How Does Bayesian Causal Discovery Fail? Structural Consequences in Linear Gaussian Networks under Latent Confounding

This paper studies how latent confounding changes Bayesian causal discovery over directed acyclic graphs. In linear Gaussian causal models with additive latent confounding between exactly two observed variables, the authors derive a critical correlation threshold above which the scoring function prefers a spurious edge between the confounded variables. The threshold decreases as sample size grows. They further identify two posterior failure regimes determined by the local graph structure and support the analysis with exact posterior computations across multiple graph structures.