This is what I think of a lot of the fancy stats. It was a commentary in the Mining Journal in 1994.
Neostatistics In Geoscience;
Neostatistical thinking will one day be as necessary as the ability to count and spell. Jon W. Merks of Matrix Consultants Ltd presents his latest persiflage on geostatistical theory and practice.
Probability and statistics are fraught with aggravating requirements that restrict their usefulness in science and engineering. A case in point is the requirement of functional or statistical independence, an obscure requirement that allegedly makes it impossible to create more data from measured data.
We examined the effect of that irksome requirement and concluded that it adds more to the cost of data acquisition in geoscience than its relevance justifies. Therefore, we have developed a variant of statistics that circumvents that silly requirement. The literature on probability theory reveals that the requirement of statistical independence evolved long ago for no apparent reason. Perhaps introduced to eliminate errors that occurred all too often when statisticians worked with abaci, logarithmic tables and slide rules, it seems to have matured into dogma (Aldrivel, 1894). The digital computer played a key role in the development of a cost-effective alternative to statistics, in evaluating the intuitive features of neostatistics, and in making all its innovative tools and techniques accessible to those who want to become qualified neostatisticians.
We set out to prove that statistical dependence is irrelevant by entering an infinite set of randomly distributed variables into a Pentagon DC/320/ with a dolby-enhanced artificial intelligence quotient (AIQ) rated at 199.98 on the Stanford-Binet scale. Its plot exhibited a perfectly normal Gaussian probability distribution without a trace of binomial interference, the discrete pattern of which would have confirmed the deconvolution of the set into independent and dependent subsets, a phenomenon not unlike the deconvolution of other types of independence in nascent state when bred in captivity near the declustered quasi-stationarity of event horizons between black holes and white dwarfs.
Based on our test results we felt justified in postulating that statistical dependence vanishes if, and only it; a computer with an above average AIQ is utilised to suppress the deconvolution of infinite sets of randomly distributed variables (any set of hyperergodic variables) into dependent and independent subsets. Hence, the requirement of statistical independence in probability theory becomes quite obsolete when computers with more than average AIQs are applied to less than infinity sets of marginally ergodic variables (preferably less than 1.96% ergodicity).
Perhaps not unexpectedly to the uninitiated who still struggle with classical statistics the irrelevance of statistical dependence makes degrees of freedom, too, vanish without a trace, Unlike statisticians who discriminate against small data sets and in particular against measures of central tendency to which they do not accord even a fraction of a degree of freedom, the neostatistician, non-conformist but scientifically astute and socially responsible, fears that even the slightest degree of freedom leads to gambling and substance abuse.
Even though the arithmetic mean is the most common measure for central tendency, it is not surprising that the weighted average has become so popular in geoscience. After all, any set. of two or more variables in an n-dimensional sample space has only one arithmetic mean but an infinite set of distance weighted averages (Krytopocus, 1994). The ordinary statistician. is mostly preoccupied with that one arithmetic mean but the neostatistician believes that far too many weighted averages go to waste.
Figure 1 shows a two-dimens:onal sample space with a set of nine measured variables and Domain A in which is plotted a subset of only sixteen distance weighted averages out of the infinite set; The practice of calculating distance weighted averages will be referred to as burting in recognition of Sir Cyril Burt's early contribution to neostatistics. Burt, a renowned psychologist and statistician, studied monozygotic twins either raised together or separated at birth. Most parents in Burt's days, unaware of his research and oblivious to the need for sound experiment design, raised twins together which caused his data base for separated twins to be so exasperatingly small that he had no choice but to augment his set of measured data with calculated data.
In neostatistics, too, it is permissible to augment or even replace a measured set with calculated data provided that additional data are either unavailable or too expensive to acquire. The most popular neostatistical technique is to first burt a robust. subset of the infinite set of distance weighted averages from the set of measured data, and then calculate burting variances and covariances for the subset. Block and global burting, macro and micro burting, ordinary and extraordinary burting, random and systematic burting, and simple coburting, are but a few of the rigorous data augmentation techniques currently available to the discriminating neostatistician (Dogmadodos, 1994, Jokewitz, 1994).
Even our staff at the Centre for Advanced Neostatistics (CAN) did not fully appreciate the power of burting until a computer was left to burt overnight unintentionally. n 1 Figure 2 shows the same two-dimensional sample space with Domain A in which is plotted, it is hoped, the infinite set of distance weighted averages (burted estimates in neostat parlance).
ni Boris Boondoggle, C4AV's former caretaker who discovered the infinite set when he forgot to switch off one of our Pentagon computers is presently working on his PhD in Applied ..Veostatiszics at the Pacific School of Mines where he will defend his thesis entitled A Study of I lie Burting: Towards Perfect correlations and Zero Variances' on April 1, 1995,
Applied neostatistics not only eliminates the need for all those irritating tables with critical values and degrees of freedom but also reduces the number of drill holes required to identify a mineable resource. While the odd ignoramus has insinuated that burting obliterates structures and redistributes grades, we find it reassuring nonetheless that somewhere in Domain A some ore grade material may well be encountered during mining, indeed there is no limit to the good CAN's team of highly qualified neostatisticians can do with even the smallest set of measured data. The Centre of Applied Neostatistics is committed to explore further the theory and practice of a unique variant of statistics with audacity and unwavering respect for scientific integrity.
References
Adrivel, M. Fehlerfreuden (The joy of erring) Zeitschraft for Okkulte Mathamatik, Volume 42, pp 1-666, :Ian 1894
Dogmadodos M. How to burt with unlimited confidence Popular Neo.statisfea, Volume 1, pp 911-913 Jan 1994
Jokewitz, A. From underburting to perfect burting Journal .7.1 for Applied Neostatistics,; Volume 1, pp 11-111,Feb 1994
Kryptopocus, A From overburting to perfect burting Neostatistical Bulletin, Volume 1, page 1, Mar 1994
Figure 1, Subset of sixteen (16) distance weighted averages c.;alculated from a set of nine (9) variables.; Figure 2, infinite set of distance weighted averages calculated from a set of nine (9) variables