A recent supplement to the GUM (GUM S1) is compared with a Bayesian analysis in terms of a particular task of data analysis, one where no prior knowledge of the measurand is presumed. For the Bayesian analysis, an improper prior density on the measurand is employed. It is shown that both approaches yield the same results when the measurand depends linearly on the input quantities, but generally different results otherwise. This difference is shown to be not a conceptual one, but due to the fact that the two methods correspond to Bayesian analysis under different parametrizations, with ignorance of the measurand expressed by a non-informative prior on a different parameter. The use of the improper prior for the measurand itself may result in an improper posterior probability density function (PDF) when the measurand depends non-linearly on the input quantities. On the other hand, the PDF of the measurand derived by the GUM supplement method is always proper but may sometimes have undesirable properties such as non-existence of moments.

It is concluded that for a linear model both analyses can safely be applied. For a non-linear model, the GUM supplement approach may be preferred over a Bayesian analysis using a constant prior on the measurand. But since in this case the GUM S1 PDF may also have undesirable properties, and as often some prior knowledge about the measurand may be established, metrologists are strongly encouraged to express this prior knowledge in terms of a proper PDF which can then be included in a Bayesian analysis. The results of this paper are illustrated by an example of a simple non-linear model.