{"ID":2887657,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.01418","arxiv_id":"2508.01418","title":"Bayesian Conformal Prediction via the Bayesian Bootstrap","abstract":"Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample sizes or model misspecification. We introduce a practical and broadly applicable Bayesian conformal approach based on the influence-function Bayesian bootstrap (BB) with data-driven tuning of the Dirichlet concentration parameter, α. By efficiently approximating the Bayesian bootstrap predictive distribution via influence functions and calibrating α to optimize empirical coverage or average log-probability, our method constructs prediction intervals and distributions that are both well-calibrated and sharp. Across a range of regression models and data settings, this Bayesian conformal framework consistently yields improved empirical coverage and log-score compared to standard Bayesian posteriors. Our procedure is fast, easy to implement, and offers a flexible approach for distributional calibration in predictive modeling.","short_abstract":"Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample sizes or model misspecification. We introduce a practical and broadly applicable...","url_abs":"https://arxiv.org/abs/2508.01418","url_pdf":"https://arxiv.org/pdf/2508.01418v1","authors":"[\"Graham Gibson\"]","published":"2025-08-02T15:54:20Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\"]","methods":"[]","has_code":false}