Current recommendations for evaluating uncertainty of measurement are based on the Bayesian interpretation of probability distributions as encoding the state of knowledge about the quantities to which those distributions refer. Given a measurement model that relates an output quantity to one or more input quantities, the distribution of the former is obtained by propagating those of the latter according to the axioms of probability calculus and also, if measurement data are available, by applying Bayes' theorem. The main objective of this paper is to show that alternative ways of applying Bayes' theorem are possible, and that these alternative formulations yield the same results provided consistent use is made of measurement data and prior information. In this context the necessity of assigning non-informative priors arises often. Therefore, the second concern of the paper is to point out, by means of a specific example, that the seemingly reasonable choice of a uniform prior for a quantity about which no information is available may not conform to the accepted rules for constructing non-informative priors.
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