On the application of Supplement 1 to the GUM to non-linear problems

Supplement 1 to the GUM (GUM-S1) produces an arbitrarily large sample from a probability distribution for the measurand which is used for the calculation of an estimate and its associated uncertainty. In the presence of Gaussian observations on one or several input quantities this distribution is equivalent to the Bayesian posterior obtained for a particular choice of a non-informative prior. Recently, a reference prior under partial information was proposed as an alternative non-informative prior in this context. Since for non-linear problems different results are obtained with this prior than by application of GUM-S1, the question arises whether GUM-S1 should actually be recommended for non-linear problems.