Agterberg's way

Here’s what Agterberg wrote to me, “It seems that you are an iconoclast with respect to spatial statistics including kriging.” He did so in his reply to my email of October 7, 2004, on the subject of The Silence of the Pundits. That’s not quite what I had written to him. I didn’t bring up spatial statistics or kriging. It seemed as if Agterberg’s tribute to Matheron had become his new reality. All I had asked were questions about the distance-weighted average. I didn’t know in 2004 that Agterberg himself had derived this distance-weighted average point grade first in his 1970 Autocorrelation Functions in Geology and once more in his 1974 Geomathematics. What kept me spellbound in this Millennium was Matheron’s mind-numbing opus after it was posted on the website of the Centre de Géosciences. Since December 12, 2008, all I get to look at is “Not found.” I was used to Matheron’s prose and symbols but did miss his primary data. I wish his collected works were posted for posterity. It is such stunning stuff.

Agterberg brought up a friend of mine with similar criticisms who had “orally presented his views at IAMG meetings.” Agterberg thought I might wish to do the same. Good grief! What I do is put my thoughts in writing. I did so with The Properties of Variances in 1993. I wanted to bring the properties of variances within the grasp of geostatistical thinkers. Many had gathered at McGill to celebrate Geostatistics for the Next Century. It sounded somewhat premature but geostatistics was growing in leaps and bounds in those heady days. The properties of real variances were rather late in coming and the Bre-X fraud was just around the corner. As luck would have it, the properties of variances didn’t quite suit the tribute to David’s work with its infinite sets of simulated values and zero pseudo variances. That sort of science fiction still underpins McGill’s curriculum for budding geoscientists. McGill University is a source of goofy geosciences.

Philip and Watson’s Matheronian Geostatistics: Quo Vadis? (MG, Vol 18, No 1, 1986) made Matheron fit to be tied up. His rebuttal took the form of a Letter to the Editor (MG, Vol 18, No 5) on the subject of Philipian/Watsonian High (Flying) Philosophy. Agterberg’s way is oral criticisms but I really liked Matheron’s written rebuttal. On the other hand, Matheron’s temper tantrum driven tirade might have boggled the odd geostatistical mind. I wrote about voodoo statistics in the 1990s but it failed to trigger another mind numbing tirade.

Matheron was called the Founder of Spatial Statistics and the Creator of Geostatistics. Why did his ramblings merit twin epitaphs? The more so since Berry and Marble’s 1968 Spatial Analysis, a Reader in Statistical Geography, makes no mention of Matheron’s work. Chapter 8 Fourier Analysis in Geology in Section IV Analysis of Spatial Distributions refers to Agterberg’s Methods of Trend-Surface Analysis. Agterberg talked about it at a 1964 symposium with Applications of Statistics in its lengthy title. Just the same, Matheron did dismiss trend surface analysis at the 1970 geostatistics colloquium. Why did the masterminds not see eye-to-eye on spatial statistics when Matheron brought his new science to the USA?

All that gibberish troubled me even more when I read Agterberg’s response to my questions of October 11, 2004. On September 23, 2004, I had posed the same questions to the Councilors of the International Association for Mathematical Geology, and to the Editor and his Associate and Assistant Editors of the Journal for Mathematical Geology.

Who lost the variance of a single distance-weighted average?

Who found the variance of a set of distance-weighted averages?

Only one Assistant Editor responded by pondering, “If geostatistics is not furthering a certain problem, a different type of mathematics may solve it.” Now there’s one partially open JMG mind at work! It didn’t tempt me into giving oral criticisms at any IAMG meeting.

Here’s what I wrote on October 12th in response to Agterberg’s Aberdeen message of October 11, 2004. “I just want to know when and on whose watch the variance of the single distance-weighted average vanished, and when and under whose tutelage the kriging variance and covariance of a set of kriged estimates became the cornerstones of geostatistics, spatial statistics, kriging, smoothing, or any other popular computation that violates the requirement of functional independence and the concept of degrees of freedom”. His way was not to respond.

Agterberg had failed to derive the variance of his distance-weighted average point grade first in 1970 and again in 1974. What he did do was make a sham of scientific integrity when he was IAMG’s President. He did call it the International Association of Mathematical Geosciences. Agterberg’s way was to stay silent. It’s the wrong way in science. The right way would be to revise Geomathematics.