Strong Inconsistency from Uniform Priors

Abstract

Behavior of this type will be called strong inconsistency. Box and Tiao [2, p. 310] might, apparently, tolerate such behavior by the simple device of ignoring (1.3), which, based on a sampling distribution, is regarded as irrelevant to the Bayesian inference. In support orf this, Box and Tiao [2, p. 304] could employ once again a form of argument used to defend a particular improper prior in their analysis of the random effects model; namely, that (a) for any particular x, we can take o-, in the proper prior measure element