Some twenty years ago my son and I submitted to CIM Bulletin a paper on Precision Estimates for Ore Reserves. David, CIM Bulletin`s reviewer, blew a fuse because we didn`t refer to `twenty years of geostatistical literature`. We did study David`s 1977 Geostatistical Ore Reserve Estimation and Clark`s 1979 Practical Geostatistics. Neither author showed how to test for spatial dependence. So, we showed how to test for spatial dependence between gold assays determined in bulk samples taken from twelve (12) rounds in a drift. CIM Bulletin was but one of several journals to reject our paper. Yet, it was praised by and published in Erzmetall 44, October 1991. We could not show how to estimate the intrinsic variance of gold because but a single bulk sample was taken from each round.
It was easy to estimate the intrinsic variance of gold in Bre-X’s phantom resource. Bre-X’s quality control program was based on selecting and testing duplicate test portions of every tenth crushed and salted core sample. The set of duplicate gold assays for Bre-X’s bonanza borehole BSSE198 gave enough degrees of freedom to estimate the analytical variance with a proper degree of precision. Fisher’s F-test proved that the analytical variance and the first variance term of the ordered set are statistically identical. Hence, the intrinsic variance of gold in BSSE198 was statistically identical to zero. Plenty of placer gold was present in crushed and salted core samples but Bre-X’s bonanza borehole BSSE198 was barren.

When APCOM 2009 asked for abstracts, I talked to my son about presenting one more paper on our home turf. His talk about EMF at some school of mines in Nantes, France, took him too far away from Vancouver to attend APCOM 2009. Our abstract was based on a bulk sampling program at the Cerattepe project in Turkey where core recovery was poor. So, I advised my client to implement an interleaved bulk sampling program in order to derive unbiased confidence intervals for in-situ gold and silver. Our abstract was accepted and Metrology in Mineral Exploration was approved.
I spoke to a small group on Thursday, October 8, 2009, at 15:30. I showed how to unscramble the Bre-X fraud, and how to derive the statistics for Cerattepe’s bulk sampling program.

The sampling variogram for gold displays a significant degree of spatial dependence at 99.9% probability

and defines a lag of 4.30 m at 95% probability. It is corrected for the extraneous measurement variance estimated from pairs of interleaved bulk samples.

The sampling variogram for silver also displays a significant degree of spatial dependence at 99.9% probability and defines a lag of 4.09 m at 95% probability.

It is also corrected for the extraneous measurement variance for silver.

After showing my audience how to derive 95% confidence limits of the masses of in-situ gold and silver, I asked why the variance of Agterberg’s distance-weighted average point grade is still missing. I didn’t get a single response. There were no questions and I got but a pinch of polite applause. My soul mate got an anonymous note together with the second coming of Clark’s 1979 Practical Geostatistics on DVD. Which APCOM 2009 sponsor ignored my question but handed my spouse an anonymous note? Was it Gemcom? Or did Geovariances do it?
I was tickled pink with that priceless gift. In her first coming Clark cooked up a semi-variogram, berated those who sloppily call it a variogram, and praised Journal and his buddies for teaching her all she knows about “the theory of the Theory of Regionalized Variables.” Journel may well have taught Clark how to assume spatial dependence between ordered sets of measured values. He might even have cautioned Clark, too, not to become “too encumbered with Fischerian [sic!] statistics”. So, what did Professor Dr William V Harper teach Dr Isobel Clark between 1979 and 2000? Sadly, Clark’s learning curve simply flat lined! Testing for spatial dependence failed to make Clark’s grade. She still scolds those who work with sloppy variograms rather than with her own sacred semi-variogram.
Statistics or geostatistics? Sampling error or nugget effect? Clark talked about those questions at WCSB4 in Cape Town on 21-23 October 2009. Sampling error adds a nice touch of Gy’ological thinking to Clark’s repertoire. Why does testing for spatial dependence still fails to make her grade? Why did she take the factor two (2) out of degrees of freedom for ordered sets? Why does she deem too sloppy a sampling variogram that shows where orderliness in a sample space or in a sampling unit dissipates into randomness? Why did a statistician such as Harper fail to notice that geostatistics is a scientific fraud? Now, Clark and Harper are ready to take Gy’s sampling theory to sampling practices in mineral exploration, mining, processing, smelting and refining? Strip the variance of Agterberg’s distance-weighted average, assume spatial dependence between measured valuee, interpolate by kriging, smooth the least biased subset of some infinite set of distance-weighted averages AKA kriged estimates, and rig the rules of real statistics with impunity!