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.

Donald Myers

Department of Mathematics

University of Arizona

Tucson, AZ 85721

http://www.arizona.edu/~donaldm
myers@...
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