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[ai-geostats] Typical sample sizes for variogram calculations

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  • Mark Coleman
    Greetings, I am coding some basic geostatistical procedures and was curious about the typical sorts of sample sizes researchers run into. I know that sizes
    Message 1 of 4 , Nov 3, 2004
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      Greetings,

      I am coding some basic geostatistical procedures and was curious about
      the "typical" sorts of sample sizes researchers run into. I know that
      sizes of n=1000 are fairly common. How about sizes of N=10,000 or
      greater? Are variograms computed on samples this large?

      Thanks,

      -mark
    • Dan Bebber
      The classic example in Isaaks & Srivastava has a lot of data points. More data gives a better description of the process, but the problem is with computation:
      Message 2 of 4 , Nov 3, 2004
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        The classic example in Isaaks & Srivastava has a lot of data points. More
        data gives a better description of the process, but the problem is with
        computation: 1000 samples gives you 499,500 pairs, whereas 10,000 samples
        gives you 49,995,000 pairs. This requires a lot of memory.

        Dan

        p.s. If you need some basic geostatistical procedures, there are plenty of
        programs out there.
        ____________________________
        Dr. Daniel P. Bebber
        Department of Plant Sciences
        University of Oxford
        South Parks Road
        Oxford
        OX1 3RB
        Tel. 01865 275060

        > -----Original Message-----
        > From: Mark Coleman [mailto:mark@...]
        > Sent: 03 November 2004 20:40
        > To: ai-geostats@...
        > Subject: [ai-geostats] Typical sample sizes for variogram calculations
        >
        >
        > Greetings,
        >
        > I am coding some basic geostatistical procedures and was curious about
        > the "typical" sorts of sample sizes researchers run into. I know that
        > sizes of n=1000 are fairly common. How about sizes of N=10,000 or
        > greater? Are variograms computed on samples this large?
        >
        > Thanks,
        >
        > -mark
        >
        >
        >
      • Dan Cornford
        Mark, this really depends on how you want to estimate the parameters of the covariance / variogram. If you want to use maximum likelihood, then due to the need
        Message 3 of 4 , Nov 4, 2004
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          Mark,

          this really depends on how you want to estimate the parameters of the
          covariance / variogram. If you want to use maximum likelihood, then due
          to the need to invert a matrix, which is O(n^3), generally sizes above
          about 1000 become rather prohibitive on a desktop computer. One possible
          alternative that attempts to retain statistical rigour but scale
          gracefully with sample size is our Sparse Sequential method:

          http://www.ncrg.aston.ac.uk/~csatol/ogp/index.html

          Alternatively you could use methods of moment estimators (i.e. the
          classic sample variogram) and fit these empirically using some function.
          Note that in computing the sample variograms one can work in a
          sequential fashion, so that not all pair comparissons need be stored,
          but they must be computed .... so it will be slower, scaling as O(n^2)
          in the computation of the sample variogram.

          cheers

          Dan

          Mark Coleman wrote:
          > Greetings,
          >
          > I am coding some basic geostatistical procedures and was curious about
          > the "typical" sorts of sample sizes researchers run into. I know that
          > sizes of n=1000 are fairly common. How about sizes of N=10,000 or
          > greater? Are variograms computed on samples this large?
          >
          > Thanks,
          >
          > -mark
          >
          >
          >
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          --

          Dr Dan Cornford d.cornford@...
          Computer Science
          Aston University
          Aston Triangle tel +44 (0)121 204 3451
          Birmingham B4 7ET fax +44 (0)121 333 6215

          http://www.ncrg.aston.ac.uk/~cornfosd/
        • Isobel Clark
          Mark Our free downloadable data sets range from 16 to over 20,000. The biggest set I worked wth was a small section of a South African gold mine - 450,000.
          Message 4 of 4 , Nov 4, 2004
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            Mark

            Our free downloadable data sets range from 16 to over
            20,000. The biggest set I worked wth was a small
            section of a South African gold mine - 450,000.

            Isobel
            http://geoecosse.bizland.com/softwares
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