Integral priors for the one way random effects model

Abstract

The one way random effects model is analyzed from the Bayesian model selection perspective. From this point of view Bayes factors are the key tool to choose between two models. In order to produce objective Bayes factors objective priors should be assigned to each model.

However, these priors are usually improper provoking a calibration problem which precludes the comparison of the models. To solve this problem several derivations of automatically calibrated objective priors have been proposed among which we quote the intrinsic priors introduced in Berger and Pericchi (1996) and the integral priors introduced in Cano et al. (2006). Here, we focus on the use of integral priors which take advantage of MCMC techniques to produce most of the times unique Bayes factors. Some illustrations are provided.