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Re: AI-GEOSTATS: AI-GEOSTATS

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  • Isobel Clark
    ... Sounds really fast, which is an advantage but is t this outweighed by the fact that you have to follow the same path every time? I understood from the
    Message 1 of 6 , Dec 1, 2000
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      > Multiple simulations following the same path,
      > co-simulation and
      > indicator simulations are all implemented.
      Sounds really fast, which is an advantage but is't
      this outweighed by the fact that you have to follow
      the same path every time? I understood from the
      literature that one should vary the path every time
      for a valid siulation.

      Since we are all putting out adverts here, maybe I
      should mention that EcoSSe does sequential gaussian
      simulation and that we speed up the simulation by (a)
      dividing the whole region into subregions and
      randomising within the subregion and (b) writing out
      intermediate grid files for "re-input" for people who
      want to get progressively finer. It's not free, of
      course, ($US1,000) but it is constantly being updated
      to include features the users suggest.

      SGS is not in the demo, but you can check it out
      anyway at
      http://uk.geocities.com/drisobelclark/Ecosse_download.html

      We'll be covering SGS etc in Volume 2, Practical
      Geostatistics 2001 but don't hold your breath as it is
      likely to be mid-year before we get it finished. In
      the meantime, look out for the 350 page "Practical
      eostatistocs 2000: Answers to the Exercises" due out
      this month. Much much more than just "Q1:
      42"..........

      Isobel Clark



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    • Edzer J. Pebesma
      ... A far superior implementation of the concept of multiple grid simulation is found in gstat, found at http://www.geog.uu.nl/gstat/ Suppose you want to
      Message 2 of 6 , Dec 1, 2000
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        Pierre Goovaerts wrote:
        >
        > The procedure can be generalized to any number of intermediate grids;
        > this number depends on the number of structures with different ranges
        > [and] final grid spacing.
        >

        A far superior implementation of the concept of multiple grid simulation
        is found in gstat, found at http://www.geog.uu.nl/gstat/

        Suppose you want to simulate a field with 100 x 100 cells. Gstat then
        starts with the coarsest 2-power grid, which has a cell spacing of
        64 x 64; this grid is placed randomly in the field. After simulating
        these four (or one) cells, following a random path, the grid is refined
        to a grid with 32 cell spacing; after this grid is simulated a 16 cell
        spaced grid is followed, ... etc...; after the grid with a 2-cell
        spacing is followed, the remaining cells are simulated on the
        original field with 1-cell spacing.

        If this sounds confusing to you, see the figure on
        http://www.geog.uu.nl/gstat/manual/node9.html

        Now how can this be done efficiently without adjusting the neighbourhood
        size after each grid refinement? Gstat uses a very efficient
        neighbourhood search algorithm (based on quadtrees, see
        http://www.geog.uu.nl/gstat/manual/node8.html and for the algorithm
        http://www.cs.umd.edu/~brabec/quadtree/index.html : Bucket PR Quadtree)
        that does not call for a neighbourhood size in terms of spatial
        distance, but only in terms of number of nearest points.
        This algorithm selects the nearest n observations at the
        start of the simulations (when data are very sparse) approximately
        as fast as it does at the end, when simulated data are abundant and
        dense.

        The advantages of this algorithm are twofold:
        - no worries about the number of grids to simulate and their densities,
        as this is done recursively;
        - no worries about how to decrease the neighbourhood search radius and
        speed of neighbourhood selection, only define the maximum number of
        nearest points in the neighbourhood.

        Multiple simulations following the same path, co-simulation and
        indicator simulations are all implemented.

        Gstat is GPL'd, so anyone can copy this stuff, to GSLIB or whatever.
        --
        Edzer

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      • Edzer J. Pebesma
        ... For maximum pure-ness: yes. (But then we should also use global neigbourhoods all the time :-) You can of course do this, if you ve got the time and
        Message 3 of 6 , Dec 1, 2000
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          Isobel Clark wrote:
          >
          > > Multiple simulations following the same path,

          > Sounds really fast, which is an advantage but is't
          > this outweighed by the fact that you have to follow
          > the same path every time? I understood from the
          > literature that one should vary the path every time
          > for a valid siulation.

          For maximum pure-ness: yes. (But then we should also use
          global neigbourhoods all the time :-)

          You can of course do this, if you've got the time and
          computing power.

          When you're doing a large Monte Carlo experiment using
          simulated random fields, and the simulation time of these fields
          is a crucial issue, the choice may be between using a
          small sample (of say 100) more `pure' fields versus a large
          sample (of say 1000) slightly correlated fields. In such a
          case, I would probably vote for the second option. [I did a
          little benchmark on 1000 simulations for 3000 cells; the gain
          in speed was about a factor 10 using a single random path.
          This factor will be more for larger fields.]

          Except for the theoretical correlation induced by following
          a single random path, has anyone ever done some computation on how
          large this correlation is in practice?
          --
          Edzer

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