This study analyzes how posterior inference in Bayesian causal discovery behaves when latent confounding is present in linear Gaussian models, specifically focusing on additive confounding between two observed variables.
- The authors derive a critical correlation threshold above which the score function favors graphs containing a spurious edge between the confounded variables.
- This threshold decreases as sample size increases, meaning more data lowers the correlation required for the spurious edge to be favored.
- Beyond this threshold, the posterior exhibits two distinct failure regimes determined by the local structure around the confounded variables.
- These findings are supported by exact posterior computations on multiple graph structures, confirming the predicted failure regimes.