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These
remarks about the bizarre behavior of the kriging
variance crop up in "A study on kriging small
blocks", a paper coauthored by Margaret Armstrong
and Normand Champigny and published in CIM Bulletin,
March 1989, under the category Ore Reserve Estimation.
Apparently troubled by the rise and fall of the
kriging variance, the authors refer to Brooker for
an explanation but, inexplicably, Brooker praises
its robustness! The ugly fact of the matter is that
geostatistical scholars supplanted the variance
of a central value with the pseudo "kriging variance" of a
set of central values. |
| That
sort of paper invariably passes with flying colors
the scrutiny of CIM Bulletin's reviewers such
as Dr A J Sinclair, PEng, PGeo, and Mr M Vallée,
PEng, My encounters with geostatistical peer reviewers
taught me that they protect their turf with brazen
disregard for scientific integrity and professional
ethics. In fact, David, the author of Geostatistical
Ore Reserve Estimation, and Sinclair reviewed
and rejected Precision Estimates for Ore Reserves
before similarly challenged scholars such as Armstrong,
Dowd, Froideveaux, Journel, and several anonymous
reviewers, dismissed the fundamentals of probability theory and mathematical statistics.
Here
are the scientific facts in a nutshell! In mathematical
statistics, each distance-weighted average has
its own variance, and the variance of a set of
distance-weighted averages is a meaningless
measure for variability and precision. In geostatistics,
however, each set of kriged estimates has its own pseudo "kriging variance" that can be used to oversmooth, smooth to perfection,
and perhaps even to undersmooth. I offered $1,000
to the first geostatistician who showed how to
calculate unbiased confidence limits for contents
and grades of ore reserves without taking degrees
of freedom into account. Not a single response
was received! Meanwhile, I obtained 95% confidence
intervals and ranges for the gold content and
grade of a reserve on the basis of test results
for more than 300 boreholes with spreadsheet software
only. Borehole statistics with spreadsheet
software, a paper that explains show how to
fingerprint boreholes and how to calculate confidence
limits in six stages, is posted under Reviewed
papers.
In 1989, twelve years after David's textbook was
published Armstrong and Champigny still didn't
know why kriging variances rise and fall. Nonetheless,
they went into kriging crisis management by issuing
a decree against oversmoothing. In other words,
the requirement of functional independence can
be violated a little but not a lot. CIM Bulletin,
unfailingly at the leading edge of geostatistics,
has already reviewed and published a paper on
perfect smoothing. |