Towards Characterising Bayesian Network Models under Selection

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be from a distribution in a causal Bayesian network (BN) model under selection. Understanding the constraints in the model under selection is the first step towards recovering causal structure in the original model. The conditional-independence (CI) constraints in a BN model under selection have been already characterised; there exist, however, additional, non-CI constraints in such models. In this work, some initial results are provided that simplify the characterisation problem. In addition, an algorithm is designed for identifying compelled ancestors (definite causes) from a completed partially directed acyclic graph (CPDAG). Finally, a non-CI, non-factorisation constraint in a BN model under selection is computed for the first time.