Not quite fit for professional statisticians

Professor Dr Michel David said so himself. He pointed out his textbook is not for professional statisticians. He was talking about his very first textbook. I bought a copy of Geostatistical Ore Reserve Estimation, and worked my way through it. David was dead on when he predicted, "…statisticians will find many unqualified statements here.” All I really wanted to know is how David derived unbiased confidence limits for metal grades and contents of ore deposits. But he didn't do it! Why would the author of the very first textbook on geostatistics fail to show how to derive unbiased confidence limits?

I had derived unbiased confidence limits for metal grades and contents of concentrate shipments. Mines and smelters want to know the risks associated with trading mineral concentrates. Metal traders were keen to work with my method and several ISO Technical Committees approved it. So, we put together an analogous method, called it Precision Estimates for Ore Reserves, and submitted it for review to CIM Bulletin. I still don’t know why our paper ended up on David’s desk. What I do know is that David blew a fuse when he saw we didn’t even refer to geostatistics let alone work with it.

In Section 10.2.3.3. Combination of point and random kriging, David refers to Maréchal and Serra’s Random kriging. These authors were with the Centre de Morphology Mathematique when they presented it at the celebrated Geostatistics colloquium on campus at the University of Kansas, Lawrence on June 7-9, 1970. In a section called Punctual Kriging these authors showed nine measured grades and sixteen functionally dependent grades.

Figure 10 - Grades of n samples belonging to
nine rectangles P of pattern surrounding x

M&S’s Figure 10 morphed into Figure 203 on page 286 of David’s 1977 book. On the same page David claimed, “Writing all the necessary covariances for that system of equations is a good test to find out whether one really understands geostatistics.” What David didn't do was take a systematic walk that visits each hole only once and covers the shortest distance. But neither did Agterberg in 1970. Nor did M&S take a systematic hike on campus at that time.

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

Each of David's sixteen points within B is in fact a distance-weighted average point grade. It makes no sense at all to derive the false covariance of a set of functionally dependent values and ignore the true variance of the set of nine measured values. David did sense something was amiss. In Section 12.2 Conditional Simulations of Chapter 12 Orebody Modelling he confessed , “There is an infinite set of simulated values which will have these properties.”

Infinite set of distance-weighted average point grades
each derived from the same set of nine holes

Counting degrees of freedom for his set of nine holes would have been a foolproof test to find out whether David really understood statistics. What he looked at in this black hole were Agterberg's distance-weighted average point grades. Each is a zero- dimensional point grade. And each one of them lost its variance on Agterberg's watch. Dr F P Agterberg, Emeritus Scientist with Natural Resources Canada, did approve Abuse of Statistics but wasn't himself into testing for spatial dependence and counting degrees of freedom.

David's 1977 Geostatistical Ore Reserve Estimation and Journel and Huijbregts's Mining Geostatistics rank among the worst textbooks I've ever read. Until David's 1988 Handbook of Applied Advanced Geostatistical Ore Reserve Estimation came along. His work was founded by the Natural Science and Engineering Research Council of Canada with Grant No 7035. What a waste!