Casting dice and tossing coins at Stanford

Behind Stanford’s motto “The wind of freedom blows” is a rich history. It was President Gerhard Casper on October 5, 1995 who put a score of fine points to it. Who could possibly object to the freedom to teach and be taught sound sciences? When President Casper spoke in 1995 the freedom to assume spatial dependence between measured values in ordered sets had been entrenched in geostatistics since 1978. Herbert Hoover, Thirty-First President and Stanford’s very first mining engineer, would have been shocked. Who would put a mine stope together by casting dice? How could geostatistics have converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource?

Here’s what I have been trying to bring to the attention of Dr J L Hennessy, Stanford’s President. Geostatistics ignores the concept of degrees of freedom and violates one-to-one correspondence between functions and variances. Agterberg’s distance-weighted average does not have a variance. Neither does David’s distance-weighted average. I pointed out that it took the Papacy 300 years to right a wrong. I did so the last time I wrote to Stanford’s President on February 13, 2008. I wrote that I thought Stanford could right a wrong much faster. He could have asked a Stanford statistician whether or not the geostatocracy has the freedom to assume spatial dependence between measured values in ordered sets. What I wrote in 2008 didn’t hit Dr Hennessy’s list of things to do.

I do appreciate my own freedom and am a stickler for degrees of freedom. So, I looked at Stanford’s statistical scholars and warmed to what I read about Professor Dr Persi Diaconis. He looked like the kind of scholar who would take seriously my crusade against the geostatocracy and its army of degrees of freedom fighters. Stanford Report of June 7, 2004, pointed out, “Persi Diaconis has spent much of his life turning scams inside out.” Now there’s a professional scam buster of sorts. It became even better than I thought it would be when I read what Professor Dr Persi Warren Diaconis had done. He left home at 14, hit the road with Dai Vernon, the famous Ottawa-born slight-of-hand magician, and got Vernon’s magic touch.

When I was searching Stanford’s website for a genuine statistician, I found out that Dr Diaconis doesn’t respond to email. I took a chance and did send him an email anyway on February 23, 2009. That was more than year after my last email to Stanford’s President. Diaconis is indeed true to his word and did not respond to my email. I had suggested that Stanford should give real statistics a fighting chance. So, I decided to call Diaconis but nobody picked up the phone. I called between March 26 and April 22, 2009, and did so between 13:00 and 16:00 PST. I called sixteen times and the line was busy twice. I could have but decided not leave a message.

Diaconis knows how to toss a coin. So much so that he can make the same side of a coin come up ten times in a row. He designed a mechanical coin tossing contraption that gives the same odds. What he did do was defy the Central Limit Theorem. Coins and dice played cameo roles when I taught sampling theory and practice in places are far apart as Greenland and Tasmania, and as Finland and the Philippines. I put in plain words how to tamper with the outcomes of tossing coins and casting dice. What I didn’t show is how to test for bias. A Stanford student should cast the same die often enough to infer absence of bias within acceptable bias detection limits. The catch-22 is that abrasion is bound to cause a bias before acceptable bias limits are obtained.

I taught sampling theory and practice on the basis of a binomial sampling unit that consists of 90% white beans and 10% of the same but red-dyed beans.

Each participant would take a small increment and a large increment, and count white and red beans in each. This simple sampling experiment made it easy to explain Visman’s sampling theory and practice, and his composition and distribution components of the sampling variance. Visman’s work proved that the most effective method to estimate the variance of the stochastic variable of interest in a sampling unit or a sampling space is to partition the set of primary increments into a pair of interleaved subsets. Of course, one pair of subsets gives but one degree of freedom. That’s why SQC programs should be implemented on a routine basis. The interleaved sampling protocol has been incorporated in several ISO standards.

The wind of freedom blows at Stanford University. What geostatistocrats have blown is the concept of degrees of freedom. Agterberg blew the variance of the distance-weighted average. Journel blew Fisher’s F-test for spatial dependence. Once upon a time Herbert Hoover wrote, “It should be stated at the outset that it is utterly impossible to accurately value any mine, owing to the many speculative factors involved. The best that can be done is to state that the value lies between certain limits, and that the various stages above the minimum given represent various degrees of risk.” Hoover’s 1909 Principles of Mining Valuation, Organization and Administration still make sense. Why then is the world’s mining industry hooked on assuming, kriging, smoothing, and rigging the rules of real statistics?