Consequences of near-unfaithfulness in a finite sample – a simulation study

Directed acyclic graphs can be used to infer associations between variables and specify their joint distribution. To infer these associations, an assumption called faithfulness must be satisfied. Faithfulness entails that the independencies that exist in the distribution are equivalent to those in the graph. Violations of the faithfulness assumption can occur because of parameter cancellations or because of certain deterministic relationships between variables. In this study, simulations have been conducted comparing inference between settings when near-unfaithfulness due to parameter cancellations is disallowed versus when it is allowed. The results of the simulations suggest that inference under a setting when near-unfaithfulness is allowed is negatively affected only slightly compared to when near-unfaithfulness is not allowed. For the more sparse models with three and four variables, the differences tended to zero with increasing sample sizes. In simulations of the largest model used in this study, with seven variables, the differences did not tend to zero with increasing sample sizes, likely because of the increased complexity of the inference method when using larger models. inferensmetoden när antalet variabler stiger.