Ted's comments on thr regulatory perpspective brings up some interesting issues, assuming this were an hazardous waste site. First, since the upper 5 percent accounts for such a high percentage of the mass of lead, a surgical cleanup targeting the "hot spots" might be sufficient. Environmental remediation is focused on reducing risk to human health and the environment, and if removing the high zones brings the average lead concentration below th risk-based threshold, then the remediation is successful.
Next, in remediation, the remediation decision support unit is as important as the sample and subsample support. A few extreme values can be "diluted" out if a large decision unit is selected. Furthermore, a "hot spot" must be defined with relation to its size and concentration (at a minimum). Then the impact of the size/support of the "hot spot" can be determined in relation to the decision unit support. So basically, the only things you need to remember in environmental characterization and decision-making are support, support, and support (sample, subsample, decision unit). As far as contouring, issues still remain. It's hard to contour yourself out of a situation you sampled yourself into. Happy Holidays and a Prosperous New Year! Jeff Myers Westinghouse Safety Management Solutions 2131 S. Centennial Dr., SE Aiken, SC 29803 [EMAIL PROTECTED] http://www.gemdqos.com -----Original Message----- From: [EMAIL PROTECTED] To: Chaosheng Zhang Cc: [EMAIL PROTECTED] Sent: 12/22/01 4:38 PM Subject: RE: AI-GEOSTATS: Summary: Extreme Values? On 22-Dec-01 Chaosheng Zhang wrote: > Dear list, > > Happy Christmas! Many thanks to all those who replied my question about > extreme values, especially Isobel Clark, Marcel Vall�e, Benjamin Warr, > Claudio Cocheo, Martin Roseveare, Pierre Goovaerts, Jeff Myers. Dear Chaosheng Xhang, Thank you for your comprehensive summary (which now enables me to delete all the interesting individual replies by others!). I'd like to add one consideration which seems not to have been mentioned by others. Especially in a regulatory ("clean-up") context, the regulator may want to have a determination of the total quantity of contaminant on a site. Your high sample values are typical of "hot-spot" values. It is a useful formula (proof by integration by parts) that integral from 0 to inf (1 - F(x)) dx = expectation of X where F(x) is the cumulative distribution function of X. Applying this (somewhat crudely, numerically speaking) to your data for Lead shows that the top second percentile (98-100%) accounts for about 1/3 of the total content, while the top 5th percentile (95-100%) accounts for well over half the total. It is therefore essential, for purposes such as the above, both to take these extreme values very seriously, and also to try to get estimates of the percentiles which are as accurate as possible. The latter is not at all easy (in fact I do not know of a satisfactory solution in the context of "grid sampling" of a contaminated site, where the amount and density of sampling which is feasible in practice is usually quite insufficient -- how do you know, for instance, that there are not much larger extremes still, somewhere, remaining unobserved? their probabilities of being sampled may be very small; but if their values are very high they could dominate everything else.) However, as far as the data are concerned, you have what you have got and you _must_ respect what it tells you. From the above, for purposes of estimating the total, rather than trying to ignore the high percentiles you would even do better to ignore the lower percentiles, since they contribute very little! And, that being said, Happy Christmas and Prosperous New Year to All! Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 167 1972 Date: 22-Dec-01 Time: 21:38:33 ------------------------------ XFMail ------------------------------ -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org -- * To post a message to the list, send it to [EMAIL PROTECTED] * As a general service to the users, please remember to post a summary of any useful responses to your questions. * To unsubscribe, send an email to [EMAIL PROTECTED] with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list * Support to the list is provided at http://www.ai-geostats.org
