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

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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
Message 1 of 1 , Jan 26, 2006
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)?

Cheers,
Paul Walline
NOAA Fisheries, Alaska Fisheries Science Center
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