Dear Mr. Merks, Dear List,
Lets analyse this answer:
On 19. Juli 2006 01:25 wrote JW:
> Don't count on my presence in Europe next spring for a free mini-workshop.
> On the contrary, I’ll offer a fee based workshop for recovering
> geostatisticians in Vancouver next spring.
In clear text: No scientific discussion, but earning money.
I understand that you do not want to discusse but to teach your form of
understanding.
This also means that I need to speak a direct language in e-mails.
> BLUP (whatever happened to the BLUE?
BLUP is Best Linear Unbiased prediction. BLUE is best linear unbiased
estimation. From your comments in this list it is quite obviouse that you
never accepted the existence of the first and insist on applying BLUE-theory.
> What is lacking in the latest spirited defense of the practice of assuming
> spatial dependence, interpolating by kriging, selecting the BLUP (whatever
> happened to the BLUE?) and smoothing the BLUP’s pseudo variance to
> perfection, is a reference to the Journelian doctrine that spatial
> dependence may be assumed unless proven otherwise,
There is absolutely no need of referencing the "engineering"-viewpoints of
Journel in a mathematical defence of a mathematical theory.
However to be clear here: Mathematically the assumption of "Spatial
dependence" is not an assumption, but in contrary the absence of the
assumption of spatial independency. The only example of a process with
spatial independence is white noise and it is obviouse for everybody with
eyes in his head that nature does not behave as white noise.
> smoothing the BLUP’s pseudo variance
Whatever is smoothed here. Calling a variance of a prediction error a pseudo
variance is nothing but warping things up.
> although with the
> proviso that “classical Fischerian [sic!] statistics” not be applied to
> prove otherwise. What should I read in the reference to “missing assumption
> of stochastic independency between observations”? Does it refer to the same
What should I read in this question from someone who claims that he
understands anything about mathematical statistics: stochastic dependence has
a clear definition, which can be found ever book about probability theory.
> spatial dependence that may still be assumed in accordance with Journel’s
> 1992 doctrine? Assuming spatial dependence does precede interpolating by
> kriging, doesn't it?
Striktly mathematically speaking: No.
A kriging predictor based on the correct covariance structure is perfectly
valid and best linear unbiased even in case of perfect stochastic
independence. The argument goes the other way: Methods making the assumption
of spatial independence get invalid in case of spatial dependence. Spatial
independence is just a special case of spatial dependece structure.
It is such simple: If an assumption of a mathematical theory (such as e.g. the
theorem of Gauss-Markov, which forms the basic of all degrees of freedom
consideration) does not hold (e.g. the assumption of independence), it can
not be applied validly to this natural phenomenon.
> Isn't
> it true that degrees of freedom for sets of measured values with variable
> weights become positive irrationals? Last year this matter came up on
To clear this nonsense first:
Degrees of freedoms are defined back in the past by numbers of random normals
to be added up and by dimensions of some spaces, which makes them nonegative
integers, which are defined for very specific situations of statistical
modelling under the assumption of independent indentically normally
distributed errors. In so far irrational degrees of freedoms are not degrees
of freedoms in the classical sense.
However meanwhile some persons have defined variouse sorts of generalisations
of that concept (e.g. Welch for introducing the famouse Welch-t-Test) to
more difficult situations in which the original (Gosset and Fisher)
definition and theory does not apply. It should be allowed to use such
generalisations and call them irrational degrees of freedom in an applied
mailing without getting this extended definitions into a discussion on
mathematical basics of the original theory.
>
> What I do not understand is what happened to degrees of freedom. I was
> taught quite a while ago that measured values give degrees of freedom but
> functionally dependent (calculated) values are not so giving. So what
> gives? Who changed the rules? When? Why? Are degrees of freedom for sets of
The whole stuff around degrees of freedom is part of a statistical
theory !!!based on the assumption of stochastic independence!!! between the
different observations.
I personally have taught this so called Gauss-Markov theory now several times
in variouse courses on for mathematicians and it is clearly a nice and good
theory. However it resides on an assumption: Stochastic independence. Thus it
does not apply if this assumption is not given.
And this is one of the causes, why I invited you to a workshop on which both
sides get speaking time: Because he needs to learn that theory on a level
that enables us to understand when and why the rules Mr. Merks was thought
apply.
If geostatistics does not fit with the concepts Mr. Merks learned back in
university, it is because he did not learn why these rules apply and is thus
not able to judge when these rules apply.
> measured values with identical weights not longer positive integers? Isn't
> it true that degrees of freedom for sets of measured values with variable
> weights become positive irrationals? Last year this matter came up on
> ai-geostats. Did the concept of degrees of freedom disappear in 2005 just
> like the variance of the single distance-weighted average did in the 1960s?
Yes, the degrees of freedom concept is simplification coming from classical
independent statistics, which some persons try to overstretch to things it
does not apply to. However this includes you.
> rock into a massive phantom gold resource. In contrast, vexatious ANOVA
> proved the intrinsic variance of Busang’s gold to be statistically
> identical to zero.
Whatever this should be:
What is vexatious ANOVA? I know Anova, Manova and several vexatious people,
including myself.
I have never heard about any statistical method able to prove that anything is
identical to zero. (For experts: not even identity tests)
> Geostatistical software converted Bre-X’s bogus grades and Busang’s barren
> rock into a massive phantom gold resource. In contrast, vexatious ANOVA
> proved the intrinsic variance of Busang’s gold to be statistically
> identical to zero. Is the Kolmogorov-Wieder-BLUP-Prediction perhaps to
> blame for Bre-X’s Busang, Hecla’s Grouse Creek, and other shrinking
> reserves and resources? I don’t care if BLUPs surf along coastlines or
> impact shrimp counts, infect bacteria counts in culture dishes, and so on.
Whoever does statistics (not only geostatistics) should bare in mind several
warnings:
1) There is always a chance that a prediction or conclusion is wrong.
2) bogus in, bogus out
2) Every method on the planet can be abused: E.g. we can take the production
logs of a fully degraded gold deposit to estimated (with kriging or by
sampling or any other method) the gold content in the rest (bare rock) and
will always get a good prediction of gold, although (as known beforehand)
nothing is left. This is an abuse of the theory because we did not mind to
assumptions. For kriging the assumption not fulfilled is that the sampling
locations must be independent of the realisation (a assumption simply given
by fixed sampling locations) and for sampling the assumption that the
locations of sampling points must be random (an assumption simple given by
random sampling). So don't blame the method, if you apply it to something it
is not made for.
> What I do care about is that the geostatistical practice of assuming
> spatial dependence, interpolating by kriging, selecting the BLUE (or is it
> the BLUP?), and smoothing its pseudo variance to perfection, no longer be
> applied to reserve and resource estimation!
What you should say is that Geostatistics is not made for interpolating data,
where the observation is stochastically dependent to its value. It is really
time to do some theory for that. Does anybody have data with this property
such that it would be possible to publish such theory with a real example?
>
>
>
> Several times I've asked IAMG’s brass and JMG’s brains to explain why the
> true variance of the single distance-weighted average was replaced with the
> pseudo variance of a set of distance-weighted averages but to no avail!
Come and visit me, contribute to a miniworkshop on basics, meet me on IAMG
Liege, or pay me the trip to you and we can discusse the difference of the
variance of
Z(x)- \sum_{i=1}^n w_i Z(x_i)
and the variance of
\sum_{i=1}^n w_i Z(x_i)
up to midnight. However just claiming again and again that JW Merks does not
belive in the difference goes has no point.
> Don't count on my presence in Europe next spring for a free mini-workshop.
> On the contrary, I’ll offer a fee based workshop for recovering
> geostatisticians in Vancouver next spring.
So let us get this right:
J.W. Merks does not want to discuss, he wants to recover.
And he wants to get money for it.
So in conclusion:
>From a mathematical viewpoint we can say that the arguments of Mr. Merks are
based on a misunderstanding of basic concepts of probability theory and the
argument that it can not be good what failed in examples.
We should under this constant attacks of ill founded critics not forget, that
there are also some well founded conserns about kriging and that it sould not
be applied without consideration.
Best regards,
Gerald v.d. Boogaart
>
>
> Kind regards,
>
> Jan W Merks
--
-------------------------------------------------
Prof. Dr. K. Gerald v.d. Boogaart
Professor als Juniorprofessor fuer Statistik
http://www.math-inf.uni-greifswald.de/statistik/
B�ro: Franz-Mehring-Str. 48, 1.Etage rechts
e-mail: [EMAIL PROTECTED]
phone: 00+49 (0)3834/86-4621
fax: 00+49 (0)3834/86-4615 (Institut)
paper-mail:
Ernst-Moritz-Arndt-Universitaet Greifswald
Institut f�r Mathematik und Informatik
Jahnstr. 15a
17487 Greifswald
Germany
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