Non local alternative priors for Gaussian directed acyclic graphical models

Prior choice for Bayesian model comparison can be problematic for several reasons. In particular, for the comparison of two nested models, it was recently pointed out that typical prior choices may produce an unsatisfactory learning behavior of the Bayes factor. More in detail, if the sub-model is not true the accumulation of evidence is exponentially fast in favor of the encompassing model, whereas it is only sub-linear in favor of the sub-model under the assumption that the latter is true. To alleviate this imbalance, it was suggested that the prior under the encompassing model be modified so that it vanishes over the sub-space corresponding to the sub-model, thus obtaining a Non Local Alternative Prior (NLAP). In this work, we develop NLAPs for the comparison of Gaussian directed acyclic graphical models, and contrast their performance with that of traditional priors.