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Re: [AI-GEOSTATS: Deterministic vs. Stochastic Interpolation Comparison]

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  • Gregoire Dubois
    Peter, the RMSE is not THE measure of cross-validation... it is only one of the possible statistics of the errors you can use. Fundamentaly, what you get from
    Message 1 of 2 , Sep 2, 2003
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      Peter,

      the RMSE is not THE measure of cross-validation... it is only one of the
      possible statistics of the errors you can use. Fundamentaly, what you get from
      cross-validations is a set of estimated values that can be compared to the
      input data. Hence, you can use various statistics of the errors (error =
      observed - estimated value): the RMSE, the MAE (mean absolute error), the
      correlation coefficient between observed values and estimates... you can also
      focus on the highest values only.

      You have to define the criteria that will quantify the "performance" of the
      interpolators before doing any cross-validation. The RMSE is probably the
      measure that is the most frequently used.

      Surfer's (version 8 only) cross-validation function seems to work fine now
      (see my posting in the archives about the bug I found a few months ago). You
      have to update your original version to 8.2.

      As you mention, a few deterministic interpolators do not allow extrapolations
      (estimations outside the boundary defined by the convex hull), but many do
      (IDW, polynomes,...).

      I don't know what kind of variables you are analysing, but geometrical
      interpolators (triangulations, thiessen polygons, nearest neighbours)
      are almost never used for estimation purposes in environmental sciences,
      unless you have very large data sets.

      Gregoire


      "Peter Pinn" <peterpinn@...> wrote:

      > Hello,
      >
      > thank you all for the great replies to my questions. This helps very much.
      >
      > I was wondering whether or not there is a way to compare the performance of

      > deterministic interpolation methods such as Linear Triangulation or Natural

      > Neighbours to Kriging or IDW !? Is there a measure similar to the RMSE
      > resulting from cross-validation ? (e.g. ESRIs Geostatistical Analyst does
      > not use these methods, whereas SURFER applies a cross-validation that I do
      > not really believe in !) I hope I am not totally wrong assuming that
      > cross-validation does not really work fine in deterministic methods, because

      > a extrapolation at edge sampling locations will not be computed...
      >
      > Thanks again :-)
      >
      > Peter
      >
      > _________________________________________________________________
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    • Peter Pinn
      Hi Gregoir, Hi Mailinglist ! thank you very much for the information ! I am analysing plants in grassland and I have the problem, that many researchers here
      Message 2 of 2 , Sep 4, 2003
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        Hi Gregoir, Hi Mailinglist !

        thank you very much for the information !
        I am analysing plants in grassland and I have the problem, that many
        researchers here use linear triangulation in r e g u l a r (20 x 20 metres)
        sampling grids to estimate the population for mapping. Natural Neighbors
        seems to be very similar.

        My question now would be what does surfer do, when the edge parts of a
        grsslandfield are cross-validated (as you already mentioned there is NO
        extrapolation) This should result in larger RMSE errors compared to any
        other extrapolation method !?? I am not shure if I can use these
        cross-validation results to compare the efficiacy or performance of a
        interpoolation method in that particular case and in general. (By the way:
        Do you think it is correct to use the best cross-validation results of a
        interoplation method to compre its performance to another method? Is a
        jackknifing nessecary in addition)

        Another question I would like to ask you is whether you think that if I
        would have the spatial location of every single plant in an area; Could I
        start comparing sampling schemes and interpolators much better ? Which way
        to do so would you choose ?

        I hope you can help me with some of your amazing answers,

        Peter


        >From: Gregoire Dubois <gregoire.dubois@...>
        >To: "Peter Pinn" <peterpinn@...>, <ai-geostats@...>
        >Subject: Re: [AI-GEOSTATS: Deterministic vs. Stochastic Interpolation
        >Comparison]
        >Date: Tue, 02 Sep 2003 16:23:25 +0200
        >
        >Peter,
        >
        >the RMSE is not THE measure of cross-validation... it is only one of the
        >possible statistics of the errors you can use. Fundamentaly, what you get
        >from
        >cross-validations is a set of estimated values that can be compared to the
        >input data. Hence, you can use various statistics of the errors (error =
        >observed - estimated value): the RMSE, the MAE (mean absolute error), the
        >correlation coefficient between observed values and estimates... you can
        >also
        >focus on the highest values only.
        >
        >You have to define the criteria that will quantify the "performance" of the
        >interpolators before doing any cross-validation. The RMSE is probably the
        >measure that is the most frequently used.
        >
        >Surfer's (version 8 only) cross-validation function seems to work fine now
        >(see my posting in the archives about the bug I found a few months ago).
        >You
        >have to update your original version to 8.2.
        >
        >As you mention, a few deterministic interpolators do not allow
        >extrapolations
        >(estimations outside the boundary defined by the convex hull), but many do
        >(IDW, polynomes,...).
        >
        >I don't know what kind of variables you are analysing, but geometrical
        >interpolators (triangulations, thiessen polygons, nearest neighbours)
        >are almost never used for estimation purposes in environmental sciences,
        >unless you have very large data sets.
        >
        >Gregoire
        >
        >
        >"Peter Pinn" <peterpinn@...> wrote:
        >
        > > Hello,
        > >
        > > thank you all for the great replies to my questions. This helps very
        >much.
        > >
        > > I was wondering whether or not there is a way to compare the performance
        >of
        >
        > > deterministic interpolation methods such as Linear Triangulation or
        >Natural
        >
        > > Neighbours to Kriging or IDW !? Is there a measure similar to the RMSE
        > > resulting from cross-validation ? (e.g. ESRIs Geostatistical Analyst
        >does
        > > not use these methods, whereas SURFER applies a cross-validation that I
        >do
        > > not really believe in !) I hope I am not totally wrong assuming that
        > > cross-validation does not really work fine in deterministic methods,
        >because
        >
        > > a extrapolation at edge sampling locations will not be computed...
        > >
        > > Thanks again :-)
        > >
        > > Peter
        > >
        > > _________________________________________________________________
        > > Add photos to your e-mail with MSN 8. Get 2 months FREE*.
        > > http://join.msn.com/?page=features/featuredemail
        > >
        > >
        > > --
        > > * 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
        > >
        >
        >
        >

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