Bayesian uncertainty analysis compared with the application of the GUM and its supplements

The Guide to the Expression of Uncertainty in Measurement (GUM) has proven to be a major step towards the harmonization of uncertainty evaluation in metrology. Its procedures contain elements from both classical and Bayesian statistics. The recent supplements 1 and 2 to the GUM appear to move the guidelines towards the Bayesian point of view, and they produce a probability distribution that shall encode one's state of knowledge about the measurand. In contrast to a Bayesian uncertainty analysis, however, Bayes' theorem is not applied explicitly. Instead, a distribution is assigned for the input quantities which is then 'propagated' through a model that relates the input quantities to the measurand. The resulting distribution for the measurand may coincide with a distribution obtained by the application of Bayes' theorem, but this is not true in general.