Integrated objective Bayesian estimation and hypothesis testing: a discussion

The paper manages the tour de force of aggregating intrinsic loss functions with intrinsic (aka reference) priors. Thus, Professor Bernardo presents us with a unified picture of Bayesian analysis as he sees it and it is obviously fitting to see this cohesive perspective appearing in the Valencia 9 proceedings as a kind of third unification! We appreciated very much the paper and our comments will thus concentrate on minor issues rather than on the big picture, since we mostly agree with it. Although the tendency in Bayesian analysis, along the years, and in particular in the Valencia proceedings (see, e.g., Polson and Scott in this volume who discuss shrinkage without a loss function), has been to shy away from the decision-theoretic perspective (see, e.g., Gelman, 2008), it is worth reenacting this approach to the field, both because it sustains to a large extent the validation of a Bayesian analysis and because it avoids the deterioration of its scope into a mechanical data analysis tool.