Dear Mr. Merks, Dear List, Summary: This e-mail invalidates every of the Mr. Merks mathematical arguments against Geostats I could find. So if the discussion should not take place in a nice workshop, with some beer and making friends, it has to take place here in the list.
Lets look at what is going on in reaction to Merks : Three people in the list are enough conserned that they would come to the proposed discussion workshop. All of them claiming themself not to be enough familiar with the theory to judge themself, searching for help to convice other people having even less idea. And someone wrote: > 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. > > Do we need a test case for kriging? We have 35 Years of good geostatistical practice now: In most cases good results, several cases of abuse (which is warned for by the people blaimed by Mr. Merks), and some single cases like Mr. Merks most beloved example gave utter nonsense. Several competitions on spatial interpolation always showing variouse types of kriging to be in the front rows. Do we need a test case for assumptions? Please look out of the window and tell me whether or not you see white noise. You should not apply kriging on the image of your detached TV-screen. So there is a little confusion, but most of us have realized that geostatsscam is sca. Let us analyse Mr. Merks not answering, but reclaiming to the list: On 20. Juli 2006 04:40 wrote JW: > Hello Readership, > > > > My case against geostatistics is documented on my website at > http://www.geostatscam.com. Preface and Chapter 1 Introduction of Sampling > and Statistics Explained can be downloaded in Adobe format. Our paper on > Precision Estimates for Ore Reserves is posted under Reviewed papers. It Mr. Merks wants us to visit his Web-Site and search it for something that is quite hidden. > was approved by Koch but rejected by Armstrong, David, Dowd, Froideveaux, > Journel, and Sinclair, in alphabetical order, before it was praised by and > published in Erzmetall. It was Stanford's Journel who wrote to JMG's Editor Ok: Here is an argument: The most famouse geostatisticians rejected it: Assumption clearly because they fear it. Ok lets analyse what Mr. Merks gives us as information about that on his web-site: E.g. He cites A. Journels "thought-provoking musings" e.g. a complicated text like: "The reason for the denominator (n-1) in the classical expression of the variance estimator is indeed correction of the bias introduced by the prior estimation of the population mean by the same n data zi. However, that correction is valid if and only if the n data zi can be considered independent one from another. In a spatial context with spatial dependence, the case is a bit more complex requiring some more detailed notations". Followed by some cartoons suggesting that A. Journel does never speak to a mathematical statistician. But now A. Journels is a perfect explanation of basic facts of mathematical statistics dating back to C.F. Gauss himself. Especially it is a much more enlighting explanation than the two pages Mr. Merks offers as explanation of degrees of freedoms, showing that degrees he only learned how to count degrees of freedom, but not what they are. Similar devaluations happen on this web-site to variouse people (e.g. Peter Dowd) trying to some corrections into Merks scam on geostats. > about assuming spatial dependence and about being encumbered with Fisher's As I explained in my last mailing: Spatial independence is an assumption not spatial dependence. But spatial dependence is the more general model. This argument is objectivly wrong Mr. Merks. It is not true that everything on earth gets independent just because this is needed by the basic statistical theories we teach to the first year students. The same is true for physics: The world does not have an Euclidean geometry, just because all physical formulae at school suggest so. > F-test. Journel's letter to JMG's Editor and the Editor's letter to me are As Journel, may others and me tell you again and again: The F-Test is not valid in cases, when stochastic independence is not given: This is what your teacher probabily called an assumption. And if he was a good teacher he told you that if assumptions do not hold the method does not apply to the situation. > both posted under Correspondence. In those days, Srivastava extolled the > miracle of Matheronian geostatistics in his inimitable way to skeptics such > as Philips, Shurtz and Watson while the gurus were chanting and cheering So proven is that Mr. Merk confuses people. And we saw the strategie: Claim right things to be wrong and conclude that what you learned in first year university is everything you could ever learn. > after they turned geostatistical peer review into a blatantly biased, > shamelessly self-serving sham. So maybe peer reviewers act like Mr. Merk suggest: Don't let pass what you do not like. And this might happen from time to time. However as I tried to make clear to the list the arguments Mr. Merk confronts us day after day with arguments based on an incomplete understanding of mathematical statistics and based on an assumption (spatial independence) which contradicts any look out of the window, and every nonhorizontal variogramm. And that might suggest something different: The leading people in geostatistics might have realized that the arguments are scam and rejected the paper because of that. > Our paper shows how to verify spatial dependence between gold grades of > ordered rounds in a drift by applying Fisher's F-test. The paper also This tells us that Mr. Merks published a test to prove the assumption of geostatistics. It does not tell us what the result was. > points out that the intrinsic variance can be estimated if the extraneous > measurement variance is determined and subtracted from the variance of the This tells us that Mr. Merk understood how to estimate the intrinsic variance of a random variable observed with error. This is a quite trivial task. > set and the first variance term of the ordered set before Fisher's F-test > is applied. Several months before Bre-X's boss salter vanished the F-test This does tell me that Mr. Merks missapplied the F-test, because the \chi^2-distribution of corrected variances is not given. By the way he did not observe a second prerequirement for the F-Test: stochastic independence. However he belives in that. > proved the intrinsic variance of Busang's phantom gold to be indeterminate. > However it was done: Ok for the first time correct: The last time we read: Was proven to be zero, which would indeed be identical to the fact that there is the same amount of gold everywhere. Now correct: Is indeterminate: There is not enough data to estimate the variance. A quite common situation in all statistics in geostatistics: Not enough data for the analysis we want. If we have not enough data for the variance, we probably do not have enough data for a variogram. Thus this is a bad example for every sort of statistics. However to be clear: The whole analysis is based on an invalid assumption It would be incorrect to think of the variogramm as an intrinsic variance > > The Kolmogorov-Wieder-BLUP-Prediction ought to be applied to Bre-X's salted > boreholes on lines SEZ-41 and SEZ-49 and to three lines of kriged boreholes > between those lines of salted boreholes. Of course, it makes sense to apply Mr. Wiener and Mr. Kolmogorov are two very famouse Mathematicians, and we started from the point that Mr. Merks tried to make us clear that kriging is wrong, because it is incompatible with math. So this point is settled now. > this KWBP test to Bre-X's bonanza borehole, which is also posted under > http://ai-geostats.jrc.it/documents/JW_Merks/. If necessary, I can provide > plenty of bogus assays for the original and duplicate test portions of > crushed and salted core samples from many more boreholes to properly > calibrate the KWBP methodology. This experiment would be of particular So we learned from his paper that in this specific case all of the variance comes from the measurement error and spatial covariation is not determinable. This would say that the covariance corresponds to pure nugget and estimation would in this special case be equivalent to classical statistics. So if this goes wrong that means that also classical statistics goes wrong and than this is not the time to blame kriging but the one who measured gold in bare rock with tramendouse measurment error to observe pure white noise and to use this for an interpolation: Scam in, scam out. > interest to geostatistical neophytes who want to do more with fewer data. I Nice warning. > look forward to the results of this test program with anticipation. I > encourage readers to print out Readme and read it! Some students may want So Mr. Merks suggests us to read a file documenting some data posted. This the feeling I get again and again on his web-site: Give so much that nobody will read it all and in the end stays with a feeling link: Maybe when I would have read more a convincing argument would have come along. > to read retro-reviews of the first three textbooks on geostatistics, which > are posted under Book reviews on my own website. Why does he suggest this here? Why only to students? Clearly because everybody else would realize that they are a pure mixture prejudgments, insultings and missunderstandings of mathematical statistics. > > > > Kind regards, > > Jan W Merks There are more questions on your web-site: We should have a right to discusse this: E.g. On the missing variance page: > In classical statistics, one-on-one correspondence between central values > and variances implies that each distance-weighted average in an infinite > set has its own variance. In geostatistics, however, variances of kriged > estimates vanished without a trace. 1) No not everything having a central value (i.e. expected value) has a variance. E.g. The Cauchy-distribution has an expeced value but no variance. 2) Yes, if every value of an infinite independent sequence has a variance the weighted averages have variances too. Now in geostatistics it is the same in case of a classical nonintrinsic random field, we loose one of the assumptions, however still the weighted averages have a variance and the kriging predictor of simple kriging has a variance, which is as stated in some geostatistical books: "Variance of the kriging predictor" = "sill"-"kriging variance" So it is no vanished as you claim 3) Things get indeed complicated in case of Matherons Intrinsic random fields a mathematical concept a little hard for non-mathematicians and I do not want to explain that whole theory in an e-mail. However: Indeed the understanding is that non of the observed values needs to have a finite variance, e.g. they could have a Cauchy distribution. Only the increments need to have a finite variance. In this case indeed the weighted average has no finite variance, but the kriging error has since it is a weighted sum of increments. Indeed complicated but in perfect compilance with mathematical statistics, but far more advanced than classical basic independence statistics. 4) Now there might be the question: Why is that complicated theory? This has two practical reasons: a) It allows more general spatial dependency structures, of which some are often observed. Things which are not stationary in the classical sense. b) The variance of the field is indeterminable for mathematical reasons if the mean is not known a priorily. This is a mathematically provable fact found by Matheron long before you employed an F-Test to prove it on a specific data set. However this implies that the variance of the kriging predictor (the weighted avarage) is itself indeterminable, even if it exists. So there is a perfect mathematical reason to use Matherons intrinsic theory and not to give a formula for something indeterminable or not even necessarily existing, even if people with limited mathematical understanding can not follow the whole theory throughly. It is the same with mathematical statistics: Did you indeed ever prove that the F-statistic you give on http://www.geostatscam.com/test_for_spatial_dependence.htm has an F-distribution. No you just used the theory you have learned. And indeed you F-statistic has no F-Distribution because numerator and denomiator are not independent (even under the 0-Hypothesis of spatial independence) And by the way on that page you imply that every variance has to have a degrees of freedom assigned to it: Did you ever realize that the degrees of freedom is a property of a specific statistic und a specific distributional assumption: E.g. the optimal variance estimation for a Poisson random variable variable is the mean of the observations and it has no degrees of freedom assigned to it. On the same page we find another missunderstanding of mathematical statistics: > The central limit theorem describes the relationship between the variance of > a set of independently measured values with equal weights and the variance > of its arithmetic mean. In Geostatistical Ore Reserve Estimation, Chapter 2, > page 33, David refers to "the famous central limit theorem". Both equations > give the variance of all types of weighted averages but both turn into the > central limit theorem for measured values with equal weights. Just the same, > the equation for the variance of a single kriged estimate is nowhere to be > found in the geostatistical literature! The central limit theorem does something totally different: it says that the limiting distribution of an infinite accordingly scaled average of (mixing or independent) random variables having mean and variance is a normal distribution with a given mean and variance. The rest of the page is blaming people for not wanting to listen. ------ Personally I wonder why you blame the words "distance weighted averages" so often on the geostatsscam page: Did you every realize that geostatistics does not do a distance weighting but something more complicated arising from the mathematical theory of generalized least squares, which is exactly that a mathematical generalisation of what you insist on so much: the least squared statistics. ------- Let us discusse on http://www.geostatscam.com/test_for_spatial_dependence.htm You propose a test for spatial dependence. I suppose with the Hypothesis: No spatial dependence versus Alternative: Spatial dependence I think this is a good thing to have such test at hand and the distribution under the Null-Hypothesis is fully computable within a classical context: However the "test" has several problems: ->It is not one test, but one test for every data. How to handle so many values? ->It does not use the spatial, but the sequential structure of the data? However the sequence is indetermined and thus the results are indeterminded -> The distribution of the Test-statistic is not a F-distribution as implied by the Text, since numerator and denominator are not independent. -> Even if the last concerne would not be relevant, the power of the test is extremly weak, since it uses only one degree of freedom for the denominator. Thus in conclusion the test might have been rejected because it is incorrect and not because it is "vexing" for the reviewers. It would be nice for the A. Journel to prove his assumption to you with a simple statistical test, as it really does as you say. Now you write in that same page that the test gives a significant result and proves spatial dependency. So the argument between you and geostatistcs is empirically decided: There is spatial dependence. By the way I personally do more F-Tests each week than variograms in a month. And speaking for other consultants like Isoble Clark I am quite sure that it is the same with them. -------- The page ends with: > Why does it make sense to either replace a set of independently measured > values or to enhance it with functionally dependent values by kriging with > the bizarre proviso to avoid oversmoothing? So violate the fundamental > requirement of functional independence a little but don't let the incredible > kriging machine run out of control. This is some of that polemic passages probably nobody can make any sense out of: Whatever it means it just does not be related to kriging in any aspekt: Kriging does not look and independent values, and does not replace them, The interpolated (i.e. functionally dependent values) are not used in the further kriging procedures. A bizarre provisio does not take place. Oversmoothing is a problem but not avoided by geostatistics. There is no fundamental requierement of functional independence, which is by the way no mathematical term. And the incredible kriging machine is a Merks word construct but nothing having any meaning. ------ On a page http://www.geostatscam.com/tolstoy_syndrome.htm on Tostoi syndrom we find many blaming on people and a list of items Mr. Merk seams to be most important in his battle against geostatistics: > Here are the irrefutable facts in mathematical statistics: > > * Central values are functionally dependent values of sets of measured values This scentence seams to totally ignore the existence of the theoretical counterpart of the mean: the expected value, which is a constant independent of any observation. And maybe because of that lacking of understanding that mathematical statistics discusses in first place the theoretical values and some statistics (defined as things functionally dependent on the data) which try to estimate these objects. So the kriging variance belongs to that class of theoretical values, which seam to have no place in the Merks universe of thinking. > * Each central value of a set of independently measured values has its own variance Each real random variable has a variance or its variance does not exists for beeing infinite. So what. > * The arithmetic mean is the central value of a set of measured values with identical weights Ok, we start with some first course basics. > * A weighted average is the central value of a set of measured values with variable weights Staring to confuse the reader: A special weighted average is the best linear estimator (BLUE) for the true expeced value (Which is a theorem, that holds under the assumption of stochastic independence). > * The distance-weighted average is the central value of a set of measured values determined at different coordinates A distance weighted average (which is not used in kriging but in other interpolation techniques!) can be seen as a central value of a set of measured values at a given coordiante > * Each distance-weighted average-cum-kriged estimate has its own variance What is average-cum-kriged? No, this is an incorrect conclusion: Not every average has a variance. It might have, but need not. This has been discussed in length early this e-mail. > * A set of n measured values with equal weights has df(r)=n-1 degrees of freedom "degrees of freedom" is a concept from the Gauss-Markov-Theory applicable to stochastic independent observations with known variances. So we start to mix two different situations. > * An ordered sets of n measured values with equal weights has df(o)=2 (n-1) degrees of freedom Geostatistical observations are not ordered. Again the concept does not apply here. > * A set of two or more measured values determined at different coordinates gives an infinite set of kriged estimates It does. A sentence like: A function evaluated at different locations gives an infinite set of values: Indeed it does. > > It is a scientific fraud to interpolate by kriging between measured values if the ordered set does not display a statistically significant degree of spatial dependence > No this is incorrect: First: No, it is perfectly mathematically correct to apply a Best Linear Unbiased Predictor to independent observations. It is just the case that in this very special case a more simple theory is available that would give the same results. Second: Nature obviously shows a spatial dependence. And this dependence is visualized in the beginning of every geostatistical Analysis, by giving the variogram. There is no need to start each clinical study using smoking as covariable to prove again and again beforehand that smooking elevates the risk of cancer. It is just a known fact visible in every single dataset displaying the relationship. Maybe we should introduce make it a standard procedure to do such test in the beginning of every geostatistical study to satisfy Mr. Merks disbelive in spatial dependence. Since the F-Test proposed on the web-site is obviously wrong, we need to look for another one. Several are available. In conclusion: We have a page looking like a big attack on geostats but merily mixing trivalities with misunderstanding. ------------------ Now we have a page: http://www.geostatscam.com/whos_what_and_where.htm which is very intersting from the point of mathematical statistics: The page is only here for insulting people. And it is obviously one of the greates honors to be on that page. However I would like to comment the small pice of scientific content here: >Here's a list of statistically challenged thinkers who lost the variance of >the distance-weighted average but found the variance of a set of >distance-weighted averages, who are troubled by the concept of degrees of >freedom but untroubled by the assumption of spatial dependence without proof Four lines, four missunderstandings: > who lost the variance of the distance-weighted average It is you who did not understand the intrinsic random functions and proclaim, that something must exist, just because it exists in the simple cases of Normal independent statistics you have seen in University. > but found the variance of a set of distance-weighted averages There is no concept of a set of distance weighted averages in geostatistics. The kriging variance is not a variance of the set of kriging predictors as some of your argumentations suggest, but it is the variance of a single random variable. It is not the fault of the people on that page that you do not understand the concept of a statistical moment. > troubled by the concept of degrees of freedom A concept that does not apply. Any many many people have up to now explained you why: In this list, in answers to review, you cite and still you insult them for stopping answering after your nonlistening, not comming and just insulting people openly. > but untroubled by the assumption of spatial dependence without proof As clearified beforehand it is a fraud to assume spatial independence, not allowing spatial dependence. The special model (i.e. spatial independence) is an assumption, not the more general one (spatial dependence). So you are blaming people for your own missunderstanding. --------- Finnally: The one example, where Kriging got wrong http://www.geostatscam.com/salted_boreholes.htm On the first page we find out that: > However, Bre-X's management and its consultants, too, could have found out > that widely spaced lines such as SEZ44 and SEZ49 did not display spatial > > dependence between boreholes within lines. So the people well knew that kriging or any other method could not give usefull results. They did a kriging map and didn't show kriging errors, and thus did not observe the rules of geostatistics and thus gave wrong results. However on the next page Mr. Merks applies a Test of spatial dependence on the krigeged data and which is obviously not admissible and never proposed in geostatistics. So what do we learn from that: Everybody can missuse everything. And the big example against geostats is just the old observation that the weakest part of all is men himself. ----- So I hope to have clearified to the list that the arguments found on this often proposed web-page are not valid and that it is enough, if from time to time someone reveals the geostatscam scam. Best regards, Gerald v.d. Boogaart -- ------------------------------------------------- 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 -------------------------------------------------- + + 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. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
