Intrinsic variance

"The question whether the variance of sampling, sample preparation and analysis should be added to the intrinsic variability of a metal in an elementary unit is debatable. After all, one would not encounter the variance of measuring an elementary unit's metal grade when mining the ore but only its intrinsic variability."

This statement can be found in Precision Estimates for Ore Reserves, a paper also rejected by the Transactions of the Institution of Mining and Metallurgy. Here's the opinion of Dr Peter A Dowd, Professor at Leeds University and Chairman of Transactions A : Mining Industry.

"This is so obviously wrong that there must be some misunderstanding here; your suggestion implies that there are no penalties for bad sampling and sample preparation. Taken to its logical conclusion this would mean that sampling is a waste of time as random numbers would provide equally valid estimates."

Apparently, Dowd is unaware that interleaving sampling protocols give unbiased estimates for total variances (the sum of the sampling, sample preparation and analytical variances), and that this total variance may be deducted from the variances of the randomly distributed and ordered set of rounds to obtain unbiased estimates for the intrinsic variance. Surely, Dowd ought to know that the intrinsic variance of gold in Bre-X's phantom gold resource is statistically identical to zero.

Bre-X's sample preparation and analytical procedures are well-documented. Core samples were not divided longitudinally but instead a 10 cm piece of each 3 m core sample was retained as a "library" sample. The remaining core samples were crushed and many were salted on the pool table whenever Bre-X's management demanded more good news for its shareholders. Cyanide leaching of 750 g test portions replaced fire assaying of 15-30 g test portions simply because analytical variances are alarmingly high for small test portions taken from crushed and salted core samples.

Fisher's F-test showed that the variances of the randomly distributed and ordered sets of test results for gold in crushed and salted core samples were statistically identical for all but Busang's bait borehole BSSE198. Bre-X's salters didn't know how to create the illusion of spatial dependence either between core samples within boreholes or between boreholes within lines. For all but a few boreholes, the analytical variance (the sum of the variance of selecting a 750 g test portion from a crushed and salted core sample and the variance of cyanide-leaching) was statistically identical to the variances of the randomized and ordered sets. Core samples from those few boreholes may have contained some intrinsic gold, which would account for a low degree of spatial dependence.

Dowd's ignorance of intrinsic variances, Journel's doctrine of spatial dependence without proof, and Armstrong's conundrum of kriging a little but not a lot, spell trouble for students who want to become proficient in sampling and statistics. After all, analysis of variance cannot possibly be applied to optimize sampling protocols, to construct sampling variograms, and to estimate intrinsic variances of in-situ ores, without taking degrees of freedom into account.