  The Gaussian theory of errors has been generalized to situations, where the
Gaussian distribution and, hence, the Gaussian rules of error propagation are
inadequate. The generalizations are based on Bayes' theorem and a suitable
measure. The following text sketches some chapters of a monograph that is
presently prepared. We concentrate on the material that is - to the best of our
knowledge - not yet in the statistical literature. See especially the extension
of form invariance to discrete data in section 4, the criterion on the
compatibility between a proposed distribution and sparse data in section 7 and
the ``discovery'' of probability amplitudes in section 9.
