Doing more with less at McGill

The First Coming of Professor Dr Roussos Dimitrakopoulos to McGill University came to pass in June 1993. He had come all the way from Down Under to chair Geostatistics for the Next Century. It was a bash where geostatistical thinkers of the world had flocked together. They had come to praise Professor Dr Michel David and his 1977 Geostatistical Ore Reserve Estimation. David wrote in his Introduction on page VII that “…statisticians will find many unqualified statements here”. Not a single thinker asked why David had done so. My son and I found some odd gaffes when we studied David’s stuff. That’s the very reason why we wrote Precision Estimates for Ore Reserves. My abstract for The Properties of Variances raised more eyebrows than interest. I have posted on my website both the paper and its review by CIM Bulletin.

When all praise was said and done and duly recorded Dr RD went back to the University of Queensland, Brisbane, Australia. That’s where he honed his skill to do more with less. So what did McGill University think it got when Dr RD came to stay? Here’s how McGill’s University Relations Office on July 13, 2005 saw his Second Coming: “…It’s no surprise, then, that a world leader in the field of mining engineering has chosen Canada as a place to pursue his scholarship.” What world leader would be driven to merge stochastic mine planning and holistic mining? And Dr RD did all that while the properties of variances stayed as far beyond his grasp as they were in June 1993. Those were the very properties I had wanted to talk about at David’s shindig.

Professor Dr Roussos Dimitrakopoulos
Spanning disciplines, spanning the globe

Doing more with less sounds so forward looking and snobbish. But Stanford had already bested McGill at doing more with less. It did so after Matheron and a few of his disciples took the new science of geostatistics all the way to North America in 1974. Some novel science it turned out to be! The distance-weighted average lost its variance and morphed into a kriged estimate. Spatial dependence between measured values in ordered sets was to be assumed. Degrees of freedom went the way of the dodo. That’s how Professor Dr Georges Matheron and his mates have managed to make a mockery of applied statistics!

Professor Dr Roussos Dimitrakopoulos had come to chair Geostatistics for the Next Century. But he was also keen to speak about Spatiotemporal Modelling: Covariances and Ordinary Kriging Systems. It was a thoughtful touch to talk about David’s work at his bash. The more so since David had written much about covariances and kriged estimates in his 1977 Geostatistical Ore Reserve Estimation. We knew in the late 1990s that David was wrong on page 286 of Chapter 10 The Practice of Kriging. Here’s where the author of the very first textbook on geostatistics had strayed away from applied statistics. Figure 10 in Maréchal and Serra’s 1974 Random Kriging made a comeback in 1977 as David’s Figure 203.

Fig. 203. Pattern showing all the points within B,
which are estimated from the same nine holes.

Here’s what the author wrote in Section 10.2.3.3 Combination of Point and Random Kriging on page 286, “Writing all the necessary covariances for that system of equations might be a good test to find out whether one really understands geostatistics!” David’s exclamation mark may well have been inserted to imply the veracity of the whole quote. The problem is not so much with this statement but with the caption under Figure 203. All the points within B are not estimated but derived from the same nine holes. As such, each and every point is a function of the same set of nine (9) holes. And each and every one of them does have its own variance in applied statistics. No ifs or buts! Counting degrees of freedom would have been a good test to find out whether one really understands applied statistics. If all holes in a set of nine (9) were equidistant, then the number of degrees of freedom would be df=n-1 for the set, and dfo=2(n-1) for the first term of the ordered set. If distances between holes are variable, then the numbers of degrees of freedom are no longer positive integers but positive irrationals. Degrees of freedom do not disappear because Professor Dr Roussos Dimitrakopoulos says so.

I have told my story on the power of applied statistics and the flaws of geostatistics to the Members of CIM’s Vancouver Branch on Friday, January 29, 1993. CIM Bulletin and its peer review process have played a key role in the proliferation of geostatistics. It’s about time to tell my story about sound sampling practices and proven statistical tests.