30 PRIOR-FREE PROBABILISTIC INFERENCE
2.3.1.3 Difficulties with objective Bayes
The motivation for the Bayesian approach comes from the classical setting where pri-
ors are meant to be subjective. Examples of such philosophical motivations include
deductions based on rationality axioms, coherence, exchangeability and de Finetti’s
theorem, and Birnbaum’s theorem on the likelihood principle, all reviewed in [111].
At best, these results suggest that a Bayesian analysis is appropriate, but they do not
say anything about what prior to use. So, when there is no prior information available,
these results are less than fully convincing.
Additional concerns, which have received less attention in the literature com-
pared to those mentioned above, are about