Bayesian test of significance for conditional independence: The multinomial model

TL;DR

This paper introduces a Bayesian significance test called FBST for assessing conditional independence in discrete data, which is crucial for learning probabilistic graphical models like Bayesian Networks.

Contribution

It proposes the FBST method specifically for conditional independence testing in discrete datasets within the PGM framework, offering an alternative to traditional p-value based tests.

Findings

FBST provides a Bayesian alternative for CI testing.

The method is effective for structure learning in Bayesian Networks.

It offers a precise hypothesis testing approach.

Abstract

Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical 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 Significance 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 \emph{p-value}).