Re: AI-GEOSTATS: global vs local ordinary kriging
Ulrich Leopold wrote: Dear list, What would you consider the most reliable ordinary kriging estimate? To use a local search neighbourhood (slightly bigger than the effective range) or set to global to include *all* data locations? Ulrich Depending on the strength of spatial correlaton and block size. If blocks are small and spatial correlation strong, the difference may be negligible. If blocks are large, relative to the domain, I would choose large neighbourhoods. In case of weak spatial correlation, you're basically estimating a local or global mean; so it depends on what you want for result: local or global mean values. -- Edzer -- * 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
Re: AI-GEOSTATS: global vs local ordinary kriging
Ulrich Depends how powerful your computer is, what algorithm you use to solve equations and how many data you have. Isobel http://geoecosse.bizland.com/0toKriging.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * 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
Re: AI-GEOSTATS: global vs local ordinary kriging
Hi Ulrich, It's not an easy question. First note that the search strategy includes not only the size of the search window but also the maximum number of observations. In may occasions, I set the search radius to a very large distance and use the number of observations as the controling parameter. Using too many observations or too large search windows may lead to oversmoothing, while estimates based on low number of observations (say less than 8 in 2D) might not be very reliable. Of course it depends also on the relative nugget effect. If it is large, even further away observations will receive a significant weight. In practice, global search windows are seldom used because: (1) no reliable semivariogram values are available for so large distances, (2) the size of the kriging system is likely very large, and (3) the stationarity assumption within the search window might become questionable. The best way to proceed would be to do some cross validation using various search strategies and investigate their impact on re-estimation scores. Regards, Pierre Goovaerts <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Dr. Pierre Goovaerts President of PGeostat, LLC Chief Scientist with Biomedware Inc. 710 Ridgemont Lane Ann Arbor, Michigan, 48103-1535, U.S.A. E-mail: [EMAIL PROTECTED] Phone: (734) 668-9900 Fax: (734) 668-7788 http://alumni.engin.umich.edu/~goovaert/ <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> On 8 Jul 2003, Ulrich Leopold wrote: > Dear list, > > What would you consider the most reliable ordinary kriging estimate? To > use a local search neighbourhood (slightly bigger than the effective > range) or set to global to include *all* data locations? > > > Ulrich > > > -- > __ > > Ulrich Leopold MSc. > > Department of Physical Geography > Institute for Biodiversity and Ecosystem Dynamics > Faculty of Science > University of Amsterdam > Nieuwe Achtergracht 166 > NL-1018WV Amsterdam > > Phone: +31-(0)20-525-7456 (7451 Secretary) > Fax: +31-(0)20-525-7431 > Email: [EMAIL PROTECTED] > http://www.frw.uva.nl/soil/Welcome.html > > Check us also out at: > Netherlands Centre for Geo-ecological Research > http://www.frw.uva.nl/icg > > > > > -- > * 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
Re: [AI-GEOSTATS: global vs local ordinary kriging]
Hi Ulrich I'm surprised we got mainly "pragmatic" answers to your question and would have expected from statisticians and mathematicians more reactions about a possible statistical heresy: the semivariogram model is fitted to an experimental semivariogram which was obtained from a certain number of points. To be mathematically correct in terms of the various hypotheses used, should one not use a search neighbourhood that is equal to the one used to obtain the semivariogram (frequently all points) ? If one tries to obtain maps that are "realistic", I mean here maps created by experts that have some additional knowledge about the investigated phenomenon, one would most probably try to get rid of various problems that can be solved by reducing the search radius or the number of neighbours . Pierre's reference to the impact of the relative nugget effect on points that are located far away is often a decisive one. On the other hand, if the main objective is to compare various algorithms (e.g. ordinary kriging versus indicator kriging, or indicator kriging versus log-kriging) or kriging variances obtained by various models, I would imagine that using a "no search" approach (all neighbours are used) would be the most reasonable approach... Just a few thoughts. Gregoire Ulrich Leopold <[EMAIL PROTECTED]> wrote: > Dear list, > > What would you consider the most reliable ordinary kriging estimate? To > use a local search neighbourhood (slightly bigger than the effective > range) or set to global to include *all* data locations? > > > Ulrich > > > -- > __ > > Ulrich Leopold MSc. > > Department of Physical Geography > Institute for Biodiversity and Ecosystem Dynamics > Faculty of Science > University of Amsterdam > Nieuwe Achtergracht 166 > NL-1018WV Amsterdam > > Phone: +31-(0)20-525-7456 (7451 Secretary) > Fax: +31-(0)20-525-7431 > Email: [EMAIL PROTECTED] > http://www.frw.uva.nl/soil/Welcome.html > > Check us also out at: > Netherlands Centre for Geo-ecological Research > http://www.frw.uva.nl/icg > > > > > -- > * 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
Re: [AI-GEOSTATS: global vs local ordinary kriging]
On Wed, 2003-07-09 at 10:06, Gregoire Dubois wrote: > I'm surprised we got mainly "pragmatic" answers to your question and > would have expected from statisticians and mathematicians more reactions > about a possible statistical heresy: the semivariogram model is fitted to an > experimental semivariogram which was obtained from a certain number of points. > To be mathematically correct in terms of the various hypotheses used, should > one not use a search neighbourhood that is equal to the one used to obtain the > semivariogram (frequently all points) ? I agree. But then you need to model the experimental semivariogram for all distances. Wouldn't this be a problem to find a reliable model fit? > On the other hand, if the main objective is to compare various algorithms > (e.g. ordinary kriging versus indicator kriging, or indicator kriging versus > log-kriging) or kriging variances obtained by various models, I would imagine > that using a "no search" approach (all neighbours are used) would be the most > reasonable approach... The objective is to compare different algorithms AND create a most realistic map at the same time by using these algorithms. So I guess there have to made some compromises. Probably cross-validation could help if I use a sub set of the data set. Ulrich -- * 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
Re: [AI-GEOSTATS: global vs local ordinary kriging]
>Hi Ulrich > >I'm surprised we got mainly "pragmatic" answers to your question and would have expected from statisticians and mathematicians more reactions about a possible statistical heresy: the semivariogram model is fitted to an experimental semivariogram which was obtained from a certain number of points. To be mathematically correct in terms of the various hypotheses used, should one not use a search neighbourhood that is equal to the one used to obtain the semivariogram (frequently all points) ? Okay, as a statistician i would say that the use of a restricted neighbourhood search in kriging is akin to the statistical concept of 'conditioning on a relevant subset'. This concept normally refers to a relevant subset in the sample space (i.e. all possible samples not just the actually observed one) while in this case it refers to a relevant subset in the observed sample given the fitted model. Probably then, an extension of the concept of relevant subset in the sample space to the case of the observed sample given a model would justify, from a statistical point of view, not to use all points in kriging. This seems reasonable too if we consider the model as taking the place of the sample space, i.e. as the mechanism generating the samples, which in turns seems consistent with the general idea of conditioning on an ancillary statistics (the ancillary here would be the spatial neighbourhood since these neighbourhood does not depend on the parameter to be estimated, namely the density of the random variable in the point being interpolated). This is off the top of my head, so please 'hande with care'. Ruben http://webmail.udec.cl -- * 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
Re: [AI-GEOSTATS: global vs local ordinary kriging]
Maybe it is worth pointing out that Ordinary Kriging with a 'global neighbourhood' (using all the points in simple speak) is the same as Simple Kriging with a neighbourhood which extends to the range of influence of the semi-variogram model (if any). Given this fact, you would be computationally safer to do Simple Kriging - otherwise known as "kriging with known mean" and saving yourself the problems of enormous and sparse matrix solutions. The only overhead to Simple Kriging is producing a reliable estimate of the global mean and, to be realistic, a standard error associated with it. Isobel Clark http://geoecosse.bizland.com/courses.htm Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://uk.messenger.yahoo.com/ -- * 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
