SADG with Markov chains?

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 want to 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 not 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 for those who are not into counting degrees of freedom!

Here are a few notes on SAGD Reservoir Characterization Using Geostat: Application of the Athabasca Oil Sands, Alberta Canada. Its authors are Jason A McLennan and Clayton V Deutsch. The latter may well remember that once upon a time at some event we shook hands. What he does not remember is one-to-one correspondence between functions and variances. It is impossible to score a passing grade on Statistics 101 by stripping the variance off the distance-weighted averages AKA kriged estimate! So I decided to look up what Clayton V Deutsch had been taught where, when, why and by whom. He earned a BSc in Mining Engineering at the University of Alberta in April 1985. Next, he got a Mac in Applied Earth Sciences (Geostatistics) at Stanford University in April 1987. Finally, he was granted his PhD in Applied Earth Sciences (Geostatistics) at Stanford University in June 1992. Now how’s that for kriging out loud!

I had mailed on November 14, 1990 a copy of Sampling and Weighing of Bulk Solids to Professor Dr R Ehrlich, Editor, Mathematical Geology. Here’s what he wrote on October 26, 1992: “Your feeling that geostatistics is invalid might be correct”. Attached to his letter was Professor Dr A G Journel’s response. The Editor’s letter and Journel’s response are posted on my website. Journel pointed out,”I’ll leave it to you to decide whether this letter should be sent to J W Merks; however, I strongly feel that Math Geology has had more than its share of detracting invectives”. Journel’s circular logic was a brazen tour de force.

I want to show what McLennan and Deutsch didn’t do in this SAGD study before putting in plain words  who set the stage for Markov chains, when, where and why.

Top Surface and Bottom Surface: Realization 50

These figures show Northing and Easting coordinates and sets of measured values for top and bottom surfaces. What comes to mind when I look at such plots are door-to-door peddlers of days gone by. They would walk such that the shortest distance is covered when each and every door is called on but once. Today’s door-to-door peddlers are into saving souls. And I’m into peddling on-line.  My eBook on Sampling and Weighing of Bulk Solids has been posted. Foremost on my mind is Metrology in Mining and Metallurgy. But I tend to slow down a bit when voodoo science drives me up a hanging wall!

 SAGD Reservoir Characterization with Applied Statistics

A spreadsheet template with SAGD statistics will be posted on geostatscam.com. In due course I’ll show how to derive the mass of oil in each block and the variance of that mass. The same method can be applied not only to in-situ ores and oils but also to mined ores and oils. All it takes is to put the additive property of variances to work. Neither Markovian chains nor Matheronian geostatistics have a role to play in mineral exploration and mining.

David’s 1977 Geostatistical Ore Reserve Estimation shows in Figure 203 on page 286 a set of sixteen (16) points. Each point is a function of the same set of nine (9) holes. One-to-one correspondence between functions and variances dictates that each point does have its own variance. David on page 323 points to the infinite set of simulated values and ponders how to make it smaller. Journel and Huibregts 1978 Mining Geostatistics on page 308 points to a zero kriging variance. None of these geostatistocrats got into counting degrees of freedom!

Here’s what Dr Isobel Clark acknowledged in the Preface to her 1979 Practical Geostatistics, “And finally to André Journel and others at Fontainebleau who taught me I know about the theory of the Theory of Regionalized Variables". It was Dr Clark who taught that each distance-weighted average AKA kriged estimate does indeed have its own variance. Stanford’s Journel didn’t know simply because Matheron didn't know. It was Matheronian thinking that has messed up ore and oil reserve estimation all over the world. A few mining giants are sold on Markov chains. Canadian regulators do not know which end of a Markov chain is up!

When to work with Marcov chains

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

Matheron’s most gifted disciple was Dr A G Journel. He put forward on October 15, 1992, “The very reason for geostatistics or spatial statistics in general is the acceptance (a decision rather) that spatially distributed data should be considered a priori as dependent one to another, unless proven otherwise”. It was a prima facie case of circular logic. He did respond to a request from Professor Dr Robert Ehrlich, Editor, Mathematical Geology. Stanford’s Journel also deemed my reading too encumbered with classical “Fischerian” statistics. So the coauthor of Mining Geostatistics put forward, “In presence of dependence the classical notion of degrees of freedom vanishes: n spatially dependent data do not provide n degrees of freedom”.

Now that’s where I didn't see eye to eye with Professor Dr A G Journel. A set of n measured values always gives df=n-1 degrees of freedom whereas an ordered set of n measured values gives dfo=2(n-1) degrees of freedom for the first variance term. Degrees of freedom are positive integers for sets of measured values with the same weight but positive irrationals for sets of measured values with variable weights. The concept of degrees of freedom has left little space for ifs and buts!

Index A. Geostatistical Concepts in my copy of 1978 Mining Geostatistics does not refer to Degrees of freedom between Deconvolution and Discontinuity at the origin of a sampling variogram. What went missing on Matheron’s watch was the variance of the distance-weighted average AKA kriged estimate. Incredibly, Matheron’s students never told him that too much was lost. On the contrary, the zero kriging variance of an infinite set of kriged estimates took on a silly life of its own. Neither does it list Markov chains above Massive deposits. Stanford’s Professor Dr A G Journel may not have been as hot on Markov chains as McGill’s Professor Dr R Dimitrakopoulos is on its role in stochastic mine planning. Unbiased confidence limits for metal contents and grades of mineral deposits can only be derived with applied statistics.

Andrey Markov (1856-1922)

A Markov chain is a mathematical system that transitions from one state to another between countable (finite) numbers of possible states. One ought to peruse the properties of variances before toiling with Markov chains. Study what McGill’s Dr RD didn’t want to know about the properties of variances when Geostatistics for the Next Century came about at the McGill Conference Office on June 3-5, 1993. What a pity that deriving unbiased confidence limits for metal grades and contents of ore reserves is still beyond Dr RD’s grasp.

Count Leo Tolstoy (1828-1910)

“I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives”.

Sir Ronald A Fisher (1890-1962) and Karl Pearson (1857-1936)

For quite a while these statisticians feuded about the chi-square distribution. Pearson worked with large data sets whereas Fisher worked with small data sets. Fisher was right! That's why the chi-square distribution takes degrees of freedom for small data sets into account. Take a long look at David’s 1977 Geostatistical Ore Reserve Estimation, Table 1.IV, Copper grade Prince Lyell. How about that? So why not reunite the distance-weighted average and its lost variance? Mining investors are bound to like it! In fact, Barrick Gold liked it before Bre-X's boss salter passed away.

Geostatistocrats such as Professor Dr Michel David (1945-2000) and UBC Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo never got into counting degrees of freedom. Why is it that one-to-one correspondence between functions and variances is sine qua non in applied statistics but irrelevant in geostatistics. Dr Michel David was once listed as a Deceased Fellow with the Royal Society of Canada. He is no longer listed but I still do not know why!

Some institutions of higher learning such as COSMO McGill Mining and Stanford University work with Markov chains to derive stochastic mining plans. What they cannot possibly derive are unbiased confidence limits for metal contents and grades of ore reserves. Geostatisticians stripped the variance off the distance-weighted average AKA kriged estimate. That’s how real functions got surreal variances!

A study on kriging small blocks

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 was never added to Matheron’s magnum opus. It was kriging small blocks that inspired Armstrong and Champigny to elaborate on what they had detected. “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.

And why was this study published in CIM Bulletin, March 1989? Here’s why! Professor Dr Michel David and Professor Dr Alastair J Sinclair, PEng, PGeo, reviewed each and every paper in which kriging popped up in those days. Dr Frederik F Agterberg, Associate Editor with CIM Bulletin would not have hesitated to approve Armstrong and Champigny’s study. Here are a few facts and figures that neither the authors nor the reviewers knew about.

Dr Isobel Clark, in Chapter 4 Estimation of her 1979 Practical Geostatistics, derives not only the distance-weighted average AKA kriged estimate but also its variance. What she didn’t do was test for spatial dependence in the sample space defined by her hypothetical uranium concentrations. She sets the stage on page 3 of Chapter 1 Introduction under Figure 1.1. Hypothetical sampling and estimation situation. On page 5 she puts forward “the convenient assumption that there is no trend within the scale in which we are interested…” On the same page she fiddled with the factor 2 for “mathematical convenience” and fumbled her fickle “semi-variogram”. What went missing in her Index on page 127 above Disjunctive Kriging is Degrees of freedom. Dr Isobel Clark credits Professor Dr Andre Jounel and others at Fontainebleau who taught her all she knows “about the theory of the Theory of Regionalised Variables”. What a pity that Dr Clark did not know how to test for spatial dependence within the sample space defined by her set of hypothetical uranium concentrations. But then neither did any geostatistical reviewer for CIM Bulletin know how to test for spatial dependence between measured values in ordered sets!

Dr Isobel Clark, author of Practical Geostatistics
BSc, MSc, DIC, PhD, FSS, FSAIMM, FIMMM, CEng

Bringing Matheron’s new science of geostatistics to the world was quite a tour de force. Scores of geologists thought it odd that so much could be done with so few boreholes. But too few knew applied statistics well enough to figure out what was wrong with geostatistics. What Matheron and his disciples had failed to grasp was not only that all functions do have variances but also that sets of measured values do give degrees of freedom. That’s about all it took to do so much with so few boreholes! CIMMP’s archive has what Matheron’s magnum opus does not have. And that’s an authentic copy of Armstrong and Champigny’s study for a mere C$20.00.


What irked was that CIM Bulletin rejected Precision Estimates for Ore Reserves. I had mailed on September 28, 1989 four (4) copies to The Editor of CIM Publications. Not surprisingly, peer review of a paper that is at variance with the central tenets of geostatistical thinking turned out to be a blatantly biased and shamelessly self-serving sham. Our peers at CIM Bulletin were Professor Dr Michel David (1945-2000) and UBC Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo. What a shame that unbiased confidence limits for metal contents and grades of ore reserves remain as rare as hen’s teeth.

Why Westray Mine trial was stayed

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.

I went to work on the Westray file shortly after October 1, 1999. It consisted of twenty–two (22) pages of text and ten (10) schedules marked A to F. I was pleased with the description of how post-explosion samples had been taken. Test results determined by Canmet and other participants in an interlaboratory test program were statistically identical. The Nova Scotia Department of Labour and the RCMP had selected test samples at intervals of 0.9 m in accordance with the Coal Mines Regulations Act. Test results for all test samples proved the average percentage combustible matter to be significantly higher than the maximum allowable limit of 35%. My report is titled Post-Explosion Sampling Procedures at the Westray Mine and was submitted on November 2, 1999.

What piqued my interest was the testimony of Andy Liney, PEng and a former mine manager and ventilation specialist from the United Kingdom. He testified that too few post-explosion samples had been taken to obtain a precise estimate for the average percentage combustible for all locations. Post-explosion samples had been taken at 0.9 m intervals. A statistical analysis of test results in samples taken by the Nova Scotia Department of Labour and the RCMP proved beyond reasonable doubt that the average percentage combustible matter in the underground workings at the Westray mine exceeded the maximum allowable limit of 35%.

Spatial dependence between measured values in ordered sets such as those taken after the explosion at the Westray Mine may or may not exist. As a matter of fact, testing for spatial dependence plays a key role in sampling practices for mined ores and mineral concentrates as defined in ISO Standards. The lead prosecutor was Herman C Felderhof. He knew as much about testing for spatial dependence at the Westray coal mine as did John B Felderhof at the Bre-X phantom gold project.

On-stream analysis of slurries in mineral processing plants became a powerful tool in the 1980s. That’s why I put together Simulation Models for Mineral Processing Plants. It was reviewed by The Metallurgical Society of CIM and published in CIM Bulletin of September 1991. On September 28, 1989 my son and I submitted for review our take on Precision Estimates for Ore Reserves. Here’s what I wrote to the Editor of CIM Publications, “The authors believe that their methodology provides a reliable measure for the risk to encounter less than the predicted grade”. What had troubled Professor Dr Michel David was that we had not only applied “our own method” but had also failed to refer to twenty years of geostatistical literature. Professor Dr A J Sinclair, PEng, PGeo was troubled because he deemed the variance of a general function a bit dated. He has been teaching generations of UBC students all he knows about geostatistics.

Variance of a general function

What I taught at UBC on November 22-24, 1989 was Sampling Precious Metal Deposits: Metrology-A New Look. Professor Dr A J Sinclair, PEng, PGeo welcomed the participants in Room 330A at 8:30AM. He didn’t object to anything I taught nor did he ask any questions. Yet, he had earlier reviewed for CIM Bulletin our take on Precision Estimates for Ore Reserves. His review was dated November 15, 1989. Surely, Emeritus Professor Dr Alastair J Sinclair, PEng, PGeo ought to explain how Gemcom software converted bogus grades and barren rock into Bre-X’s phantom gold resource. APEGBC ought to get a copy as soon as UBC's Emeritus Professor has explained why the variance was stripped off the distance-weighted average AKA kriged estimate!

Professionals pine for public trust

Professional designations are powerful symbols. The public at large tends to trust those who do 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.

Professor Dr A J Sinclair, PEng, PGeo

Since the 1990s I have explained in rich detail on my website and in my blogs why geostatistics is a scientific fraud. Why then do so many APEG Members ignore one-to-one correspondence between functions and variances? One would expect that sort of scientific fraud to be at variance with APEG’s Code of Ethics. What I want to know most of all is whether or not the properties of variances have ever been a matter of any concern to APEG’s Members. So I tend to ask a lot of questions. Where have degrees of freedom gone? Who lost the Central Limit Theorem? What has happened to unbiased confidence limits for masses of contained metals? Dr Alastair J Sinclair, PEng, still does not accept one-to-one correspondence between functions and variances. He is still teaching his students all about assuming spatial dependence between measured values in ordered sets, interpolation by kriging, smoothing and rigging the rules of applied statistics with impunity.

Assume, krige, smooth and be happy!

Here’s what Mr Tom Sneddon, MSc, PGeol, Manager of Geoscience Affairs, APEGGA Calgary wrote in response to my emessage of March 2, 2012:

“The Vancouver Sun article you refer to was placed by our sister organization, the Association of Professional Engineers and Geoscientists of British Columbia, but its content applies equally to the practice of geosciences anywhere in Canada as we pledge a common code of ethics and we all play by the same rules of conduct. You are quite right in saying that geologists and geoscientists in Alberta are bound to use only techniques and software that the practitioner is completely familiar with and understands. That is a fundamental rule of professional practice. Further, Alberta geoscientists are mostly industrial practitioners who are pretty pragmatic about what kind of methods they use in exploring for oil, gas and minerals. If a particular body of knowledge or set of techniques or algorithms don’t find dollars, their ultimate objective, they are not going to use those techniques.

As your publications suggest, good science (and by extension applied science) depends on a healthy load of skepticism and debate before an idea or concept can even be conditionally accepted as good professional practice. APEGGA provides one particular platform where ideas are openly and enthusiastically discussed, sometimes at great length: the Readers’ Forum in our bi-monthly magazine, the PEG. If you would like to have your views known and engage in a debate with our over 63,000 members, please send a note to George Lee, The Editor in Chief of the PEG (glee@apegga.org) allowing him to print you letter. Since many of our members use geostatistics as a tool for mineral exploration and development, I look forward to hearing the range of views they will surely express.”

PEG's Editor in Chief wrote: “This is not a debate we’ll get into, for at least three reasons. First, the subject matter is not part of our mandate as a non-technical publication. Second, the complexity of the subject and the need to present both sides, in fairness to UBC and Dr Sinclair, would require a full story, which we don’t have the space or the mandate for. And finally, it’s set in B.C. – our focus is Alberta. Sorry we can’t help you. All the best”.

Sound statistics or goofy geostatistics?

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 2007 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 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.

Practical geostatistics

The odd mining mogul seems to pine for moral integrity but I pine for scientific integrity. Scores of scientists pay attention to my take on geostatistics. On November 14, 1990 I mailed the first of several letters to Professor Dr Robert Ehrlich, Editor of the Journal of Mathematical Geology. I did so by snail mail and enclosed copies of Precision Estimates for Ore Reserves and of Sampling and Weighing of Bulk Solids. On October 26, 1992 JMG’s Editor wrote, “Your feeling that geostatistics is invalid might be correct”. Attached to his letter was what Stanford’s Professor Dr A G Journel had written “a bit reluctantly”. I have also posted the letter on my website under Correspondence. It seemed to Journel that “my anger arises fro a misreading of geostatistical theory, or a reading too encumbered by classical “Fischerian” statistics”.

The next paragraph shows another ad verbatim example of goofy geostatistical thinking:

1 – Data and degrees of freedom

"The very reason for geostatistics or spatial statistics in general is the acceptance (a decision rather) that spatially distributed data should be considered a priori as dependent one to another, unless proven otherwise. It is that spatial dependence which allows differentiated local interpolation and mapping in general. Were the data independent one from another then only global statistics can be retrieved. In presence of dependence the classical notion of degrees of freedom vanishes; n spatially dependent data do not provide n degrees of freedom”.

Another stunning farce was Geostatistics for the Next Century. Geostatisticians from far and wide had flocked to McGill, Montreal, Canada on June 3 to 5, 1993. They had come to honor Professor Dr Michel David for his contribution to Matheron’s new science of geostatistics. I tried to get on the program but my paper on The Properties of Variances didn’t arouse any interest.

Way too many years I have been exposed to geostat drivel. It has made me a perfect cynic. But I do have friends. A true friend is a precious gift. Sometimes it’s tough to find out who your true friends are. Dr.-Ing Reinhard Wohlbier is a true friend. Trans Tech Publications in 1985 printed my textbook on Sampling and Weighing of Bulk Solids. Thanks to Reinhard it has now been posted on my website as a PDF file. Various papers I have put together for Trans Tech Publications through the years are about to be posted on my website. Reinhard has formidable knowledge of the handling of materials in bulk. I wish Reinhard and Ute well.

Todd Higden, too, is a true friend. He is Creative Director of Frontline Multimedia. He has set up most of my first take on Geostatscam.com. My website went online in September 2005. Todd has posted scores of downloadable PDF files in 2012. It takes less than ten minutes at legal speed to drive to Todd’s Office. I have more papers to scan and to post on my website. I want my readers to know the difference between sound statistics and surreal geostatistics. Todd does not need to know much about either but he'll get to know a little!

My partner for life and my son are far more than true friends. Hennie has never been awarded a PhD in Psychology for putting up with her driven hubby. In contrast, Ed was awarded a PhD in Computing Science at Simon Fraser University in 1992. He was also awarded the Dean’s Medal in 1986 and in 1992. My son and I did put together Precision Estimates for Ore Reserves. It was thrashed by our geostatistical peers at CIM Bulletin. In spite of that Erzmetall praised it for “splendid preparation” and published it in October 1991. We have also put together Precision and Bias for Mass Measurement Techniques. ISO did like it. So much so that it became ISO 12745:2008. Nowadays Ed leads the top-level Eclipse Modeling Project as well as the Eclipse Modeling Framework subproject. He has put on the same page his blog, my blog and the bulk-online blog. Now that’s cool!

A tale of two papers

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 given too few references to the geostatistical literature. Professor Dr Alastair J Sinclair found the variance of a general function a bit dated!

Variance of a general function

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

Applied statistics has always played a key role in my teaching. The published paper was based on process simulation with the pseudo-random number generator of the standard uniform distribution. The variance of the general function as defined by Volk in his Applied Statistics for Engineers was of critical importance. This function made it simple to derive confidence limits for metal contents of mined ores and mineral concentrates. So I was delighted that the Metallurgical Society of the Canadian Institute of Mining had approved my paper. The more so since MetSoc had not found any errors. That’s how it came to pass that CIM Bulletin did publish this paper in September 1991.

A few years later I did spot a mistake not only in Simulation models for mineral processing plants but also in my book on Sampling and Weighing of Bulk Solids. The number of degrees of freedom for the first variance term of measured values in an ordered set is df=2(n-1) rather than df=2n-1. I also found out that the number of degrees of freedom for sets of measured values with variable weights are no longer positive integers but become positive irrationals. Both my book and my paper have been corrected.

Merks and Merks’s Precision estimates for ore reserves was the first paper on this topic that my son and I had put together. When Gy had sent me a copy of his 1979 Sampling of particulate materials, Theory and practice, I found out about David’s 1977 Geostatistical ore reserve estimation. It struck me as odd for any author to predict “…statisticians will find many unqualified statements…” Why hadn’t he asked a real statistician to peruse his work? And why had geostatistics been hailed as a new science in the 1970s? What I decided to do at that time was to keep David’s 1977 opus for scrutiny. The time for scrutiny came about in the late 1990s!

One would expect those who ignore degrees of freedom not to be entrusted with the works of those who do count degrees of freedom. CIM Bulletin did trust geostatistical peer review but I called it a blatantly biased and shamelessly self-serving sham. Let me briefly explain why! We had submitted our paper on September 28, 1989. We did expect the Geology Division of CIM to review our paper in an unbiased manner. I was tickled pink when the Editor of CIM Bulletin wrote on November 23, 1989 that both reviewers recommended publication with major revisions. But I turned red when I read what “mayor revisions” were necessary. So who had asked for major revisions? Professor Dr Michel David and Professor Dr Alastair J Sinclair had been entrusted with the task to protect the central tenets of Matheron’s new science of geostatistics.

David was in a tiff when he wrote “the authors had presented their own method”. Good grief! Whose method had David expected? What the author of the first textbook on geostatistics did expect most of all were scores of references to the geostatistical literature. We did find what David himself had predicted that statisticians would find. He wrote:"...statisticians will find many unqualified statements here". We did indeed! What David also felt is that we should have made reference to Gy’s 1979 Sampling of Particulate Materials, Theory and Practice. We should have pointed out that Gy's sampling constant does have its own variance whether his followers like it or not! Too few scientists and engineers are grasping what problems the French sampling school has caused!