Saturday, March 06, 2010

Voodoo statistics at IAMG

Acronyms serve to make long tags short. Ranking high among the world’s most famous acronyms are USA and IBM. Laser and taser are well-known objects that have but rhyme in common. EMF stands for Eclipse Modeling Framework. ASTM, DIN and ISO are familiar to those who develop and work with national and international standard methods. IAMG stood for the International Association for Mathematical Geology from 1968 to 2007. IAMG’s Council in January 2008 called it the International Association for Mathematical Geosciences. What IAMG's Council never did was set up an ISO Technical Committee on Reserve and Resource Estimation.

Professor Dr Georges Matheron may well have thought that he was peerless. In way too many ways he was indeed without peers. It was a blessing of sorts in disguise. All of his work is so richly embellished with symbols that tallied up to a tangle of formulas. All of it fell far short of a clear and concise text. He made up all sort of terms if and when required. But what he didn’t do was provide primary data sets. So, his work does not make an easy read even in French let alone in English. What does matter is that CdG's website has made Matheron's work accessible to the world.

So it came about in 1970 that Matheron’s new science of geostatistics got all geared up to do more with less. That was the very year it made its way to the University of Kansas, Lawrence. D F Merriam, Chief of Geologic Research, Kansas Geological Research, and IAMG Historian, called it a colloquium. It was a thoughtful touch that he dedicated the proceedings to ‘all geostatisticians and statistical geologists’. Matheron had come all the way from his Centre de Morphologie Mathematique to talk about Random Functions and their Application in Geology. His tour de force was to somehow force Brownian motion along a straight line. He didn’t spell out what Brownian motion and ore deposits could possibly have in common. What did matter most was that his so-called random functions are continuous along intervals between measured values in ordered sets.

Matheron was not the only geostatistical scholar from his Centre de Morphologie Mathematique. A Marechal and J Serra had come along to talk about Random Kriging. What captured my attention was M&S’s Figure 10. It turned out to be a dead ringer for Figure 203 in David’s 1977 textbook. Both figures showed how to derive a set of sixteen (16) distance-weighted averages from the same set of nine (9) holes. It may look like the miracle at the wedding of Cana in Galileo. But that’s what geostatistics is all about. Agterberg derived but a single distant-weighted average point grade from a set of five (5) measured values. Marchal, Serra and David derived a set of sixteen (16) distance-weighted averages. Each and every so-called kriged estimate is a zero-dimensional and variance-deprived weighted average point grade. It turned into the heart and soul of Matheronian geostatistics.

Infinite set of distance-weighted average point grades

When Matheron's new science of geostatistics struck the University of Kansas, Lawrence in June 1970 it didn’t hit any raw nerves. At that time, IAMG stood for International Association for Mathematical Geology. And Matheronian geostatistics kept coming along by hook and by crook.

Assume, krige, smooth, be happy!

IAMG’s News Letter No 38 reported that all members of its discipline belong to one of three schools of thought: Those who practice and strongly advocate geostatistics, those who are violently (and vocally) opposed to geostatistics, and the silent majority, who wonder what all of the shouting is about. The same newsletter shows Michel David accept the Krumbein Medal from IAMG’s President John Davis. News Letter No 38 did put into perspective why our paper on Precision Estimates for Ore Reserves troubled David as much as it did. He didn’t know how to derive unbiased confidence limits for the mass of metal in a volume of in-situ ore. Why then did David expect Merks & Merks to refer to twenty years of geostatistical literature? Many questions and but few answers. Stay tuned for sound statistics!