When my son and I were working on Precision Estimates for Ore Reserves in the late 1980s, we had copies of David’s 1977 Geostatistical Ore Reserve Estimation and Clark’s 1979 Practical Geostatistics. We wanted to know how geostatisticians derive confidence limits for metal contents of ore reserves. The problem is they don’t! By contrast, ISO/TC183 did approve in 1993 a homologue of the same method to derive confidence limits for copper, lead and zinc contents of concentrate shipments.
One of the few geologists who still talked to me in those days gave me his copy of Journel and Huijbregts’ 1978 Mining Geostatistics. My reviews of the first three textbooks are posted on my website. I have offered to review more recent textbooks and study the latest innovations in geostatistical theory and practice. I’ve yet to receive a single copy! So, don’t let a textbook of a more recent vintage gather dust on your bookshelf. Mail it to me and I’ll post my review where it’s easy to find. By the way, I don’t sell anything on my website. I give away advice on sound sampling practices and proven statistical methods. For example, Precision Estimates for Ore Reserves was thrashed by enforcers of geostatistical dogma but praised by and published in Erzmetall 44, Oct, 1993. This paper and several others are posted on my website under Reviewed papers.
Visit and click “a wonderful kriging game of chance” on my Home page. Play this game with Clark’s hypothetical uranium data. Enter different coordinates and see what you get. Don’t enter the moon’s coordinates because it creates too much hypothetical uranium in space. And Clark’s distance-weighted average hypothetical uranium grades get too close to the arithmetic mean grade. Clark wondered whether or not the Central Limit Theorem holds. Fortuitously, Agterberg and Matheron had already eliminated that ubiquitous theorem behind sampling practice
And don’t test for spatial dependence in Clark’s sample space by applying Fisher’s F-test to var(x), the variance of the set, and var1(x), the first variance term of the ordered set. I never walk to the beat of kriging drums. What I do is walk a systematic walk that covers the shortest possible distance between all coordinates and derive the first variance term of the ordered set. Given that the observed value of F=var(x)/var1(x)=4,480/2,161=2.07 does not exceed F0.05;4;8=3.84, it follows that Clark’s set of hypothetical uranium data does not display a significant degree of spatial dependence. Hence, the distance-weighted average hypothetical uranium concentration of 371 ppm is not necessarily an unbiased estimate.
Surely, assuming spatial dependence beats the odds of finding no spatial dependence at all! And it makes counting pesky degrees of freedom unnecessary! Just assume, krige, smooth, rig the rules of real statistics, and be happy.