# Bayes-optimal prediction with frequentist coverage control

arXiv: https://arxiv.org/abs/2105.14045 · HTML: https://mlsanity.com/paper/2105.14045/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2021.

## Built on by (most cited first, 20 of 20)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Conformal Prediction Sets with Limited False Positives](https://mlsanity.com/paper/2202.07650/) (2022)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Efficient and Differentiable Conformal Prediction with General Function Classes](https://mlsanity.com/paper/2202.11091/) (2022)
- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)
- [FAB-PPI: Frequentist, Assisted by Bayes, Prediction-Powered Inference](https://mlsanity.com/paper/2502.02363/) (2025)
- [Conformal Prediction as Bayesian Quadrature](https://mlsanity.com/paper/2502.13228/) (2025)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Conformalized Deep Splines for Optimal and Efficient Prediction Sets](https://mlsanity.com/paper/2311.00774/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimation](https://mlsanity.com/paper/2601.22298/) (2026)
- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)
- [On the Out-of-Distribution Coverage of Combining Split Conformal Prediction and Bayesian Deep Learning](https://mlsanity.com/paper/2311.12688/) (2023)
- [Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means](https://mlsanity.com/paper/2605.07964/) (2026)
- [Fair Conformal Classification via Learning Representation-Based Groups](https://mlsanity.com/paper/2605.12195/) (2026)
- [Conformalised imprecise inference for robust extrapolation under limited data](https://mlsanity.com/paper/2605.25882/) (2026)
- [Robust Bayes-Assisted Conformal Prediction](https://mlsanity.com/paper/2607.04236/) (2026)

## Abstract (arXiv)

This article illustrates how indirect or prior information can be optimally used to construct a prediction region that maintains a target frequentist coverage rate. If the indirect information is accurate, the volume of the prediction region is lower on average than that of other regions with the same coverage rate. Even if the indirect information is inaccurate, the resulting region still maintains the target coverage rate. Such a prediction region can be constructed for models that have a complete sufficient statistic, which includes many widely-used parametric and nonparametric models. Particular examples include a Bayes-optimal conformal prediction procedure that maintains a constant coverage rate across distributions in a nonparametric model, as well as a prediction procedure for the normal linear regression model that can utilize a regularizing prior distribution, yet maintain a frequentist coverage rate that is constant as a function of the model parameters and explanatory variables. No results in this article rely on asymptotic approximations.