  Bayesian inference --- although becoming popular in physics and chemistry ---
is hampered up to now by the vagueness of its notion of prior probability. Some
of its supporters argue that this vagueness is the unavoidable consequence of
the subjectivity of judgements --- even scientific ones. We argue that priors
can be defined uniquely if the statistical model at hand possesses a symmetry
and if the ensuing confidence intervals are subjected to a frequentist
criterion. Moreover, it is shown via an example taken from recent experimental
nuclear physics, that this procedure can be extended to models with broken
symmetry.
