Objective priors for hypothesis testing in one‐way random effects models

The Bayes factor is a key tool in hypothesis testing. Nevertheless, the important issue of which priors should be used to develop objective Bayes factors remains open. The authors consider this problem in the context of the one‐way random effects model. They use concepts such as orthogonality, predictive matching and invariance to justify a specific form of the priors for common parameters and derive the intrinsic and divergence based prior for the new parameter. The authors show that both intrinsic priors or divergence‐based priors produce consistent Bayes factors. They illustrate the methods and compare them with other proposals.