Isobel Clark praised "Andre Journel and others at Fontainebleau who taught her what she knows about the theory of The theory of Regionalized variables". So she became a dependent thinker. Why did she strip the factor 2 off df=2(n-1) degrees of freedom for "mathematical convenience"? Didn't she want to apply Fisher's F-test to verify whether or not hypothetical uranium concentrations display a significant degree of spatial
dependence within her sample space. In fact, her set is randomly distributed within this sample space.
Dr Andre G Journel, Matheron's most
gifted disciple, stripped the variance off the distance-weighted
average and called what was left kriged estimate. He found zero kriging
variances, assumed spatial dependence
but does not count degrees of freedom. He only teaches those who have a PhD in geostatistics. His latest
flavor is stringing Markov chains. Good grief!!!
Dr Roussos Dimitrakopoulos was born to be McGill's
miracle man and JMG's Editor-in-Chief. He
knows all about stochastic mine planning optimization
with Markov chains. He has not yet shown what stochastic
mining plan would pop up for Bre-X's phantom gold resource.
In November 1989, Merks and Merks applied
Fisher's F-test in Precision
Estimates for Ore Reserves
and confirmed spatial dependence between gold grades of ordered
rounds in a decline. Testing for spatial dependence troubled
Dr M David, CIM
Bulletin's most dedicated enforcer of Matheronian geostatistics.
Scores of similarly gifted geostatistocrats postulated
spatial dependence may be inferred unless proven otherwise.
Stanford's Journelwas troubled
Fischerian statistics" proved
a significant degree of spatial dependence between gold grades of ordered rounds.
Fisher's F-test proved the intrinsic variance of
Bre-X's bogus gold in Busang's barren rock to be statistically
identical to zero, as it ought to be. Sound statistics
did so several months before Bre-X's boss salter vanished!
Bre-X's original and duplicate bogus assays for a few
early boreholes could have proved that a salting
scam was in progress at the Busang project!
Dr R Dimitrakopoulos, Editor-in-Chief, Journal for
Mathematical Geosciences, stand on guard against
genuine variances. His journal got a
new name and Markov chain is a reborn game. Dr RD teaches McGill's students all he knows about stochastic
modeling with Markov chains. When he chaired in June
1993 a forum on Geostatistics for the Next Century,
he did not even know that each and every kriged estimate does
have its own variance. JMG's Editor-in-Chief got into
playing games with Markov chains. Surely, McGill's
students should know how to derive the variance
of the distance-weighted average AKA kriged estimate. Students should also know that stochastic
modeling of ore reserves with Markov chains is a scientific fraud.
Voodoo variances are doomed to generate junk statistics.
The world's mining industry
is caught in a Catch-22. The problem
is that grades and contents of mineral inventories
in annual reports are due to shrink during mining. David
dabbled at geostatistical
grade control in his 1988 handbook. He was
proud that his kriged
block was larger than
his so-called erratic
block. But he did not
show that his kriged block had a significantly lower
grade. Less pay dirt in mined ores add up to more tailings! Invalid grade control in exploration and
mining. Statistical grade and quality control with
ISO standards in smelting and refining!
Now that's a Catch-22! Sound statistics in smelting
and refining but surreal geostatistics in exploration and mining!
The National Securities Regulator ought to rule it is a scientific fraud to assume ore between boreholes.
The more so since Bre-X showed more red flags than a Bolshevist parade.
The OSC watched the parade with Felderhof in front! Incompetence
is rampant but not deemed a crime. I explained to
in 1994 and to the SEC
in 2003 why Matheronian geostatistics is a flawed variant
of applied statistics. Infinite sets of kriged estimates,
zero pseudo kriging variances and lack of degrees of freedom
make goofy geostatistics! All of it seems to make sense to CRIRSCO's
new Chair and her flock of Crirsconians!
Matheron's quixotic work
is posted with the On-Line
Library of the Centre de Géostatistique.
Matheron was not a born genius at probability but a self-made
wizard of odd statistics. One-to-one correspondence between
functions and variances remained beyond his grasp until
his passing in 2000. Matheron did fumble two variances whereas
Agterberg fumbled the same variance twice. Scores of qualified persons accept geostatistics as
much as do geostatistocrats and krigeologists!
Statistically challenged experts talk confidently
about confidence without limits. Applied statistics does
give unbiased confidence limits for metal contents of
mined ores and mineral concentrates. I have done so for Barrick Gold. It can be done not only
for metal contents and grades of ore reserves but also
for proven ore within inferred resources. Borehole
Statistics with Spreadsheet
Software shows how to derive 95% confidence
intervals and ranges for masses of metals in volumes of
in-situ ores. It's high time to set up an ISO
Technical Committee on reserve and resource estimation.
But Barrick Gold, BHP Billiton, Rio Tinto and Vale prefer stochastic mine planning with voodoo variances.
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