[ai-geostats] Re: Who is J. W. Merks???
- Jan Merks is an expert in sampling theory and works as
an independent consultant out of Vancouver, Canada. He
has a web site which I don't have to hand, where all
of these opinions are repeated and amplified.
Jan first starting publishing anti-geostatistics
articles in 1991 or 1992 and the article
"Geostatistics or Voodoo Statistics" appeared in every
mining publication from the Engineering and Mining
Journal to the Northern Miner newspaper. He
republishes every so often and had one a few years ago
in the Mining Journal on April 1st.
The articles start with a quotation from Tolstoy to
the effect that even the most intelligent of people
can turn a blind eye to facts that don't fit their own
world view. It is ironic that he does not realise this
quotation is apropriate to his own world view too.
His basic premise is that geostatistics is a con job
foisted on an unsuspecting industry by consultants
trying to rip them off for large sums of money. He
supports this view by pointing out that the
semi-variogram is divided by the number of pairs of
samples (N) and not by N-1 when every statistician
knows that variances are divided by N-1 not N. The
point missed here is that variances are divided by N-1
because we estimate the population mean.
Semi-variograms are not divided by N-1 because we
assume the population mean (difference) to be zeto and
do not estimate it.
His second point is that kriging with (say) k samples
should have k-1 degrees of freedom. This is not true
becuase the variance/covariance or semi-variogram
terms used in the kriging system are based on the
total number of pairs used in the construction of the
graph. I once asked Noel Cressie about this and he
said that the degrees of freedom in the kriging system
would be n(n-1) where n is the total number of samples
in the data set.
Back in 1992, I invited Dr Merks to come down to a
course I was giving in Reno to put his point of view
and debate it with myself and the students and staff
at University of Nevada-Reno. I still have his letter
on file. It basically says, I don't see the point you
aren't going to listen anyway.
Before you ask, the only reason I did this was because
his articles referred to only two geostatistical
publications: Michel David's Mining Geostatistics and
my Practical Geostatistics (1979). He also couldn't
spell my name right and I wanted to give him the
opportunity to change that. It was several years
before an editor pointed out to him that there is no
'e' on the end of "Isobel Clark".
- Thanks, Isobel, for the explanation. Some people never get it,
the difference between design-based and model-based methods.
From the other side it is also true that there are
geostatisticians, even famous ones, who keep arguing that design-
based methods (methods that essentially assume independent
observations) are not applicable to spatial problems, even
when spatial random sampling has been used.
A useful reference for design-based methods is:
DE GRUIJTER, J. J. & C. J. F. TER BRAAK (1990), Model-Free Estimation
from Spatial Samples: A Reappraisal of Classical Sampling Theory.
Mathematical Geology 22, pp. 407-415.
I think this man just wants to get more attention by making some noise.
Geostatistics is the great contribution of geoscientists outside the
mainstream of statistics to the science. I also ever met a reviewer.
The guy never agree that parameters should estimated from correlated
At the beginning of the development of kriging, I guess Professor G.
Matheron must met lots of challenges. As Professor Journel pointed out,
geostatistics does not pursue recognition of mainstream mathematics, it
pursues recognition from practioners. It is great because it is useful.
If just checking geostatistics purely from the view of conventional
mathematics, there are lots of places to attack.
But our understanding of geostatistics also should not stop on the
conventional geostatistics. Geostatistics is also evolving. The recent
proposed multi-point geostatistics is quite innovative. In addition,
Markov chains are also evolving toward a new non-kriging geostatistics.
University of Wisconsin
Department of Geography
550 North Park Street
Madison, WI 53706-1404
426 Science Hall
----- Original Message -----
From: "Edzer J. Pebesma" <e.pebesma@...>
Date: Saturday, April 30, 2005 6:51 am
Subject: Re: [ai-geostats] Re: Who is J. W. Merks???
> Thanks, Isobel, for the explanation. Some people never get it,
> the difference between design-based and model-based methods.
> From the other side it is also true that there are
> geostatisticians, even famous ones, who keep arguing that design-
> based methods (methods that essentially assume independent
> observations) are not applicable to spatial problems, even
> when spatial random sampling has been used.
> A useful reference for design-based methods is:
> DE GRUIJTER, J. J. & C. J. F. TER BRAAK (1990), Model-Free Estimation
> from Spatial Samples: A Reappraisal of Classical Sampling Theory.
> Mathematical Geology 22, pp. 407-415.
- AI Geostats Subscribers, Isobel Clark(e),
It seems that Merks is his own worst enemy. As a matter of interest, when
one is a member of the geostatistics church - ie member of a known
geostatistical union, it is easy to criticise Merks for both his opacity and
his criticism. Where there is smoke there is fire. The moment you believe
your own hypothesis you are a dead duck scientifically.
What geostatisticians never come to grips with in economic geology, where
Merks consults for some of the senior players, is that your 'nugget effect'
and the 'geologist's' nugget effect are homenyms for unreliability; but they
do not mean the same thing. Practicing miners know that fudge factors, mine
call factors, cutting, are used in the majority of metal mines in the
world, simply because geostatistical forecasts are only accurate about 50%
of the time (Aus IMM Special Publ. on Best Practices). It's garbage in,
garbage out; bad data in bad data out. Danie Krige, however, actually
published a summary paper in 2001 in SAJG in which he stated that the
scientific mathematical underpinnings of geostatistics were well understood
and not a lot of future research would be required in this field. He
stopped just short of calling geostatistical theory a paradigm. I take
issue with a field in which hundreds of data points, thousands of data
points and perhaps tens of thousands of data points do not yield a
trustworthy mean 50% of the time. I, like Merks believe that 30 or 31
values should tell the tale: semi-variograms excepted. That means I accept
them. I do not know whether Merks does or not. I find the semivariogram
model intellectually satisfying.
I do not accept averages or cut weighted averages for a block of ore, a
stope in a mine, or a global average - for an annual report. This is where
the voodoo operates.
I have found ore bodies to be chaotic. Sampling with a drill is very
reliable in order to define the geometry, volume, and specific gravity of a
deposit. Drill an oriented pattern and a few angle holes the opposite
direction to test your imagination and the tonnage of a deposit can be
estimated with a fair degree of accuracy. To ask a drill to sample for
grade is another story. Every metal distribution is diferent. Metal
concentrations depend upon the distribution of nucleation sites or
structural preparation of the host rock. Assays are rarely reproducible.
Twinned holes are rarely reproducible. Give me the mean and standard
deviation and standard error of the mean of a global ore reserve from a
typical 'nuggety' ore deposite, and I can reproduces those statistics with a
similar drill program of twinning holes. However, only 10 or 11% of the
twinned holes will be similar; a few will be identical twins, a few will be
fraternal and the rest of the twins will be just family. Some may deny
their paternity/maternity completely. This mystery has got a common name in
geostatistics but I do not remember what Krige calls it today. For the 50%
of deposits that behave as predicted, bravo for (GEO)statistics. However,
what about the rest? We sweep them under the rug and rely on cutting or the
mine call factor and wait a year to adjust the numbers with a fudge factor.
In the Old Lead Belt of Missouri, the 'dilution' factor was 10%. When the
miners moved to the new lead belt they applied 10% dilution, but it was not
enough and 15% 'dilution' was called for. ...And the new lead belt was
known for massive galena. At Elmwood, Tennessee Zinc held off production
for a time while they attempted to reconcile assay from underground mine
opening samples to nearby drill holes; it didn't work. They just went ahead
an mined it and worked backward from concentrate grade and tailings to
determine the feed grade.
Ore deposit grades are chaotic and, if you will, the sample we take is too
small at least 50% of the time. We then split the sample to laboratory
size, and the laboratory then splits it to a smaller size 50 - 30 - 15
grams, depending on the cost of the assay (the budget). Bigger aliquots
cost more. 50% of the time these samples are too small. Shall I say 50% of
the deposits need custom sampleing. And the worst part of it is that we do
not seem to account for that potentially fatal flaw at the beginning of the
exercise. Colomak, NWT had a 25% shortfall from low grade ore. We do not
think it significant to test for what the deposit is telling us before we
begin the SOP of QCQA. [Standard Operating Procedure of Quality Control and
Quality Assurance]. I say GIGO [Garbage in; garbage out.]. Isobel Clark
calls it a systematic error - an error in data due to the method of
collecting. Isobel also explains, near the back of her book, that if there
is a systematic error, geostatistical methods are useless. At least that's
my reading of it.
For 50% of gold deposits, there is an error in data that results in lower
ounces produced than estimated and higher cost per ounce than budgeted.
This gives Merks his energy.
I have found that by considering the sample assay collections to be random
numbers from a uniform distribution, I can determine the minimum feed grade
for a stope, or a global average for an annual report. This results in cost
saving of not crushing, grinding and reacting rock to produce metal that is
not present in the ore due to the 'inadequate sample effect', commonly known
as the 'nugget effect'. Before continuing the assassination of Mr. Merks,
it would be a good idea to address that 50% of gold deposits with the
'nugget effect. As I have alluded, base metal mines have mine call factors
too. How can we have such a wealth of numbers and not have better
Outside the envelope, how about the application of regionalized variables to
global warming, cooling, or whatever is happening. What is going on with
cosmology/astronomy where we take very small samples of a virtually infinite
universe? There are people who attempt to estimate meteorite impact
frequency without understanding the 'inadequate sample effect'. It's not my
business, but I'll say it anyway - Merks has his atitude because of his
perception of treatment by most prelates of the geostatistical church. The
better question then is why is J.W. Merks reacting from his experience.
Artesian Geological Research, Toronto, Ontario