Dear philosophers, of the order of the dwarf. > Prediction intervals have no meaning.
> Suppose that ordinary kriging predicts that I am a dwarf (or giant) > with the height H. > be small (it means that predicted value "comes from" the tail of > distribution not that estimation is "good"). ... > Predition intervals are defined as random intervals (random because data dependent) containing the unkown but true value with a given high probability. So any prediction method can predict an intervall of small values altough the value is high. However it is quite improbabile, that the true value is not contained in the prediction intervall. And to me this is a nice meaning of a prediction interval. And at least for Gaussian fields we can prove: Conditioned on what ever height you have, the conditional probability that your height is in the predictive intervall is 95%. The true problem about prediction intervals with kriging is that they depend on the variogram (which is estimated and might be wrong) and do not model local heteroskedastisity of the process, if we forgot to model it (e.g. by failing to do lognormal approaches) and do not model deviations from normality, when we apply the most simple methods (e.g. when we forget to model that e.g. by histogram reproduction). So, my conclusion is that we should invest more in thinking on our own models and applications, rather than blaming the most simple model (e.g. ordinary kriging) for beeing simplicistic. Best regards, Gerald v.d. Boogaart Am Donnerstag, 5. Oktober 2006 15:40 schrieb tom andrews: > Dear Mario > > I agree with You. > > Suppose that ordinary kriging predicts that I am a dwarf (or giant) > with the height H. > Since for e.g. gaussian distribution holds > P(H)=0 > we have to introduce > P(H - s < h < H + s) = p > where s is a square root of kriging variance and p is an area under > the gaussian curve for the interval (H-s,H+s) in its tail. > Knowing a total area under the curve we can compute probability. > No matter, am I a dwarf or not, the probability of being a dwarf > (with some height tolerance) is not high so kriging variance will > be small (it means that predicted value "comes from" the tail of > distribution not that estimation is "good"). > Prediction intervals have no meaning. > > > Suppose that ordinary kriging predicts that I have a mean height. > Now, kriging variance (minimized error variance) is the estimator of > variance of random variable (sigma^2) and reaches maximum. > Probability that I have a mean height +/- sigma is high and known > but it is only property of distribution of random variable. > Any prediction intervals have no meaning too. > > > > Best Regards > tom > > > --------------------------------- > Want to be your own boss? Learn how on Yahoo! Small Business. -- ------------------------------------------------- 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/
