THE SELECTION OF PRIOR DISTRIBUTIONS BY FORMAL RULES

Subjectivism has become the dominant philosophical foundation for Baye sian inference. Yet in practice, most Bayesian analyses are performed with so-called ''noninformative'' priors, that is, priors constructed by some formal rule. We review the plethora of techniques for construc ting such priors and discuss some of the practical and philosophical i ssues that arise when they are used. We give special emphasis to Jeffr eys's rules and discuss the evolution of his viewpoint about the inter pretation of priors, away from unique representation of ignorance towa rd the notion that they should be chosen by convention. We conclude th at the problems raised by the research on priors chosen by formal rule s are serious and may not be dismissed lightly: When sample sizes are small (relative to the number of parameters being estimated), it is da ngerous to put faith in any ''default'' solution; but when asymptotics take over, Jeffreys's rules and their variants remain reasonable choi ces. We also provide an annotated bibliography.