GEOSTATS: back transforms, caution
- just a word of caution. The comments that have appeared previously
pertaining to backtransforms and in particular after the use of a log
transform all assume that the random function has a multivariate lognormal
distribution (univariate is not sufficient). Journel's paper (cited from
Math Geology) makes this very clear.
One of the reasons that non-linear transforms are not so widely used in
geostatistics (as perhaps in other parts of statistics) pertains to the
problem of backtransforms. Some uses in statistics do not require the use
of a backtransform and hence the problem does not arise. Note that
indicator kriging uses a non-linear transform but ordinarily the use of
indicators does not require a backtransform.
Unfortunately when the data consists of a non-random sample from one
realization of the random function then there are no statistical tests for
multivariate normality or multivariate lognormality. While it is common
practice to look at the histogram of the data or the log transformed data,
this is not quite an estimator of the distribution of the random function.
Rather it is an estimator of the spatial distribution.
The histograms provide some evidence of the reasonableness of the
assumptions but do not provide a statistical test.
Department of Mathematics
University of Arizona
Tucson, AZ 85721
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