheron’s Synopsis to Gy’s opus is dated January 15, 1967. It was translated into English, Spanish, and German. Gy’s work consists of Volume 1 with but 168 pages of dense text, and of Volume 2 with a whopping 470 pages.

Gy did refer to a pair of articles by G Gould and a set of eight (8) by Dr J Visman. Both of them were true experts who did grasp the properties of variances. Gy and Matheron have never grasped why degrees of freedom play a key role in sampling practice. In fact, confidence limits for metal contents and grades of in-situ ores and mined ores demand that degrees of freedom be taken into account. But one question is why French sampling gurus do not count degrees of freedom. Another is why not all functions do have variances!

National Science and Engineering Research Council of Canada had funded David’s 1988 work with NSERCC Grant 7035. National Research Council of Canada had earlier funded David’s 1977 work with NRC Grant 7035. Professor Dr Michel David’s 1977 work did not respect the requirement of functional independence and ignored the concept of degrees of freedom. His 1988 work was just as flawed but a bit more slipshod. My case against geostatistics has been brought to the attention of several NSERCC officials. One of those thought my message should have been sent to Natural Resources Canada. I had done so long ago but to no avail.

Dr Frederik P Agterberg
Ex Emeritus Scientist
Natural Resources Canada

The text that had been transmitted on December 14, 2011 reads as follows: