Bayesian Inference for Confounding Variables and Limited Information

2025-09-05

AI Summary

Unobserved confounding in observational data leads to biased causal estimates and underestimated uncertainty. To address this, we propose an information-theoretic Bayesian causal inference framework that relaxes the strong ignorability assumption of no unmeasured confounding. Our method introduces entropy-regularized priors to explicitly model latent confounders and information incompleteness, enabling principled quantification of estimation uncertainty. Through latent-variable modeling and full Bayesian inference, the approach maintains logical consistency in canonical settings such as Simpson’s paradox; posterior distributions exhibit substantially widened credible intervals, better reflecting true uncertainty. The key innovation lies in embedding high-entropy priors directly into the causal graph structure—constituting the first systematic integration of information-theoretic principles with confounding-robust modeling within the Bayesian paradigm. This enhances the robustness and reliability of causal effect estimation from observational studies.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningCognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude the possibility of unobserved confounders, leading to posterior inferences that overstate certainty. We develop a Bayesian framework that relaxes these assumptions by introducing entropy-favoring priors over hypothesis spaces that explicitly allow for latent confounding variables and partial information. Using the case of Simpson's paradox, we demonstrate how this approach produces logically consistent posterior distributions that widen credibly intervals in the presence of potential confounding. Our method provides a generalizable, information-theoretic foundation for more robust predictive inference in observational sciences.

Problem

• Addressing confounding variables in statistical inference
• Relaxing ignorability assumptions for latent confounders
• Providing robust Bayesian framework for observational sciences

Innovation

• Bayesian framework with entropy-favoring priors
• Handles latent confounding and partial information
• Produces logically consistent posterior distributions