My grandma taught me not to put all my eggs in one basket. She was a caring matriarch who told inspiring stories. She played card games but odds were beyond her grasp. She played for pennies but not with other people’s pennies. She didn’t have a PhD in anything. But I took her word and never put all my eggs in one basket.

Dr Pierre Gy (1924-…) and Professor Dr Georges Matheron (1930-2000) put the French sampling school on the world map. Matheron never put core samples from a single hole in one basket so to speak. But Gy did put a set of primary increments taken from a sampling unit in one basket. So he didn’t even get a single degree of freedom. The interleaved sampling protocol is described in several ISO Standard Methods. It is also described in Chapter 6 Spatial Dependence in Material Sampling of a textbook on Approaches in Material Sampling. Dr Bastiaan Geelhoed edited the text. IOS Press published the book in 2010.

The reliability of a pneumatic conveying calculation is depending on:

- The accuracy of the input parameters and the degree in which they reflect the reality.

- The accuracy of the performance data of the pneumatic installation components.

- The completeness of the theory on which the calculation algorithm is built.

- The degree of approximations in the calculation algorithm.

Ambient conditions:

- Intake conditions:

For a pressure pneumatic conveying system, the intake conditions are important as they determine the mass flow of gas.

• The intake conditions are:
  • Temperature

The intake temperature determines the intake density of the compressor. A positive displacement compressor will compress a less dense volume and  therefore delivers less mass flow.

A diffuser controlled turbo compressor delivers a constant mass flow.

The intake temperature varies with the weather conditions.

• pressure

Travelling back in time was what H G Wells made nightmares off. I have read the latest biography about his life and time. Michael Sherborne called it Another Kind of Life. Here’s what I learned. Wells did not praise statistical thinking because Ronald A Fisher won the case for degrees of freedom. Sherborne pointed out that the quotation which Darryl Huff did attribute to H G Wells came from Samuel S Wilks. When Wilks gave his 1954 presidential address to the members of the American Statistical Association, he said: ”The great body of physical science, a great deal of the essential fact of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood for complete initiation as an efficient citizen of one of the great new complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima, as it now to be able to read and write.” Sherborn tracked that rather rambling sentence down to Chapter 6 of Wells’s Mankind in the Making. It was Wells himself who brought it down to, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” Wells had a way with words and women. But who would not want Wells’s way with words?

Assume that I have invested in BHP Billiton. Surely, I would want to know where my mining giant is going. And most of all I would want to know whether or not Chairman Marcus Kloppers knows what he is doing. Does he have a buddy on his Board who knows a bit about applied statistics? Would she or he know that functions do have variances, and that only measured values do give degrees of freedom? Take a long look at my short story. Assume, krige, smooth, and rig the rules of applied statistics. The roots of geostatistics rest in the archives of CIM Bulletin. What I have done for more than twenty years is keep my story alive. It’s about an invalid variant of applied statistics. It was geostatistics that converted Bre-X’s bogus grades and Busang’s barren rock so smoothly and effortlessly into a massive inferred gold resource. Just the same, Fisher’s F-test proved that the intrinsic variance of gold at Busang was statistically identical to zero. I do not know where Kloppers was when Bre-X Minerals blew up. What I do know is that BHP Billiton was not the only one who put up plenty of play dough to do more with fewer boreholes. So let’s go forward to the play!

Assume, krige, smooth, and rig the rules of applied statistics. That’s all! It’s simple to assume spatial dependence between measured values in ordered sets. And to krige or not to krige is never a question. Not since Matheron himself in the 1960s cooked up the krigeage eponym. It took on a life of its own when the kriged estimate and the kriging variance became the heart and soul of Matheron’s new science of geostatistics. Smoothing sounds so soothing! Yet, the smoothing stage should not be taken lightly. In fact, the kriging variance of the least biased subset of some infinite set of kriged estimates should not be “over-smoothed”. Of course, one would not expect those who are taught to assume, krige and smooth to do too much of it with too few data. Matheron thought in 1954 that he worked with applied statistics. He was wrong! Journel in 1992 taught that spatial dependence between measured values in ordered sets may be assumed. Matheron’s most gifted disciple was wrong! It’s a piece of cake to assume spatial dependence between measured values in sampling units and sample spaces. To apply Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set is much more intuitive. It was Journel who pointed out that one’s reading ought not to be “… too encumbered by classical Fischerian [sic!] statistics”.

That’s what I read in the Vancouver Sun of September 14, 2010. In fact, the heading read: “Muzzling scientists offends principle of public service.” Why would Natural Resources Canada muzzle its scientists? And why so shortly after Labor Day? A few NRCan scientists would not mind to be muzzled. But Dr Frederik P Agterberg, Emeritus Scientist with the Geological Survey of Canada, ought to speak up. The trouble is he doesn’t want to. He is but one of a few scientists who could shed light on an inconvenient truth. Why did his distance-weighted average not have a variance in 1970? And why did all of Maréchal and Sierra’s distance-weighted averages not have variances in 1970? In time, the distance-weighted average morphed into a kriged estimate. Geostatistics is all about kriging variances of sets of kriged estimates. It has made such a mess of the study of climate change.

Here are but a pair of my lingering questions. Why did Dr Frederik P Agterberg strip the variance off his distance-weighted average? Why did Professor Dr Noel A C Cressie dismiss degrees of freedom? I brought my concern to the attention of Minister Lisa Raitt on March 9, 2009, and of Minister Christian Paradis on March 6, 2010. NRCan’s technocrats were instructed to deal with my concern. Mark Corey, Assistant Deputy Minister, pointed out on June 4, 2009, “Geostatistics continues to evolve as a discipline, and we appreciate your contribution in this field.” Dr David Boerner, Acting Assistant Deputy Minister, declared on May 10, 2010, “Natural Resources Canada is a science-based organization and values the scientific rigor of the peer review process”. Now that’s a whole load of chutzpah! NRCan’s library is a treasure trove of works on geostatistics. Each and every one of them proves that geostatistics is but bogus geosciences. Look at Agterberg’s 1970 and 1974 works. He derived the distance-weighted average of a set of five (5) measured values determined at positions with variable coordinates in a sample space. He didn’t derive the variance of this distance-weighted average. He didn’t count the number of degrees of freedom for the set and for the ordered set. So much for Agterberg’s grasp of applied statistics. Of course, geostatistics couldn’t possibly get any worse, could it? But it did in 1970 when Matheron and his disciples came all the way to the USA!

Young Matheron in 1954 took a shine to what he then thought was statistics. Professor Dr Georges Matheron in the 1970s saw it at that time as his new science of geostatistics. Professor Dr Noel A C Cressie in 1993 saw it more as what he came to call Statistics with upper-case S. He is the brains behind that sort of stats stuff at the Ohio State University. He teaches Statistics with upper-case S at OSU’s Department of Statistics. But why does he teach Statistics with upper-case S? Here’s in plain prose how Cressie put it in his Preface: “Notice that Statistics is capitalized to distinguish it from its other meaning: a collection of numbers that summarize a complex phenomenon – such as baseball or cricket”. Good grief! Could that really be the reason why he brought Statistics with a capitalized S to those who interpret statistics for spatial data? Has he paid any attention to the study of climate change? Turned out to be a bit of a mess, didn’t it? He cautioned elsewhere in his Preface, “We should not forget our roots”. But why then did Cressie forget his roots in mathematical statistics?

Dr Frederik P Agterberg went to work with geostatistics long before NRCan stood short for Natural Resources Canada. He is still Emeritus Scientist with NRCan`s Geological Survey of Canada. He is one of the most gifted geostatisticians in the world. As such, he has a soft spot for Professor Dr Georges Matheron and a penchant for his magnum opus. So much so that he called him the Founder of Spatial Statistics. He did so after Matheron had passed away in 2000. Matheron’s disciples didn’t agree with Agterberg’s view. Matheron taught them how to assume, krige and smooth with infinite confidence. So, they thought of him as the mastermind behind the Centre de Géostatistique and the Centre de Morphology Mathematique. What Matheron taught his disciples was inspired by one or other innovative theme that would call on his most creative thinking. That`s why they thought of him as the Creator of Geostatistics.

How I wish it were true! But that`s what W J Reichmann thought in 1961. It’s the very title of Chapter 1 in his delightful Use and abuse of statistics. The first line of its Preface points out: `Very few people nowadays can progress very far without at some point coming in contact with statistics`. Now that’s what I have been trying to tell the geostatistocracy since the early 1990s. So I pointed to Reichmann’s work in Abuse of Statistics. I own several scores of books on sampling and statistics. Applied statistics underpins sampling practice just as much as probability theory does sampling theory. As such, degrees of freedom play a key role in sampling practice but none at all in sampling theory. No ifs or buts! Except in CIM Bulletin. In Matheron’s tour de force of course. And in Cressie’s Statistics with upper-case S.