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890GEOSTATS: back transforms, caution

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  • Donald Myers
    Jun 30 10:55 AM
      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


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