Counterfactual Covariate Causal Discovery on Nonlinear Extremal Quantiles

Causality is an active relationship that transforms possibility into actuality, underscoring the limitation of relying on averages to address rare events. This study proposes a counterfactual covariate causal discovery mechanism on nonlinear extremal quantiles (CCCD-NEQs) to impute potential outcomes, measure unobservable causalities, and unveil hidden causal relationships in safety-critical systems. We created a multilevel statistical model called mixed-effect and causal-covariate statistical model with dynamic quantiles (MCSM-DQs), which incorporates mixed effects, causal covariates, and dynamic quantiles. Leveraging the exponential family distribution over MCSM-DQ ensures simplified parameter estimation and enhanced computation efficiency, enabling the bootstrapping prediction of counterfactual outcomes at dynamic quantiles to reveal causal relationships and mitigate confounding effects. We applied the CCCD-NEQ approach to identify the potential causal effects among aircraft configuration, decision-making capabilities, and flight safety. Results revealed previously unknown causal relationships concerning rare safety incidents that cannot be detected using conventional instrumental analytics. Our new counterfactual causal discovery mechanism provides opportunities to uncover hidden causality on nonlinear extremal quantiles, highlighting the forward design and optimization of systems for adaptability, robustness, intelligence, and safety.