|
Hello Readers,
There's no need 'to stalk the lost variance' because the correct
formula is posted on ai-geostats.org/ documents. Also posted is an Excel
template that shows how degrees of freedom for sets of measured values
with variable weights become positive irrationals. The correct formula gives the
variances of area, count, density, distance, length, mass and volume weighted
averages. However, there's an urgent need to study the validity of kriging
variances and covariances.
Given that weighted averages are functionally dependent values of sets of
measured values with variable weights, it follows that each weighted average has
its own variance. Readers have a right to know why the variance of the
distance-weighted average was replaced with the kriging variance of a
subset of some infinite set of kriged estimates. David, on page 286 of his 1977
textbook, claims, '(W)riting all the necessary covariances for that set of
equations is a good test to find out whether one really understands
geostatistics'. His covariances are meaningless measures for spatial dependence
because his set of sixteen functionally dependent (calculated!) boreholes has
precisely zero degrees of freedom whereas the set of nine measured boreholes
gives df(r)=n-1=9 for the randomized set and df(o)=2(n-1)=18 for the ordered
set.
Stanford's Journel, in his letter of October 15, 1992, to the
Editor-in-Chief of Mathematical Geology, postulates, '(T)he very reason for
geostatistics or spatial dependence in general is the acceptance (a decision
rather) that spatially distributed data should be considered a priori as
dependent one to another, unless proven otherwise'. Readers have a right to know
who decided that spatial dependence can be assumed a priori. In the same letter
Journel speculates, 'Mr Merks' anger arises fro [sic] a misreading of
geostatistical theory, or a reading too encumbered by classical Fischerian [sic]
statistics'. Surely, Readers have a right to know how Journel proves
otherwise.
Journel's 1992 prevarications were triggered by "Precision Estimates for
Ore Reserves", a paper that explained how to verify spatial dependence by
applying Fisher's F-test to the variance of gold grades of a set of rounds
in a drift and the first variance term of the ordered set. Rejected by
Mathematical Geology but reviewed and published by Erzmetall, it is posted on my
website under 'Reviewed papers'. In March 2005, MG's current Editor-in-Chief was
interested in a paper on testing for spatial and charting sampling variograms so
I obliged. Early this year, he wanted me to put his degrees of freedom in
my paper. So I withdrew the paper and suggested he and his reviewer study
Fisher's F-test for spatial dependence as defined and approved by Technical
Committee 69-Applications of Statistical Methods. Cerattepe gold, which gives
the stats for one of the data sets on which my paper is based, is posted on
ai-geostats.org/ documents. Shortly, I'll post the unadulterated version of this
paper on my website.
Assuming spatial dependence between dense data in small sample spaces may
well make scientific sense most of the time but it makes no sense between
sparse data in large sample spaces. Assuming continued mineralization between
widely spaced boreholes is a scientific fraud but verifying spatial dependence
between ordered ore zones within lines of boreholes makes scientific sense.
Bre-X's phantom gold resource was atypical but Fisher's F-test played a role in
unraveling the salting scam. The F-test was also applied to a set of
ordered blasthole grades at Hecla's Grouse Creek gold mine where it showed
that spatial dependence dissipated into randomness between 10 m and 20 m.
Barrick-Placer's Deep South shrunk by a whopping 50%! Oversmoothed, I
assume! To find out what smoothing is all about, click 'A Study on Kriging Small
Blocks' under 'Articles and letters' on my website. Can the requirement of
functional independence be violated a little but not a lot? Of
course, Readers have a right to know!
Jan W Merks
|
* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm )
* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
