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  • WARR Benjamin
    Hi All, When performing SIS we have a choice of the max. no. of data nodes and simulated nodes to use . Is there a general rule defining the number of
    Message 1 of 6 , Nov 21, 2000
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      Hi All,

      When performing SIS we have a choice of the max. no. of data nodes and
      simulated nodes to use . Is there a general rule defining the number of
      simulated nodes ? A ratio between the two, beyond which we are really
      risking artefact creation ? Or any work which highlights the effect of
      using either a dense set of simulated nodes as opposed to a sparse set. I
      have thought about the issue and other than an effect on the time taken to
      simulate the full domain I can't see why a choice of the number of simulated
      nodes will alter the realisations to a great extent. Any conficting
      thoughts.

      Benjamin Warr
      Research Associate to Prof. Ayres,
      PhD Student of Geostatistics for Natural Resource Evaluation at Reading
      University, Soil Science.

      Postal Address:
      Centre for the Management of Environmental Resources (CMER)
      INSEAD
      Boulevard de Constance,
      77305 Fontainebleau Cedex,
      France

      Tel: 33 (0)1 60 72 40 00 ext. 4926
      Fax: 33 (0)1 60 74 55 64
      e-mail: benjamin.warr@...



      [Non-text portions of this message have been removed]
    • Isobel Clark
      The number or density of nodes which you simulate depends solely on why you are doing the simulation and the resolution you need for your study. Also, of
      Message 2 of 6 , Nov 21, 2000
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        The number or density of nodes which you simulate
        depends solely on why you are doing the simulation and
        the resolution you need for your study.

        Also, of course, how much of your life you wish to
        spend waiting for th ecomputer to finish!

        Speed up your simulations in two possible ways:

        (1) simulate a sparse grid, add this to your samples,
        simulate a denser grid, add this to your samples,
        simulate a denser grid and so on. The advantage to
        this is that you can reduce your search radius at each
        iteration. Most of your time is spent searching for
        the "closest" samples;

        (2) simulate in sub-regions. Divide your study area
        into smaller regions and follow a similar process to
        (1)

        You can mix and match (1) and (2) and also randomise
        the points for better realisations.

        I don't use SIS but all of the above work nicely for
        sequential gaussian, which is essentially the same
        thing.

        Isobel Clark

        PS: look out for simulation methods in Volume 2 of
        Practical Geostatistics (2001)




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      • Pierre Goovaerts
        Hi, One of the primary objectives of stochastic simulation is to reproduce patterns of spatial variability and in sequential simulation it is ensured by using
        Message 3 of 6 , Nov 30, 2000
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          Hi,

          One of the primary objectives of stochastic simulation
          is to reproduce patterns of spatial variability and
          in sequential simulation it is ensured by using
          previously simulated values to derive probability
          distributions to be sampled randomly. As a consequence, you
          should make sure that the number of selected points
          (data and simulated values) and the size of the search window
          is large enough to allow one to incorporate information
          up to the range of spatial correlation.
          Of course, this may become impractical as the number of simulated
          values increases, hence the concept of multiple-grid simulation
          implemented in the new version of Gslib and that I strongly
          recommend to use.

          Here is the description that I give in my book, page 379.

          "The use of a search neighborhood limits reproduction of the input
          covariance model to the radius of that neighborhood. Another obstacle
          to reproduction of long-range structures is the screening of distant
          data by too many data closer to the location being simulated. The
          multiple-grid concept (G\'omez-Hern\'andez, 1991; Tran, 1994) allows
          one to reproduce long-range correlation structures without having to
          consider large search neighborhoods with too many conditioning data.
          For example, a two-step simulation of a square grid 500X500
          could proceed as follows:

          1. The attribute values are first simulated on a coarse grid (e.g.,
          25x25) using a large search neighborhood so as to reproduce
          long-range correlation structures. Because the grid is coarse, each
          neighborhood contains few data, which reduces the screening effect.

          2. Once the coarse grid has been completed, the simulation continues
          on the finer grid 500X500 using a smaller search neighborhood
          so as to reproduce short-range correlation structures. The
          previously simulated values on the coarse grid are
          used as data for the simulation on the fine grid.

          A random path is followed within each grid.

          The procedure can be generalized to any number of intermediate grids;
          this number depends on the number of structures with different ranges
          final grid spacing.

          Pierre
          <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

          ________ ________
          | \ / | Pierre Goovaerts
          |_ \ / _| Assistant professor
          __|________\/________|__ Dept of Civil & Environmental Engineering
          | | The University of Michigan
          | M I C H I G A N | EWRE Building, Room 117
          |________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
          _| |_\ /_| |_
          | |\ /| | E-mail: goovaert@...
          |________| \/ |________| Phone: (734) 936-0141
          Fax: (734) 763-2275
          http://www-personal.engin.umich.edu/~goovaert/

          <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>


          On Tue, 21 Nov 2000, WARR Benjamin wrote:

          > Hi All,
          >
          > When performing SIS we have a choice of the max. no. of data nodes and
          > simulated nodes to use . Is there a general rule defining the number of
          > simulated nodes ? A ratio between the two, beyond which we are really
          > risking artefact creation ? Or any work which highlights the effect of
          > using either a dense set of simulated nodes as opposed to a sparse set. I
          > have thought about the issue and other than an effect on the time taken to
          > simulate the full domain I can't see why a choice of the number of simulated
          > nodes will alter the realisations to a great extent. Any conficting
          > thoughts.
          >
          > Benjamin Warr
          > Research Associate to Prof. Ayres,
          > PhD Student of Geostatistics for Natural Resource Evaluation at Reading
          > University, Soil Science.
          >
          > Postal Address:
          > Centre for the Management of Environmental Resources (CMER)
          > INSEAD
          > Boulevard de Constance,
          > 77305 Fontainebleau Cedex,
          > France
          >
          > Tel: 33 (0)1 60 72 40 00 ext. 4926
          > Fax: 33 (0)1 60 74 55 64
          > e-mail: benjamin.warr@...
          >
          >



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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 4 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 5 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 6 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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