Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than
that the posted formula for the weighted average converges on the variance of the arithmetic mean when variable weighting factors converge on 1/n. What she or he may not know that this variance is called the Central Limit Theorem. If you really want to know more about sampling and statistics, you should visit my website. What you should not do is blame me if you become addicted to commonsensical sampling practices and scientifically sound statistical methods. Kind regards, Jan W Merks - Original Message - From: tom andrews To: JW Cc: ai-geostats@jrc.it Sent: Sunday, July 16, 2006 4:05 PM Subject: Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than Dear Jan W Merks !--[if !supportEmptyParas]-- !--[endif]-- I have a simple question that should be a piece of cake for such great expert like You. For a set of N input samples I can do by kriging the only ONE estimate and compute kriging variance for this single estimate. So, why do You call the kriging variance the variance of some set of kriged estimates? or variance of a set of distance-weighted averages et al ? !--[if !supportEmptyParas]-- !--[endif]-- Best Regards Tomasz Suslo --- --- Do you Yahoo!? Get on board. You're invited to try the new Yahoo! Mail Beta. -- - 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 ai-geostats@jrc.it + 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/
Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than
Hello Everybody, What is lackingin 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, although with the proviso that “classical Fischerian [sic!] statistics” not be applied to prove otherwise. What should I read inthe reference to “missing assumption of stochastic independency between observations”? Does it refer to the same 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? What I do not understandis 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 measured values with identical weights not longer positive integers?Isn't it true that degrees of freedomfor 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? Geostatistical software converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. In contrast, vexatiousANOVA provedthe 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 careif BLUPs surf alongcoastlines orimpactshrimp counts,infect bacteria counts in culture dishes, and so on.What I do care aboutis thatthe 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! 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! Don't count on my presence inEurope next spring for a free mini-workshop. On the contrary, I’ll offer a fee based workshop for recovering geostatisticians in Vancouver next spring. Kind regards,Jan W Merks
Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than
Hello Tomasz, What you should do with a set of N measured values, determined in samples selected at positions with different coordinates in a finite sample space is verify spatial dependence by comparing the calculated F-value between var(x), the variance of the set, and var1(x), the first variance of the ordered set, with F0.05;n-1;2(n-1) and F0.01;n-1;2(n-1), the tabulated values of F-distributions at 5% and 1% with the proper degrees of freedom. If the set does not display a significant degree of spatial dependence, its distance-weighted average-cum-kriged estimate is not necessarily an unbiased estimate for the central values of the set. However, the variance of a single distance-weighted average is a genuine variance irrespective of the degree of spatial dependence. In fact, it would be misleading to compute confidence limits for that central value. What you ought not to do is compute pseudo kriging variances of sets of kriged estimates because a set of N functionally dependent kriged estimatesgives exactly zero degrees of freedom. In fact, a compelling case can be made that the concept of degrees of freedom evolved to ensure that infinite sets of kriged estimates become the equivalent of perpetual motion in data acquisition. What a pity that Krige, Matheron, and scores of first generation geostatisticians, were not aware that each distance-weighted average had its own variance long before it was reborn as an honorific but variance-deprived kriged estimate. Heres a link that may guide you into mathematical statistics http://ai-geostats.jrc.it/documents/JW_Merks/ What you may want to do is print out Readme and do read it. Most high school graduates are able to deductthat the posted formula forthe weighted average converges on the variance of the arithmetic mean when variable weighting factors converge on 1/n. Whatshe or he may not know that this variance is calledthe Central Limit Theorem. If you really want to know more about sampling and statistics, you should visit my website. What you should not do is blame me if you become addicted tocommonsensical sampling practices and scientifically sound statistical methods. Kind regards,Jan W Merks - Original Message - From: tom andrews To: JW Cc: ai-geostats@jrc.it Sent: Sunday, July 16, 2006 4:05 PM Subject: Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than Dear Jan W Merks !--[if !supportEmptyParas]--!--[endif]-- I have a simple question that should be a piece of cake for such great expert like You. For a set of N input samples I can do by kriging the only ONE estimate and compute kriging variance for this single estimate. So, why do You call the kriging variance the variance ofsome set of kriged estimates? or variance of a set of distance-weighted averages et al ? !--[if !supportEmptyParas]--!--[endif]-- Best Regards Tomasz Suslo Do you Yahoo!?Get on board. You're invited to try the new Yahoo! Mail Beta.
Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than
Dear Jan W Merks KRIGING VARIANCEFor a set of N input samples I can do by kriging the only ONE estimate and compute kriging variance for this single estimate.So, kriging variance is a variance (derived from the model) of single unknown true value minus single weighted average.Kriging variance isnt any variance of a set of weighted averages. We dont need any other single weighted average.FUNCTIONAL DEPENDENCE There are the rivers on the Earth.There are the towns on the Earth.The man needs a water to live.The man lives in a town.The rivers and towns are functionally dependent.So, we can see the towns at the rivers (or the rivers inside the towns), there is some constraint.I dont think that kriged estimates are functionally dependent since I can do by kriging the only one estimate at any coordinate I just want. It means that kriged estimates dont see each other, there is no constraint.DEGREES OF FREEDOM For infinite sample the variance in the global case = sum of deviation squares divided by the size of sample (all weights are equal). For finite sample the deviation squares are weighted by identical weights ONLY in the case of gaussian noise.Experimental variance = sum of deviation squares that is scaled by degrees of freedom can be applied only in the case of gaussian noise. So, such variance is useful for analysis of grades in the school not in the mine. Increasing (by degrees of freedom) the denominator of weights we can blow the confidence intervals to infinity. In such case the forecasting always will match the observation. But its not goal of (geo)statistics.F-TEST As above (degrees of freedom, sum of deviation squares), postulated F-TEST for so-called spatial dependence in fact is the test for trend (drift) in high-noised data (gaussian noise) and can be useful to analyse the pupils progress in the school not to analyse spatial dependence in the core.The famous F-TEST for Clark's hypothetical uranium data in fact is the test for trend in the data under assumption that there is no correlation structure in the data. KRIGING ESTIMATORKriging estimator, for gaussian noise, simplifies to the least-squares estimator that was introduced to statistics by Mr. Gauss. Best RegardsTomasz Suslo How low will we go? Check out Yahoo! Messengers low PC-to-Phone call rates.
AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than
OriolDownload for free, my old book Practical Geostatistics. Chapter 4 tells you all about calculating the variance for any weighted average estimator. Follow links from http://www.kriging.comIsobelOriol Falivene [EMAIL PROTECTED] wrote: Dear Colleagues,Im a PhD student working on interpolation of categorical variables(like facies).I would like to know if its possible to generalize the kriging varianceto other average-based estimators different than kriging, such askriging with an areal trend, indicator kriging or inverse distanceweighting?; if its possible could you send me some references where Ican find that?.Thank you.Best regardsOriol--__Oriol Falivene[EMAIL PROTECTED]http://www.ub.es/ggactel. (+34) 93 4034028fax (+34) 93 4021340Fac. de Geologia,Univ. de Barcelona++ To post a message to the list, send it to ai-geostats@jrc.it+ 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/
Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than
Hello Oriol, Isobel gave good advice when she suggested to download Chapter 4 of her Practical Geostatistics. This book taught me more than David's Geostatistical Ore Reserve Estimation and Journel and Huijbregts's Mining Geostatistics combined because of its many practical examples. For example, look at Clark's hypothetical uranium data (see Clark and the Kriging Game at http://www.ai-geostats.org/documents/JW_Merks/ ) and find out what happens if the variance of the distance-weighted average were to resurface after it went missing on Krige's watch at the Witwatersrand gold reef complex in South Africa in the 1950s. You should also peruse http://en.wikipedia.org/wiki/Geostatistics to find out why statistically astute thinking was lacking when pioneering geostatisticians replaced the genuine variance of a single distance-weighted average with the pseudo kriging variance ofsome set of kriged estimates. Study Clark's hypothetical uranium data step-by-step as outlined on the Geostatistics talk page. It is possible to make the variance of the distance-weighted average vanish again by the condition that thisvariance be replacedwith thekriging variance ofsome set of kriged estimates if, and only if, the absolute difference between the true variance and the Central Limit Theorem exceeds say 1% or perhaps5%.Conditional switching between real variances and voodoo variancesmay not be a bright idea so early in your career. Kind regards,Jan W Merks - Original Message - From: Isobel Clark To: Oriol Falivene Cc: ai-geostats@jrc.it Sent: Wednesday, July 12, 2006 6:06 AM Subject: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than Oriol Download for free, my old book Practical Geostatistics. Chapter 4 tells you all about calculating the variance for any weighted average estimator. Follow links from http://www.kriging.com IsobelOriol Falivene [EMAIL PROTECTED] wrote: Dear Colleagues,Im a PhD student working on interpolation of categorical variables(like facies).I would like to know if its possible to generalize the kriging varianceto other average-based estimators different than kriging, such askriging with an areal trend, indicator kriging or inverse distanceweighting?; if its possible could you send me some references where Ican find that?.Thank you.Best regardsOriol--__Oriol Falivene[EMAIL PROTECTED]http://www.ub.es/ggactel. (+34) 93 4034028fax (+34) 93 4021340Fac. de Geologia,Univ. de Barcelona++ To post a message to the list, send it to ai-geostats@jrc.it+ 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/
