Loading ...
Sorry, an error occurred while loading the content.

Re: [AI-GEOSTATS: global vs local ordinary kriging]

Expand Messages
  • Gregoire Dubois
    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
    Message 1 of 4 , Jul 9, 2003
    • 0 Attachment
      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 <uleopold@...> 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: uleopold@...
      > 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 ai-geostats@...
      > * 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 majordomo@... 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 ai-geostats@...
      * 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 majordomo@... 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
    • Ulrich Leopold
      ... 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? ... The
      Message 2 of 4 , Jul 9, 2003
      • 0 Attachment
        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 ai-geostats@...
        * 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 majordomo@... 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
      • Ruben Roa
        ... have expected from statisticians and mathematicians more reactions about a possible statistical heresy: the semivariogram model is fitted to an
        Message 3 of 4 , Jul 10, 2003
        • 0 Attachment
          >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 ai-geostats@...
          * 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 majordomo@... 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
        • Isobel Clark
          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
          Message 4 of 4 , Jul 11, 2003
          • 0 Attachment
            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 ai-geostats@...
            * 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 majordomo@... 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
          Your message has been successfully submitted and would be delivered to recipients shortly.