A Note Concerning a Selection “Paradox” of Dawid's

This article briefly reviews a selection “paradox” of Dawid's, whereby Bayesian inference appears to be unchanged whether or not treatments have been selected for inspection on the basis of extreme values. The problem is recast in terms of a hierarchical model. This offers an alternative explanation of the paradox but also reveals a disturbing dependence of inference on prior specification. The example may also be used to deepen students' understanding of the implications of using conjugate nonhierarchical priors in Bayesian analysis. To illustrate, some simulations are presented.