ASTM ought to shred geostats standards

ASTM Committee D18 on Soil and Rock had arranged an International Symposium on Geostatistics for Environmental and Geotechnical Applications. The stage was set at the Hyatt Regency, Phoenix, Arizona on January 24-25, 1995. One of its co-chairs was R Mohan Srivastava. His point of view on geostatistics was already an integral part of BC Environment Guidelines. Environment Canada has a handbook called The Inspector’s Field Sampling Manual. I read it when EC took a client of mine to court. Here’s what EC’s inspectors are taught, “Systematic samples taken at regular intervals can be used for geostatistical data analysis, to produce site maps showing analyte locations and concentrations. Geostatistical data analysis is a repetitive process, showing how patterns of analytes change or remain stable over distance or time spans”. It refers to shellfish samples taken at 1-km intervals along a shore, and to water samples taken from varying depths in a water column. It’s just as short of primary data sets and derived statistics as is Matheron’s whole magnum opus. The question is then why geostatistical data analysis underpins the joint study of the Great Lakes by Canadian and US governments. It boils down to blind ambition and blatant contempt for the properties of variances.

Founder of Geostatistics
Founder of Spatial Statistics

ASTM Committee D18 was set up after Geostatistics for the Next Century came about somewhat early in 1993. That’s when geostatisticians from far and wide had flocked together at Montreal, Canada. They had come to praise David’s 1977 Geostatistical Ore Reserve Estimation. Nobody asked David why he had not derived the variance of the distance-weighted average. The more so since Dr Isobel Clark did derive this variance in her 1979 Practical Geostatistics. Sadly, she wasn’t present at McGill. All I had wanted to do was point out that functions do have variances. Alas, my view was as unpopular at Geostatistics for the Next Century as it was when Professor Dr Michel David was the chief enforcer of geostatistics with CIM Bulletin.

David’s peers had come not only to praise his 1977 textbook but also to peddle their own geostat stuff. For example, Journel peddled Modeling Uncertainty: Some Conceptual Thoughts. What David had done in this textbook was derive sixteen (16) distance-weighted averages from nine (9) boreholes. He didn’t derive the variance of each distance-weighted average. He didn’t test for spatial dependence between ordered boreholes. Neither did he count degrees of freedom. David did come up an infinite set of what he then called “simulated values”. Journel derived the zero kriging variance of David’s infinite set of simulated values AKA kriged estimates. Here’s in a nutshell what Professor Dr Georges Matheron has taught all of his disciples. Assume spatial dependence between measured values in ordered sets, interpolate between measured values, smooth the least biased subset of some infinite set of kriged estimates, and rig the rules of applied statistics with impunity. He did all of his thinking about Brownian motion along a straight line in this gloomy edifice.

Centre de Géostatistique
Centre de Morphology Mathématique

Matheron invoked it on this continent in June 1970. Brownian motion set the stage to assume spatial dependence between measured values in ordered sets rather than test for it by applying Fisher’s F-test. One of Matheron’s most gifted disciples was Stanford’s Journel. Not surprisingly, Journel never did what Matheron had not taught him to do. But surely, Journel knew a bit of spatial stuff!

Merks and Merks Precision Estimates for Ore Reserves was praised by and published in Erzmetall. All we did was test for spatial dependence between gold grades of an ordered set of twelve (12) rounds in a drift. Here’s what Stanford’s Journel wrote on October 15, 1992 to Professor Dr Robert Ehrlich, JMG’s Editor, “…Mr. Merks’ anger arises fro [sic!] a misreading of geostatistical theory, or a reading too encumbered by classical “Fischerian” [sic!] statistics.” Journel beat a bit more around the bush when he wrote, “The very reason for geostatistics or spatial statistics in general is the acceptance (a decision rather) that spatially distributed data should be considered a priori as dependent one to another, unless proven otherwise.” He ponders on page 6 of his clarification, “I’ll leave it to you to decide whether this letter should be sent to J. W. Merks; however, I strongly feel that Math Geology has had more than its share of detracting invectives.” Professor Dr Robert Ehrlich, JMG’s Editor, wrote on October 26, 1992, “Your feeling that geostatistics is invalid might be correct.” JMG's Editor did attach a copy of Journel’s 6-page letter. Distracting invectives? I’ll say!

How many Stanford students did he teach about Brownian motion along a straight line? What a silly notion when measuring mineral inventories. What’s more, Fisher’s F-test is forbidden where spatial dependence is deemed to exist a priori. That’s why ASTM ought to shred all standard methods cooked up by ASTM Committee D18 on Soil and Rock. These letters and many others are or will soon be posted on my website under Correspondence. Of course, ASTM Committee D18 ought to be dismissed. Soon I’ll post where we were before we met Dr Ricardo R Stone and his partner. He passed away shortly after we met. Ricardo was an IBM Fellow and a Member of ASTM E11 on Quality and Statistics.