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2362[ai-geostats] Normal score transform for conditional sequential simulations

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  • Paul Walline
    Jan 26, 2006
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      I’ve been a ‘lurker’ for a while, and have learned a lot from reading the
      discussions, so thanks in advance for that.

      My question concerns the use of the normal score transform when making
      repeated conditional sequential Gaussian simulations using GSLIB. I believe
      the criticism that the backtransform would give biased results (as discussed
      in the Saito and Goovaerts 2000 paper in the discussion about Multi-Gausinan
      Kriging) does not apply to simulations because at each point to be
      simulated, a single normal score value is drawn at random from the cdf
      obtained by kriging. The averaging takes place in the original data space. I
      came to this conclusion from trying to figure out how I could apply the
      correction described in the Saito and Goovaerts paper.

      But even if the above is true, I may still have a problem because of the
      high percentage of zeros in my data sets, which ranges from 4 to 22%. I
      (the GSLIB program actually) rank these zero values randomly and I don’t
      know how to implement the suggestion (of Goovaerts, citing Verly 1986) of
      ranking them based on the average value in a search radius so that zeros
      near high densities have higher ranks than those in low density areas. For
      my purposes, I calculate the total ‘abundance’ for each realization, and use
      the frequency distribution of these totals to calculate empirical confidence
      intervals, so I’m mostly interested in the variability in these total
      abundance realizations. How would the zeros affect this? Someone has
      suggested that doing the ranking randomly would increase the nugget effect
      of the normal score variograms. However, I have 6 data sets and the ones
      with the highest % of zeros are not the ones with the largest nuggets. If
      the nugget has been artificially inflated because zeros are not correlated
      after nscore transform when in fact they are correlated in the raw data
      space, is it reasonable to say that the variability of the simulated total
      abundances would be overestimated (and thus conservative)?

      Paul Walline
      NOAA Fisheries, Alaska Fisheries Science Center