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

AI-GEOSTATS: curve fitting summary

Expand Messages
  • Carolina Garcia Imhof
    Here is the summary to my question: I have used geoeas until now, which uses a limited number of models. However, I found a program, CurveExpert (AVAILABLE AT
    Message 1 of 5 , Nov 20, 2002
    • 0 Attachment
      Here is the summary to my question:

      I have used geoeas until now, which uses a limited number of models.
      However, I found a program, CurveExpert (AVAILABLE AT
      http://www.ebicom.net/~dhyams/cvxpt.htm), which finds the best fitting
      model, which is
      usually different from the options in geoeas. For example, for my data, I
      foundthat the best fitting models were a 4th level polynomial model and a
      "Hoerl" model.
      Is there any program (downloadable if possible) that would krige with a
      custom
      model?
      Thanks,
      Carolina

      Pierre Goovaerts, Donald E. Myers and Isobel Clark answered


      You can not fit any type of curve to
      your experimental variograms since the model
      needs to be permissible, hence the practice
      to fit only a limited number of models
      that are known to be permissible.

      Pierre


      Our software, EcoSSe, is enormously flexible and could
      easily be modified to take a generic model, but it
      does cost US1,000
      When you fit a model you might want to consider a
      Cressie-like statistics which weights inversely by the
      model value (or distance) and directly by the number
      of pairs.


      Isobel



      A 4th level polynomial can not be a valid variogram/covariance or even
      a generalized covariance, consequently you would not want a
      geostatistics package that would allow the use of such a "model". The

      problem is that in general the the kriging system would not have a
      unique solution (in fact might not have a solution at all). While there
      are more possible valid models (some of which can be obtained by
      "nesting" the basic models in GeoEas, it is not entirely clear that
      this
      would improve the results.

      To be a valid covariance function, it must be positive definite (as a
      function). In particular this implies that the function is bounded
      (hence no polynomials)

      To be a valid variogram, it must be conditionally negative definite and
      have a growth rate that is less than quadratic.

      Donald E. Myers

      --
      * 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
      ... I hate to sound ignorant here, but aren t most of the standard semi-variogram models polynomials of one kind or another? I remember seeing a paper a few
      Message 2 of 5 , Nov 21, 2002
      • 0 Attachment
        > To be a valid covariance function, it must be
        > positive definite (as a function). In particular
        > this implies that the function is bounded
        > (hence no polynomials)
        I hate to sound ignorant here, but aren't most of the
        standard semi-variogram models polynomials of one kind
        or another?

        I remember seeing a paper a few years ago by a coupl
        eof blokes from Pretoria University on a generalised
        polynomial fit which would be positive definite. I
        don't have it to hand but can probably track it down
        if given sufficient motivation ;-)

        Isobel Clark
        http://geoecosse.bizland.com/news.html

        __________________________________________________
        Do You Yahoo!?
        Everything you'll ever need on one web page
        from News and Sport to Email and Music Charts
        http://uk.my.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
      • Colin Daly
        I think that Pierre and Don Myers gave the correct response. For beginners the lesson must be that you cannot use any old function (and in particular a
        Message 3 of 5 , Nov 22, 2002
        • 0 Attachment
          I think that Pierre and Don Myers gave the correct response. For beginners
          the lesson must be that you cannot use any old function (and in particular a
          polynomial) as a covariance function. It will lead to singular kriging
          matrices for some configurations of data points. That is why we stick to a
          few tried and tested covariance functions in most computer packages. In fact
          there are lots of 'esoteric' covariance functions known. You don't have to
          just stick to the spherical, exponential and Gaussian ( it might be an idea
          to have a list of covariance functions somewhere on the AI geostats site)

          To get after the point that Isobel said about polynomials - the facts are
          best stated in terms of the type of random function

          If the random function is stationary - then a covariance function C(h)
          exists and is bounded - C(h) is a positive definite function so absolutely
          no polynomials allowed whatsoever!

          If the data is from an intrinsic function of order 0 (IRF-0) then the
          variogram must have growth less than h**2, so the only polynomial is of
          the form "gamma(h) = a+b*h where b>=0" (Of course you can have "gamma(h)
          = h**c where c<2 but the only polynomial is with c=1)

          If the data has more general nonstationarity such as the IRF-k, then the
          generalised covariance can be a polynomial. However
          1) the polynomial is not arbitrary (there are constraints on the
          coefficients)
          2) it is definitely not found by fitting a curve to the experimental
          variogram - you need special fitting techniques which are not found in many
          packages


          In other words, if your variogram appears to grow without bounds, you have
          got non staionarity. You can either try a linear model (if appropriate) or
          try to tackle the non-stationarity head on by removing the trend from your
          data and then using ordinary variogram fitting techniques to the stationary
          residuals (or by applying an IRF-k model if you have the software)

          For more details, see the book by Chiles and Delfiner for example (or for
          the real purist you can go to Matheron's original publication. "The
          intrinsic random functions and their applications Adv. App. Prob., 5, pp
          439-468" but beware the maths is not simple in Matheron's paper)


          Regards


          Colin Daly



          ----- Original Message -----
          From: "Isobel Clark" <drisobelclark@...>
          To: <ai-geostats@...>
          Sent: Thursday, November 21, 2002 10:23 AM
          Subject: Re: AI-GEOSTATS: curve fitting summary


          > > To be a valid covariance function, it must be
          > > positive definite (as a function). In particular
          > > this implies that the function is bounded
          > > (hence no polynomials)
          > I hate to sound ignorant here, but aren't most of the
          > standard semi-variogram models polynomials of one kind
          > or another?
          >
          > I remember seeing a paper a few years ago by a coupl
          > eof blokes from Pretoria University on a generalised
          > polynomial fit which would be positive definite. I
          > don't have it to hand but can probably track it down
          > if given sufficient motivation ;-)
          >
          > Isobel Clark
          > http://geoecosse.bizland.com/news.html
          >
          > __________________________________________________
          > Do You Yahoo!?
          > Everything you'll ever need on one web page
          > from News and Sport to Email and Music Charts
          > http://uk.my.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


          DISCLAIMER
          This message contains information that may be privileged or confidential and is the property of the Roxar Group. It is intended only for the person to whom it is addressed. If you are not the intended recipient, you are not authorised to read, print, retain, copy, disseminate, distribute, or use this message or any part thereof. If you receive this message in error, please notify the sender immediately and delete all copies of this message.

          --
          * 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.