Geostatistics continues to evolve as a discipline

That's what Mark Corey wrote when Canada's Minister of Natural Resources asked him to respond to my message. Mark Corey is Director General Mapping Services Branch and Assistant Deputy Minister, Earth Sciences Sector. He is the chief mapmaker for NRCan so to speak. I was ticked off big time when he called geostatistics a discipline. But I told myself it could have been worse. He could have called it a scientific discipline. He is also one of several experts behind NRCan's 2008 "bulletproof" climate report. He testified at the Senate Committee for Energy, Environment and Natural Resources. I wish I could have asked him a few questions.
What I wanted him to tell me in plain words is why each and every distance-weighted average point grade doesn't have its own variance. Dr Frits P Agterberg thought his distance-weighted average point grade didn't have a variance in the early 1970s. Agterberg was wrong then. He's wrong now. It's high time for NRCan's Emeritus Scientist to explain why his distance-weighted average point grade still doesn't have a variance in 2009!
None of the five (5) points in the next picture have anything to do with pixels on a map. Each point stands for some sort of hypothetical uranium concentration that was measured in some way in samples selected in this sample space at positions with known Easting and Northing coordinates. I didn't make it up but Dr Isobel Clark did in her 1979 Practical Geostatistics. She worried whether or not the Central Limit Theorem would hold so she didn't derive it. Clark's figure would have been a dead ringer for Agterberg's 1970 and 1974 figures if it were not for her hypothetical uranium concentrations.

Fig. 1.1. Hypothetical sampling and estimation situation
Fig. 4.1. Hypothetical sampling and estimation situation - a uranium deposit

I want to prove Clark's set of hypothetical uranium concentrations does not display a significant degree of spatial dependence. So, let's take a systematic walk that visits each point only once and covers the shortest possible distance. Clark's selected position is not equidistant to each of her hypothetical uranium concentrations. That's why the number of degrees of freedom is not a positive integer but a positive irrational. Applying Fisher's F-test to var(x) = 4,480, the variance of the set, and var1(x) = 3.640, the first variance term of the ordered set, gives an observed F-value of F = 4,480/3,640 = 1.23. This observed F-value does not exceed the tabulated F-value of F0.05;4;4.90 = 6.38 at 95% probability. Therefore, Clark's distance-weighted average hypothetical uranium concentration of 371 ppm is not an unbiased estimate.
Clark didn't need Agterberg's approval to derive confidence limits and ranges for this point grade. Neither did I and came up with a 95% confidence interval of 95% CI = +/-111 ppm or 95% CI = +/-29.8%rel, and a 95% confidence range with a lower limit of 95% CRL=261 ppm and an upper limit of 95% CRU=482 ppm.
Here's what I would want Mark Corey to do. Visit NRCan's Emeritus Scientist in the privacy of his ivory tower and borrow his 1974 Geomathematics. Go to Chapter 6 Probability and Statistics and look at Fisher's F-test in Section 6.13. That will be all. At least for now!