Predictive Bayes factors

Bayes factors represent one of the most well-known and commonly adopted tools to perform model selection and hypothesis testing according to a Bayesian flavour. Nevertheless, they are often criticized due to some interpretative and computational aspects, including that of not being able to be used with improper priors, or their intrinsic lack of calibration. Another criticism refers to the fact that they measure the model weight of evidence in terms of prior-predictive distributions, but they are rarely used to measure the predictive accuracy arising from competing models. In this paper we tried to ll this gap by proposing a new algorithmic protocol to transform Bayes factors into measures that evaluate the pure and intrinsic predictive capabilities of models in terms of posterior predictive distributions.