Saturday, May 09, 2009

Geostatistical data analysis - Quo Vadis

More than 20 years ago G M Philip and D F Watson posed the question Matheronian Geostatistics - Quo Vadis? Philip and Watson’s question was published in Mathematical Geology, Vol 18, No 1, 1986. The text consisted of 21 pages and the list of references counted 86 works. Sir R A Fisher’s 1959 Statistical methods and scientific inference is on the list. Fisher’s ubiquitous F-test is applied to test for spatial dependence in sampling units and sample spaces alike. To assume spatial dependence appealed more to Matheron than to verify it by applying a sort of test cooked up by some kind of knight across the Channel. So, counting degrees of freedom failed to make Matheron’s list of things to do. He worked mostly with symbols and rarely with real data. Shortsighted thinking still runs rampant at the Centre de Géostatistique, 5 Rue St Honoré, Fontainebleau, France.

Matheron’s edifice groupe de réflexion statistique nouveau

Matheron’s rebuttal in his Letter to the Editor was called Philipian/Watsonian High (Flying) Philosophy. It was published in Mathematical Geology, Vol 18, No 5, 1986. It shed a bright light on Matheron’s mind when he ranted, “But all of this is clear now: geostatistics is just a dastardly conspiracy organized with diabolic cunning, by a secret order of one-dimensional Jesuits.”

Assume, krige, smooth, and be happy

Here’s what Matheron’s new science of geostatistics is all about. Matheron in 1954, in his very first Note Statistique No 1, failed to derive variances of weighted average lead and silver grades of ordered core samples of variable length and density. In his 1960 Note Geostatistique No 28 Matheron coined his honorific krigeage eponym. What he didn’t do was test for spatial dependence between ordered block grades. In his 1970 Random functions and their applications in geology Matheron brought to light a likeness of some sort between ore deposits and Brownian motion. That’s why Matheron and his flock took to working with Riemann integrals rather than with Riemann sums. It explains why counting degrees of freedom failed to make the grade in Matheronian geostatistics. Blatant disrespect for Fisher’s F-test, for degrees of freedom, and for the Central Limit Theorem, prove my point. Professor Dr Georges Matheron was a self-made wizard of odd statistics.

Once upon a time I was an accidental reader of A Sampling Manual and Reference Guide for Environment Canada Inspectors. It was also called The Inspector’s Field Sampling Manual. I read the First edition. I thought about reading a Second edition and got headache. Will that be crafted by the most gifted geostatistocrat in Canada? Or will some lowest bidder put it together? But who put Geostatistical data analysis in the First edition? Did Environment Canada, too, have a geostatistically qualified Emeritus Scientist on board?

Section 2.1.2 Sampling Approaches points to random sampling, systematic sampling and judgement (sic) sampling. EC’s inspectors are also taught, “Systematic samples taken at regular time 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 analyte change or remain stable over distances and time spans.” Close but not quite close enough for EC’s average inspector. What a pity that meaningful examples are missing as much in EC's First edition as they are in Matheron's magnum opus.

One example points to shellfish samples taken at 1-km intervals along a shore. What EC’s Inspectors are not taught is how to test for spatial dependence between ordered shellfish counts. A sampling variogram would give much more valuable information than a simple test for spatial dependence. EC's inspectors should not even think about charting semi-variograms. The status quo is unacceptable if Environment Canada wants to study climate change. So, what's EC's brass waiting for? Students at Canadian Universities may want to explore EC's National Climate Data and Information Archive. Many student's do not even know why geostatistical data analysis is a scientific fraud. It's time to call a scientific inquiry!