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}).
Highlights
Barlow and Pereira [1] discussed a graphical approach to conditional independence
We propose the full Bayesian significance test (FBST) as a test of conditional independence for discrete datasets
This paper provides a framework for performing tests of conditional independence for discrete datasets using the Full Bayesian Significance Test
Summary
Barlow and Pereira [1] discussed a graphical approach to conditional independence. A probabilistic influence diagram is a directed acyclic graph (DAG) that helps model statistical problems. Algorithms, such as the IC-algorithm (inferred causation) described in Pearl and Verma [3], have been designed to uncover these structures from the data This algorithm uses a series of conditional independence tests (CI tests) to remove and direct the arcs, connecting the variables in the model and returning a DAG that minimally (with the minimum number of parameters and without loss of information) represents the variables in the problem. The problem of constructing the DAG structures based on the data motivates the proposal of new powerful statistical tests for the hypothesis of conditional independence, because the accuracy of the structures learned is directly affected by the errors committed by these tests.
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