Robust Causal Inference in Financial Markets: A Bayesian Activation–Inhibition Noisy-OR (BAINOR) Framework

The noisy-OR (NOR) model provides a computationally efficient representation of systems with multiple interacting causes, yet its classical formulation is limited in financial applications. Causal probabilities are typically expert elicited, assumed constant across observations, and estimated without formal treatment of parameter uncertainty. These assumptions are difficult to justify in financial environments characterized by limited data, nonstationarity, and evolving market conditions, where causal mechanisms are unlikely to remain stable over time. To address these limitations, in this article a novel Bayesian activation–inhibition noisy-OR (BAINOR) framework is proposed. The model extends the classical NOR architecture by introducing latent activation and inhibition mechanisms, with probabilities specified as functions of continuous covariates and estimated directly from data, while incorporating prior expert knowledge through Bayesian inference. Preserving the interpretability and causal transparency of classical NOR systems, the formulation enables empirical learning from data and propagation of parameter uncertainty into estimates. Robustness to potential model misspecification is achieved through a Kullback–Leibler divergence-based measure. Empirical evidence further underscores the predictive strength of BAINOR in financial applications, with a pooled out-of-sample classification accuracy of 78.7% and an area under the curve of 0.88 under an expanding-window cross-validation scheme. Additionally, benchmark comparisons suggest that BAINOR delivers predictive performance that is strongly competitive with established statistical and machine learning models, with superior performance observed in several respects. Crucially, this is achieved while preserving full probabilistic transparency, causal interpretability, and explicit uncertainty quantification, which are often sacrificed or only weakly represented by more flexible black-box learning algorithms.