He hummed and huffed but didn’t speak to the matter of the missing variance. All I wanted to know is why the variance of his distance-weighted average went missing. I pointed out that the Central Limit Theorem pops up if all of his measured points are equidistant to his selected point. NRCan’s Emeritus Scientist beats around the bush with the best. His textbook does refer to the Central Limit Theorem in Chapter 6 Probability and Statistics and Chapter 7 Frequency Distributions of Independent Random Variables but not in Chapter 10 Stationary Random Variables and Kriging. NRCan’s Emeritus Scientist has yet to give a clear and concise explanation why the Central Limit Theorem doesn’t apply to his distance-weighted average point grade.
I included Agterberg’s problems in my talk about Metrology in Mineral Exploration. I wanted to make a case at APCOM 2009 that distance-weighted average point grades do have variances. Nobody was ready for my show-and-tell but I got a gift. It was Clark’s Practical Geostatistics 2000. I found out that semi-variograms are still alive and below par. Here’s Clark’s problem. Her set of five (5) hypothetical uranium data doesn’t display a significant degree of spatial dependence. Thus, the concentration at the selected coordinates is not necessarily an unbiased estimate. Let’s find out what happens when coordinates are selected beyond her sample space.
Who expects the distance-weighted average point grade to converge on zero? And who expects it to converge on the arithmetic mean? It's a good test to find who is geostatistically gifted and who is not. I would rather test for spatial dependence between measured values in ordered sets and chart sampling variograms that show where spatial dependence dissipates into randomness. Come hell, high water, global cooling, polar warming, or another Bre-X.
My first APCOM affair was just as cluttered with geostat drivel as are all of IAMG’s shindigs. McGill’s Professor Dr Roussos Dimitrakopoulos sought to shed light on stochastic mine planning optimization. He is Editor-in-Chief, Journal for Mathematical Geosciences. That’s why all his work passes his own litmus test for scientific integrity with flying colors. Somehow, it may have slipped his mind how geostatistical software converted Bre-X’s bogus grades and Busang’s barren rock so smoothly into a massive phantom gold resource. But then, the geostatocracy has worked long and hard to ensure mining professionals never get a grasp of classical statistics.
It brings me back to my chat with NRCan’s Emeritus Scientist. I brought to his attention that a good test to verify McGill's stochastic mine planning optimization would be to apply it to Bre-X’s data. Agterberg saw it differently because Bre-X's data was “no real data”. No real data? But mining investors thought Bre-X was real! Didn't Gemcom’s software convert Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource? And wasn't the battle to take over Bre-X Minerals a really bizarre affair?
This was my second chat with NRCan’s Emeritus Scientist after we had found out in 1989 that geostatistics is a scientific fraud. It brought back an odd dialogue in 1992 with Dr W D Sinclair, Editor, CIM Bulletin, and Dr F P Agterberg, Associate Editor. We talked about a technical brief on Abuse of Statistics. I'll keep that tangled tale for some other place and time!