Bayesian Conformal Prediction via the Bayesian Bootstrap
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918112220151808 |
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| author | Gibson, Graham |
| author_facet | Gibson, Graham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Conformal Prediction via the Bayesian Bootstrap Gibson, Graham Methodology Statistics Theory 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. |
| title | Bayesian Conformal Prediction via the Bayesian Bootstrap |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2508.01418 |