A Bayesian paradox and its impact on the GUM approach to uncertainty

The paper presents ideas and observations about the use of the frequentist and the Bayesian approach to estimation and uncertainty. The merits and the pitfalls of the Bayesian approach, compared with the frequentist one, are illustrated using a simple example, which gives rise to an instructive paradox. The impact of the paradox on the GUM approach to uncertainty prescribed in Supplement 1 is highlighted and discussed.

► An example of Bayesian and frequentist measurement, leading to contradictory results, is analysed.
► The relevance of the paradox for the GUM, especially Supplement 1, is highlighted by examples taken from the Supplement.
► The problem of choosing between the frequentist and the Bayesian approach to uncertainty is discussed.
► The convenience of including in the GUM both frequentism and Bayesianism is suggested.