After I finished my previous post it occurred to me that there is a kind of truth-valued assumption to which one can appeal in order to provide a performance-based justification for a Bayesian analysis: that the true hypothesis is within the set of hypotheses on which the method performs well relative to a set of relevant alternatives. Roughly speaking, one can assume that one has chosen good priors for the problem at hand.

I suggest that it would be appropriate to use the term “objective” with reference to Bayesian statistics to refer not to views that prescribe rules for choosing priors, but instead to the view that insofar as a given Bayesian analysis is justified, it is justified not by the Likelihood Principle or the usual coherence arguments, but instead by the assumption that the priors used are well chosen relative to the true state of affairs. [Read more…]