Incorporating structural uncertainty in causal decision making
This addresses a distinct source of uncertainty often overlooked in practice for practitioners making decisions based on causal effects, though it is incremental as it complements existing robust causal inference approaches.
The paper tackles the problem of ignoring structural uncertainty in causal decision making, establishing that Bayesian model averaging over competing causal structures is beneficial under specific conditions like moderate to high uncertainty and substantial effect differences, with optimality proofs and simulations showing modern causal discovery methods can quantify this within limits.
Practitioners making decisions based on causal effects typically ignore structural uncertainty. We analyze when this uncertainty is consequential enough to warrant methodological solutions (Bayesian model averaging over competing causal structures). Focusing on bivariate relationships ($X \rightarrow Y$ vs. $X \leftarrow Y$), we establish that model averaging is beneficial when: (1) structural uncertainty is moderate to high, (2) causal effects differ substantially between structures, and (3) loss functions are sufficiently sensitive to the size of the causal effect. We prove optimality results of our suggested methodological solution under regularity conditions and demonstrate through simulations that modern causal discovery methods can provide, within limits, the necessary quantification. Our framework complements existing robust causal inference approaches by addressing a distinct source of uncertainty typically overlooked in practice.