I read this article by Jim Berger. I agree with much of it, except that I think he unnecessarily privileges certain improper prior distributions. More and more, I’m thinking it makes sense to have noninformative (or weakly-informative) prior distributions that are proper but vague (see here, for example). In addition, I think Berger’s approach would be improved by model checking. Objective Bayesian analysis can be so much more effective when its worst excesses are curbed via model checking. See this paper from the International Statistical Review for some theory and Chapter 6 of our Bayesian book for some examples.
Enjoyed reading this paper – but not convinced “objective” is the “least wrong” term. Science is about making claims to others on the basis of arguments and observables that they can try to replicate if they wish – if they can’t your claim is nullified while on the other hand if they can come up with better arguments and observables they trump your claim (unless others can’t replicate them). The three main points I construed from Berger were 1. an avoidance of misconstrued priors by noting unanticipated and less than acceptable consequences 2. an avoidance of claims of any meaningful posterior without having a meaningful prior (due to casual use of a “default” prior or impracticality of obtaining a realistically meaningful prior) and 3. given you can’t get want you want (a meaningful posterior) do determine if you got what you need (or can get by with) good repeated sampling properties (i.e. confidence interval coverage). Given this, I would prefer “perceptive” or “pragmatic” Bayesian Analysis to “objective”.
Keith