Variance of a general functionDr 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 1999.
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!
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