Hierarchical and Empirical Bayes Extensions

Abstract

In the previous chapters, we have noticed the ambivalent aspect of Bayesian analysis: It is sufficiently reducing to produce an effective decision, but this efficiency can also be misused. For instance, the subjective aspects of Bayesian analysis can always be modified so that it produces conclusions fixed in advance. Of course, the same misappropriation is possible in a frequentist framework through the choice of the loss or of the estimation criterion, while the classical approach does not distinguish between the subjective and the objective inputs of the analysis. The main point is that, as mentioned in Chapter 3, the choice of a prior distribution should always be justifiable by the statistician, i.e., it must be based on sound (or “repeatable”) arguments. So the fact that Bayesian tools may lead to dishonest inferences cannot be taken as a flaw of the Bayesian paradigm.