Hello geostats aficionados,
My thanks to Dr Isobel Clark for compiling an abbreviated biography. I
should point out that Dr Merks is my son, a PhD in computing science and a lead
architect of the Eclipse Modeling Framework. He is also the coauthor of
"Precision Estimates for Ore Reserves", a paper that was praised by and
published in Erzmetall after it was thoroughly thrashed by CIM's David and
Sinclair, by JMG's Journel, Froideveaux and Armstrong, and by IMM's Dowd.
I should also mention that I sent an email to Clark on June 30, 2004, and
that she responded on July 18, 2004, "Sorry not to get back to you sooner.
Things are a little crazy here. Will look at this stuff next week hopefully".
Things may have remained crazy for quite some time because she never answered my
questions, "Do you agree or disagree that each distance-weighted average has its
own variance?" and, "Do you agree or disagree that the variance of a set of
distance-weighted averages is a mathematical aberration?"
Attached to my email was a spreadsheet template based on Clark's
hypothetical uranium concentrations presented in her "Practical Geostatistics".
Clark's set does not display a significant degree of spatial dependence within
its sample space but she interpolates just the same. When Clark's coordinates
stray beyond the sample space, the distance-weighted averages converge on the
arithmetic mean and their variances on the central limit theorem as the
weighting factors converge on 1/n. This spreadsheet template is posted on my
website. Mathematical statistics is so foolproof and predictable!
When I was toiling in the trenches at Hecla's Grouse Creek mine to
investigate why Hecla's assayers could not find the predicted gold grades, I
found out that spatial dependence between blasthole grades dissipated between 10
and 20 m. Hecla's own staff geologist had developed a geostatistical model on
the basis of widely spaced borehole grades that smoothed a few high grade
stringers into a large block of high grade ore and blew a cool $93 million in
the process. His father, a geostatistical scholar at the Colorado School of
Mines, taught him everything he knew. So why should I go to the Colorado School
of Mines and learn all about the junk science of interpolation without
justification. The more so because I studied Clark's "Practical Geostatistics"
when we wrote "Precision Estimates for Ore Reserves". A retro review of Clark's
textbook is also posted on my website.
Geostatistics converted Bre-X's bogus grades and Busang's barren rock into
the largest phantom gold resource the world has never seen. Yet,
geostatisticians persist in assuming spatial dependence, kriging, smoothing, and
rigging the rules of mathematical statistics. If I were a betting man, I would
wager that Dr Isobel Clark is the most likely geostatistician to encounter an
epiphany and become a borne-again statistician.
So do distance-weighted averages have variances or not? Are variances of
SETS of distance-weighted averages valid or not? Prominent pundits such as
Armstrong, Clark, Journel and Krige have yet to respond to these fundamental
questions. Meanwhile, I have posted on my website the formula for the long lost
variance of the distance-weighted average (kriged estimate or kriged estimator
in geostats parlance).
J W Merks