Coherence and calibration: comments on subjectivity and "objectivity'' in Bayesian analysis (comment on articles by Berger and by Goldstein)

Abstract

In this contribution to the discussion of "The case for objective Bayesian analysis" by James Berger and "Subjective Bayesian analysis: principles and practice" by Michael Goldstein, I argue that (a) all Bayesian work is inherently subjective and needs to be guided simultaneously by considerations of both coherence and calibration, and (b) "objective" (diffuse) prior distributions are sometimes, but not always, useful in attaining good calibrative performance---it depends (as usual) on your judgment about how knowns (e.g., past observables) and unknowns (e.g., future observables) are related.