Hello, I am glad that Edzer reminded everyone that only in simple kriging do the kriging weights become zero beyond the range of autocorrelation. One issue that has not been discussed yet is the assumption of quasi-stationarity.. which means that in ordinary kriging (OK) the mean is assumed constant within the search window, while the trend coefficients (e.g. slope for linear trend) are assumed constant within the search window for kriging with a trend (KT). These assumptions entail that the use of a large search window in OK enhances the smoothing effect of kriging and so using more data often leads to worse predictions. Except as examples for my book and to convince my short course students that more complicated method might not lead to better predictions, I never used KT. KT with local search windows often creates artifact discontinuities in the map and produces kriging estimates that can vary widely, leading to negative kriging estimates or extremely large estimates.. In summary, in 2D I typically use OK with 24 to 36 data to reach a balance between stable estimates (using enough observations) and reasonable smoothing effect... I also set the search radius to a very large number so that anywhere in the study area the maximum number of observations is always found regardless of the local sampling density. As for other kriging parameters, it is always good practice to use cross-validation to compare alternative search strategies. Search strategies are especially critical in 3D but this might be the topic of another discussion... Pierre Pierre Goovaerts Chief Scientist at BioMedware Inc. Courtesy Associate Professor, University of Florida President of PGeostat LLC Office address: 516 North State Street Ann Arbor, MI 48104 Voice: (734) 913-1098 (ext. 8) Fax: (734) 913-2201 http://home.comcast.net/~goovaerts/
________________________________ From: [EMAIL PROTECTED] on behalf of Edzer J. Pebesma Sent: Sat 7/1/2006 8:32 AM To: Ashton Shortridge Cc: Alí Santacruz; [email protected] Subject: Re: AI-GEOSTATS: newbie question Hi, I like the question too. The statement that weights for points beyond the variogram range get zero weight is true for simple kriging, but not for ordinary and universal/ext.drift kriging; I think this hint is sufficient to find out why. The statement that local kriging is always faster than global is also not always true; for global kriging you have to decompose the covariance matrix only once, and back solve for each prediction, for local kriging you have to decompose (a smaller system) at each prediction location. The decomposition is the most expensive part, O(n^2), whereas back substitution is O(n) with n the neighbourhood size. Also, neighbourhood selection can, depending on the strategy (smart indexing?) used, be more or less expensive. I tend to use all data if the total is less than say 1000; another (disputable) issue is that in this case you have to explain less. I must admit that this is usually in a universal kriging (aka ext.drift) setting, where trend estimates can go wild in case of small neighbourhoods. I did an extensive neighbouhood size ,cross validation excercise for SIC2004, using ordinary kriging, and it turned out to be a factor of little imporatance (I recall that there was an optimum for this data set at n=125). -- Edzer Ashton Shortridge wrote: >I like this question. > >The more points you use, presumably the better the estimation will be. In >practice however, the influence of distant observations, especially with >intervening closer observations, is very slight. Computationally the solution >grows much more complex as the number of observations is increased. It's more >efficient to solve many many small systems (n=4 closest points) than one >global system (n=all points), for example. > >I don't think there is any reason to include points more distant than the >range of your covariance structure(s), as those observations won't have any >weight. > >Personally, I tend to use between 8 and 16 points, but others with more >experience may employ more. I'm probably just more impatient for results! > >Yours, > >Ashton > >On Friday 30 June 2006 10:43 am, Alí Santacruz wrote: > > >>Dear list members, >> >>I have a very simple question (I think): >> >>When I want to perform a kriging, I must define the number of nearest >>observations that should be used for the kriging prediction, or a maximum >>distance from the prediction location. >> >>What criteria should I use to set these parameters? Which is the optimum >>number of nearest neighbors? >> >>Any comment is welcome. >> >>Sincerely, >> >>Alí M. Santacruz >>M.Sc. Geomatics, Student >>National University of Colombia >>Bogotá D.C. >> >>_________________________________________________________________ >>Charla con tus amigos en línea mediante MSN Messenger: >>http://messenger.latam.msn.com/ >> >>+ >>+ 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/ >> >> > > > + + 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/ + + 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/
