Trying to be precise about vagueness

Abstract

A previous investigation by Lambert et al., which used computer simulation to examine the influence of choice of prior distribution on inferences from Bayesian random effects meta-analysis, is critically examined from a number of viewpoints. The practical example used is shown to be problematic. The various prior distributions are shown to be unreasonable in terms of what they imply about the joint distribution of the overall treatment effect and the random effects variance. An alternative form of prior distribution is tentatively proposed. Finally, some practical recommendations are made that stress the value both of fixed effect analyses and of frequentist approaches as well as various diagnostic investigations.