The effect of parameter priors on Bayesian relevance and effect size measures

The application of Bayesian network based methods is increasingly popular in several research fields where the investigation of complex dependency patterns are of central importance. Bayesian networks provide a rich, graph-based language for the refined characterization of relevance types, and has a built-in mechanism for the correction of multiple testing. In the paper we discuss two main topics: the effects of priors and the applicability of Bayesian structure based odds ratio. The selection of an adequate prior is generally required by Bayesian methods and yet there is no general method for prior selection in the multivariate case. Here we analyze the effects of different priors and propose a method for prior selection based on expected effect size. In the second part of the paper we investigate structural and parametric aspects of relevance, and demonstrate a hybrid effect size measure that allows an integrated analysis of these aspects.