Bayesian test of significance for conditional independence: The multinomial model

Conditional independence tests (CI tests) have received special at-tention lately in Machine Learning and Computational Intelligence re-lated literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graph-ical Models (PGM)–which includes Bayesian Networks (BN) models– CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Sig-nificance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist’s significance tests (characterized by the calculation of the p-value).