Tuesday, August 07, 2012

From human error to scientific fraud

Such reads the caption that these days graces my website. A few changes have been made since it was posted in 2003. What pleased me most was that loads of facsimiles and scores of snail mails could be whittled down to links. It didn’t take Merks and Merks long to figure out why geostatistics is an invalid variant of applied statistics. All it took was a close look at geostatistics when CIM Bulletin did reject Precision Estimates for Ore Reserves. We did so since it was praised by and published in Erzmetall 44 (1991) Nr 10. It was easy  to find out what was wrong with geostatistics. It matters not at all that the distance-weighted average is called a kriged estimate. What does matter is that it did somehow shed its variance.  Geostatistocrats have not yet put into plain words why each and every kriged estimate has lost its variance.  

Matheron’s new science of geostatistics has made landfall on this continent in 1970. A geostatistics colloquium in North America took place on campus at The University of Kansas, Lawrence on 7-9 June 1970. Its proceedings were recorded by Daniel F Merriam and published by Plenum Press, New York-London, 1970. A Maréchal and J Serra had graduated at the Centre de Morphologie Mathématique at Fontainebleau, France. They had come to shed light on Random Kriging. The authors point to Punctual Kriging in Figure 10. It shows how to derive a set of sixteen (16) grades from a set of nine (9) grades. It looked a bit of a slight of hand but it seemed to make sense to Professor Dr Michel David. So he posted  Maréchal and Serra’s Figure 10 on page 286 in Chapter 10 The Practice of Kriging of his 1977 textbook.

Figure 10 – Grades of n samples belonging to
nine rectangles P of pattern surrounding x
Figure 203 – Pattern showing all points within B,
which are estimated from the same nine holes

Why geostatistics is but a bogus variant of applied statistics is simple comme bonjour! Functions do have variances. No ifs or buts! That’s why one-to-one correspondence between functions and variances is sine qua non in applied statistics. Degrees of freedom are positive integers when all measured values in the set have the same weight. Degrees of freedom are positive irrationals when all measured values in the set have variable weights.

The power of applied statistics has served me well throughout my career. It did because so much of applied statistics is intuitive. For example, any set of measured values has a central value, a variance, a standard deviation and a coefficient of variation. The central value is either its arithmetic mean or some weighted average. Numbers of measured values in sets define confidence limits for central values. Testing for spatial dependence between measured values in ordered sets shows where orderliness in sample spaces or sampling units dissipates into randomness. Never did it make any sense in my work to assume spatial dependence between measured values in ordered sets.  What does make sense is testing for spatial dependence, skewness and kurtosis.

The central limit theorem defines the relationship between a set of measured values and its central value. Even David did refer to “the famous central limit theorem”. Yet, he didn’t deem it famous enough to add to his Index. Testing for spatial dependence between measured values in sample spaces and sampling units plays a key role in scores of applications in a wide range of disciplines. Participation in several standard committees served to make applied statistics indispensable in so many ways. I do have but a few simple questions at this stage. Why did Professor Dr Georges Matheron (1930-2000) cook up such a silly variant of applied statistics? Why was Matheron’s work deemed beyond peer review! Why didn’t anybody point out to him that all functions do have variances? Why doesn’t the mining industry care about unbiased confidence limits for metal contents and grades of reserves and resources?

Today I woke up as a certified octogenarian. I took a ride on my stationary bike and got nowhere. Yet I felt good. But I am still sick and tired of those who play games with other people’s money.  All I want to do at this stage of my life is show how to work with sound statistics and how to get rid of bogus science.

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