Re: AI-GEOSTATS: Re: generalize kriging variance to average-based estimators different than

[JW]

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 estimates gives 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. Here’s 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 deduct 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.