LETTER TO THE EDITOR — Geotstat theorists pine for perfect world

Gary Raymond was kind when he mentioned that I had little knowledge of geostatistics (“Experience key to reliable geostat data,” T.N.M., Dec. 14-20/98), because I knew precisely nothing about it in the early 1980s. Raymond taught me what kriging is all about, but I did not teach him quite enough about sampling and applied statistics.

Sampling theory applies not only to stochastic systems but also to static stochastic systems. Confidence limits for volume, mass, content and grade can be calculated regardless of whether stochastic systems are dynamic or static.

I found kriging convoluted (why is a little good but a lot bad?), counter-intuitive (do deposits respond to kriging?), and confusing (why doesn’t every kriged estimate have its own variance?). Raymond reviewed The Properties of Variances, published by the Canadian Institute of Mining, Metallurgy and Petroleum (CIM) in November 1992, in which I derived the formula for the variance of a single kriged estimate (a homologue of the central limit theorem). He praised the variance formula but claimed that “degrees of freedom no longer makes sense for very small sample weights.”

Raymond’s praise of the variance formula was frowned upon by those who object to “opinions that run against the popular view” and reject “papers that do not back up their opinions with scientific fact,” as stated in an editorial in De Geostatisticis. Yet even a cursory glance at “A study on kriging small blocks” in the March 1989 CIM Bulletin reveals that kriging variances converge toward zero — so much so that the authors cautioned against oversmoothing.

Not otherwise troubled by the striking effect of violating the requirement of functional independence in probability theory, the shrinking of the kriging variance inspired the search for the perfect degree of smoothing. Incredibly, almost 10 more years of creative abuse of applied statistics later, Gouchang Pan, in his April 1998 CIM paper “Smoothing effect, conditional bias and recoverable reserves,” discusses how to smooth neither too little nor too much, but simply to perfection.

Undisturbed by bogus or dwindling deposits, shrinking variances and vanishing degrees of freedom, the geostatistical theorist remains wrapped up in perfect smoothing, conditional probability and conditional bias. Will perfectly smoothed, conditional reserves be next?

Could somebody please explain why CIM entrusts those who ignore fundamentals of probability and statistics with the review of papers on applied statistics in mineral exploration? Surely, mineral exploration and mining stand to benefit from probability theory and applied statistics as much as mineral processing, smelting and refining.

Jan Merks

Matrix Consultants

Coquitlam, B.C.