About the Frequentist and the Bayesian Approach to Uncertainty

There are two well-known and different approaches to statistical inference and hypothesis testing, i.e. the frequentist (or orthodox) and the Bayesian one. Consequently, there are also (if one stays in the framework of probability theory) two rival approaches to uncertainty. The present work is partly a tutorial, aimed at explaining the basic aspects of the two approaches, and their relationship with the GUM; and partly a demonstration that the implementation of the Bayesian approach in the GUM Supplement 1 is too rigid. In particular, objective Bayesianism is incompatible with the propagation of distributions prescribed in Supplement 1.