Hello all, It has been with some interest that I have followed the discussions, (as with all) - theory being a weak point of mine and I appreciate the questions and answers posted. I wonder, however, if a test case is needed now?
Regards Craig. -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Gerald van den Boogaart Sent: Thursday, 20 July 2006 00:12 To: JW Cc: [email protected] Subject: AI-GEOSTATS: The Merks-Theory of geostatistics 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/ Bro: 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 fr Mathematik und Informatik Jahnstr. 15a 17487 Greifswald Germany -------------------------------------------------- + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. 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