Bayesian Conformal Prediction via the Bayesian Bootstrap

Graham Gibson

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arXiv · 2508.01418

Bayesian Conformal Prediction via the Bayesian Bootstrap

Graham Gibson

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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, {\alpha}. By efficiently approximating the Bayesian bootstrap predictive distribution via influence functions and calibrating {\alpha} 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.

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Graham Gibson. 2025-08-02. Bayesian Conformal Prediction via the Bayesian Bootstrap. https://arxiv.org/abs/2508.01418

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