Saturday, September 29, 2012

Setting new standards?

The Bre-X fraud inspired the Toronto Stock Exchange (TSE) and the Ontario Securities Commission (OSC) to set up a task force. Its objective was to take a close look at National Instrument 43-101. The Members of the task force are given in this Interim Report. Mr Morley P Carscallen, OSC’s Vice Chair, and Mr John W Carson, TSE’s Senior Vice-President, took on this task in April 1997. It is a fact that Bre-X’s bogus gold grades and Busang’s barren rock were made to look by hook and by crook like a gold resource. But who were the crooks? And who set the hook for Bre-X’s shareholders? OSC’s own qualified persons have yet to grasp the fact that geostatistics is a scientific fraud! Perhaps ironically, it was geostatistical software that made Bre-X’s bogus grades and Busang’s barren rock to look like massive gold resource!

I have put on paper why geostatistics is a scientific fraud. A few simple steps were all it took to cook it up! The first step was to strip the variance off the distance-weighted average. The second step was to call what was left a kriged estimate to honor D G Krige and his work. Matheron taught his disciples how to work with infinite sets of kriged estimates and zero kriging variances. What a shame that such a simple scientific fraud underpinned what was called a new science. Matheron himself never got into counting degrees of freedom. Neither did Stanford’s Journel, UBC’s Sinclair, and similarly gifted scholars.  

Young Dr A J Sinclair took to geostatistics in the 1970s. He may well have thought that Matheron had a fresh take on applied statistics. In those days Sinclair was entrusted with teaching UBC’s students all about Earth Sciences. CIM Bulletin asked Sinclair in 1990 to review Precision Estimates for Ore Reserves. My son and I had shown how to test for spatial dependence between a set of gold grades determined in ordered rounds in a drift. Given that interleaved bulk samples had not been selected, it was impossible to estimate the intrinsic variance of gold. Professor Dr A J Sinclair, PEng, PGeo rejected our article. We were pleased that it was praised by and published in Erzmetall, October 1991.

What a surprise that David’s peers wanted to praise his 1977 Geostatistical Ore Reserve Estimation! Why would his peers want to praise infinite sets of simulated values? The stage for an international forum was set at McGill University on June 3-5, 1993. It was called Geostatistics for the Next Century. What is so striking in retrospect is the fact that Bre-X Minerals was already drilling in Borneo when David was praised by his peers! Nobody was interested in the properties of variances in 1993! Yet, the additive property of variances in a measurement chain played a key role in unscrambling the Bre-X fraud.

 Measurement variance included

 Measurement variance subtracted

The Mining Standard Task Force released its Final Report in January 1999. Why had MSTF not pointed out that geostatistical software had convert Bre-X’s bogus grades and Busang’s barren rock so slickly into a massive phantom gold resource? MSTF’s Final Report was made public in January 1999. On a positive note, Dr A J Sinclair no longer graces National Instrument 43-101. On a negative note, Setting New Standards still didn’t explain at all how the Bre-X fraud could have been nipped in the bud. So it was that the Mining Standard Task Force ended up as a farce. The properties of variances were nowhere to be found. Sinclair still teaches students at UBC's Department of Earth and Ocean Sciences how to assume spatial dependence, krige, smooth, and rig the rules of applied statistics with impunity. So much for scientific integrity!

I have set up several sources of information on my website. Under Correspondence are listed all sorts of letters in a context of source and time. Academic freedom to teach a scientific fraud makes no sense at all. The fact that "geostatistics has flourished in the scientific literature for more than four decades" does not imply that spatial dependence between measured values in ordered sets may be assumed. Neither does it imply that degrees of freedom need not be counted.

Thursday, September 06, 2012

To krige or not to krige?

Not only is it a verb with a touch of a noun but it is also a true eponym. Matheron had written in 1960 what he himself had called Krigeage d’un panneau rectangulaire par sa périphérie. Nowadays it is posted as Note géostatistique No 28. An anthology of Matheron’s life and time, and of his creation of geostatistics, is posted on a massive website. Danie G Krige had put together a Preface to David’s 1977 Geostatistical Ore Reserve Estimation. References to Krige pop up on many pages. Journel’s 1978 Mining Geostatistics, too, refers not only to D G Krige but also to the zero kriging variance. 

Geostatistical software made Bre-X’s bogus grades and Busang’s barren rock look like a massive gold resource. So why had geostatistics been hailed as a new science in the 1970s. The Bre-X scam was well on its way when geostatisticians got together to praise David’s 1977 Geostatistical Ore Reserve Estimation. He was praised at a celebration called Geostatistics for the Next Century at Montreal on June 3-5, 1993. My take on The Properties of Variances clashed with the celebrations at McGill University. What applied statistics did do is prove that the intrinsic variability of Bre-X’s gold was statistically identical to zero. How about that? The geostatocracy is still poised in 2012 to assume, krige, smooth, and rig the rules of applied statistics with impunity.  

David’s 1977 textbook displayed his tenuous grasp of applied statistics. The author points on page 33 of Chapter 2 to what he calls “the famous central limit theorem”. On page 286 in Figure 203 he shows how to derive a set of sixteen (16) “famous central limit theorems” from the same set of nine (9) holes. Next, he points out on this page, “Writing all the necessary covariances for that system of equations is a good test to find out whether one really understands geostatistics”. Counting degrees of freedom would have  shown that the author of the first textbook on geostatistics did grasp applied statistics.

It is simple to verify spatial dependence between measured values in an ordered set by applying Fisher’s F-test to the variance of the set and the first variance term of the ordered set. The F-test requires that degrees of freedom be counted. Stanford’s Journel claims that spatial dependence between measured values may be assumed. For crying out loud! He did so in his letter to JMG’s Editor. Now how’s that for a nouveau science! Surely, spatial dependence in sample spaces should be proved beyond reasonable doubt. It took but two steps to go from goofy geostatistics to a genuine fraud. The first step was to strip the variance off the distance-weighted average. The second step was to call a kriged estimate what had once been a distance-weighted average with a variance. Now that’s simple comme bonjour, n’est ce pas? Kriging is a stacked game of chance. Thou shall not krige when scientific integrity matters!

Mineral Inventory Studies of Precious Metal Deposits in British Columbia is one work of geostatistical fiction that I have kept on file. The study that peeked my interest most of all was Ordinary Block Kriging with Geological Control, A Practical Approach to Estimating Mineral Inventory, Nickel Plate Mine, Hedley, British Columbia. I did so simply because primary data are given. The authors of this study were A J Sinclair et al. It hit the spotlight on June 3-5, 1993 when “Geostatistics for the Next Century” was hailed for no reason whatsoever!   

Dr A J Sinclair, Professor Emeritus (Geological Engineering), was 2000-2001 recipient of a distinguished lecturer award. Sinclair talked about “Geology and data analysis: essential components of high quality resource/reserve estimation”.  He talked across the country in both official languages. His paper on Ordinary Block Kriging with Geological Control, A Practical Approach to Estimating Mineral Inventory, Nickel Plate Mine, Hedley, BC was presented when David was praised at McGill in June 1993. I applied Fisher F-test to test for spatial dependence.

Fisher's F-test for spatial dependence
The set of production data didn’t display a significant degree of spatial dependence. Neither did the set of ordinary block kriging data. Bartlett’s chi-squared test would have shown significant discrepancies not only between variances of sets but also between first variance terms of ordered sets. 
95% Confidence limits for arithmetic means

The central values in this table are arithmetic means. Confidence intervals and ranges are derived in Excel spreadsheet files. Shortly, a link to both files will be be posted.
The Society for Mining, Metallurgy, and Exploration published in Volume 308 Transactions 2000 a reviewed paper entitled Borehole statistics with spreadsheet software. The paper shows how to fingerprint boreholes. Its reviewer expected it would “stir up a hornets’ nest” but it never did! This paper underpins a report in which confidence limits for a large gold reserve had been derived. It was submitted to Barrick Gold early in 1998.