Bayesian--AI Fusion for Epidemiological Decision Making: Calibrated Risk, Honest Uncertainty, and Hyperparameter Intelligence

Modern epidemiological analytics increasingly use machine learning models that offer strong prediction but often lack calibrated uncertainty. Bayesian methods provide principled uncertainty quantification, yet are viewed as difficult to integrate with contemporary AI workflows. This paper proposes a unified Bayesian and AI framework that combines Bayesian prediction with Bayesian hyperparameter optimization. We use Bayesian logistic regression to obtain calibrated individual-level disease risk and credible intervals on the Pima Indians Diabetes dataset. In parallel, we use Gaussian-process Bayesian optimization to tune penalized Cox survival models on the GBSG2 breast cancer cohort. This yields a two-layer system: a Bayesian predictive layer that represents risk as a posterior distribution, and a Bayesian optimization layer that treats model selection as inference over a black-box objective. Simulation studies in low- and high-dimensional regimes show that the Bayesian layer provides reliable coverage and improved calibration, while Bayesian shrinkage improves AUC, Brier score, and log-loss. Bayesian optimization consistently pushes survival models toward near-oracle concordance. Overall, Bayesian reasoning enhances both what we infer and how we search, enabling calibrated risk and principled hyperparameter intelligence for epidemiological decision making.