A Good Measure for Bayesian Inference

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.