Friday, January 21, 2011

Stochastic mine planning at McGill

Mrs Heather Monroe-Blum, Principal and Vice-Chancellor at McGill University, has not yet responded to my email of November 9, 2010. Neither did Dr Jacques Hurtubise, Chair, Department of Mathematics and Statistics, or Dr Christophe Pierre, Chair, Department of Engineering. I explained why geostatistics is an invalid variant of applied statistics. Here’s what I wrote ad verbatim:

On November 5, 2010 I perused Canada’s University Innovation Leaders. Something struck me as odd at McGill University. Stochastic mine planning is taught by Professor Dr Roussos Dimitrakopoulos at the Department of Mining and Materials Engineering. Stochastic mine planning with kriging variances is at odds with genuine variances in applied statistics as McGill students are taught at Mathematics and Statistics. Here’s what McGill students should know about applied statistics and geostatistics. Applied statistics morphed into geostatistics under the leadership of Professor Dr Georges Matheron, a French geologist-cum-probabilist and a self-made wizard of odd statistics. My 20-year campaign against the geostatocracy and its army of degrees of freedom fighters is chronicled on my blogs and my website.

Dr Frederik P Agterberg is Emeritus Scientist with Natural Resources Canada and Past President of the International Association for Mathematical Geosciences. He called Professor Dr Georges Matheron (1930-2000) in his eulogy the Founder of Spatial Statistics and ranked him on a par with giants of mathematical statistics such as Sir Ronald A Fisher (1890-1962) and Professor Dr J W Tukey (1915-2000). Agterberg was wrong! Young Matheron in 1954 derived the degree of associative dependence between lead and silver grades determined in core samples of variable lengths. On second thought he even derived length-weighted average lead and silver grades. What he did not derive were weighted variances of sets of metal grades, and the variances of length-weighted average metal grades. The Founder of Spatial Statistics never tested for spatial dependence between measured values in ordered sets. He never counted degrees of freedom. He did not know that the number of degrees of freedom is a positive integer for a set of measured values with identical weights but a positive irrational for a set of measured values with variable weights.

Agterberg himself didn’t derive the variance of the distance-weighted average in his 1970 Autocorrelation Functions in Geology or in his 1974 Geomathematics. Agterberg’s problem is that as few as a pair of measured values, determined in samples selected at positions with different coordinates in a finite sample space or sampling unit, gives an infinite set of zero-dimensional, variance-deprived distance-weighted averages. Distance-weighted averages morphed into kriged estimates. Agterberg's work ignores that his distance-weighted average point grade converges on David’s ...famous central limit theorem... when all measured values do have identical weights.

Infinite sets of kriged estimates and zero kriging variances are the very reason why the world's mining industry embraced geostatistical mineral resource/ore reserve estimation with reckless abandon. Geostatistics converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. I applied Fisher’s F-test to prove that the intrinsic variance of Bre-X’s gold at its Busang property was statistically identical to zero. I did so for Barrick Gold several months before Bre-X's boss salter passed away.

Lord Kelvin (William Thomson 1824-1907) once said, “…when you can measure what you are speaking about, and express it in numbers, you know something about it, but when you cannot express it in numbers your knowledge is of the meagre and unsatisfactory kind…” Lord Kelvin knew more about degrees Kelvin and degrees Celsius than about degrees of freedom and the study of climate change. Lord Kelvin and Sir Ronald A Fisher (1890-1960) were marginal contemporaries. Lord Kelvin would have wondered about the wisdom behind assuming spatial dependence between measured values in ordered sets. Sir Ronald A Fisher could have verified spatial dependence by applying his F-test to the variance of a set of measured values and the first variance term of the ordered set.

Not all scientists need to know as much about Fisher's F-test as do geoscientists. Far too few know how to test for spatial dependence by applying Fisher’s F-test, and how to derive sampling variograms that show where orderliness in our own sample space of time dissipates into randomness. So much concern about climate change! So little concern about sound sampling practices and proven statistical methods! I make a clear and concise case against geostatistics on my blogs and on my website. What I have been teaching most of my life ought to be taught at all universities on our little planet and be implemented in all international standards. I’m working hard to make it happen. Applied statistics should be given a chance! McGill students should not be taught stochastic simulation with kriging variances. Please peruse my case against geostatistics. Please do respond to my message before the end of this year.

Yours truly,
Jan W Merks