# Conformal Bayesian Computation

arXiv: https://arxiv.org/abs/2106.06137 · HTML: https://mlsanity.com/paper/2106.06137/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2021.

## Built on by (most cited first, 30 of 39)

- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)
- [Conformalized Physics-Informed Neural Networks](https://mlsanity.com/paper/2405.08111/) (2024)
- [Stop Reducing Responsibility in LLM-Powered Multi-Agent Systems to Local Alignment](https://mlsanity.com/paper/2510.14008/) (2025)
- [Discrete-Event Controller Synthesis for Autonomous Systems with Deep-Learning Perception Components](https://mlsanity.com/paper/2202.03360/) (2022)
- [Conformal Intent Classification and Clarification for Fast and Accurate Intent Recognition](https://mlsanity.com/paper/2403.18973/) (2024)
- [Conformal Bayes under Label Shift: Post-Hoc Calibration vs. In-Training Adaptation](https://mlsanity.com/paper/2606.11865/) (2026)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Adaptive Uncertainty Quantification for Generative AI](https://mlsanity.com/paper/2408.08990/) (2024)
- [Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry](https://mlsanity.com/paper/2602.01667/) (2026)
- [The Benefit of Being Bayesian in Online Conformal Prediction](https://mlsanity.com/paper/2410.02561/) (2024)
- [Online scalable Gaussian processes with conformal prediction for guaranteed coverage](https://mlsanity.com/paper/2410.05444/) (2024)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Design-based conformal prediction](https://mlsanity.com/paper/2303.01422/) (2023)
- [From Conformal Predictions to Confidence Regions](https://mlsanity.com/paper/2405.18601/) (2024)
- [Building Conformal Prediction Intervals with Approximate Message Passing](https://mlsanity.com/paper/2410.16493/) (2024)
- [From predictions to confidence intervals: an empirical study of conformal prediction methods for in-context learning](https://mlsanity.com/paper/2504.15722/) (2025)
- [Conformalized Regression for Continuous Bounded Outcomes](https://mlsanity.com/paper/2507.14023/) (2025)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Bayesian Conformal Prediction as a Decision Risk Problem](https://mlsanity.com/paper/2602.03331/) (2026)
- [Conformal Bayes for Two-Sided Censored Gaussian Regression under Label Shift](https://mlsanity.com/paper/2607.02173/) (2026)
- [Conformal inference for regression on Riemannian Manifolds](https://mlsanity.com/paper/2310.08209/) (2023)
- [Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influence](https://mlsanity.com/paper/2507.20272/) (2025)
- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)
- [Optimizing In-Context Learning for Efficient Full Conformal Prediction](https://mlsanity.com/paper/2509.01840/) (2025)
- [Weighted Bayesian Conformal Prediction](https://mlsanity.com/paper/2604.06464/) (2026)
- [On the Out-of-Distribution Coverage of Combining Split Conformal Prediction and Bayesian Deep Learning](https://mlsanity.com/paper/2311.12688/) (2023)
- [Prediction-Oriented Subsampling from Data Streams](https://mlsanity.com/paper/2508.03868/) (2025)

## Abstract (arXiv)

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, p(y mid x), characterize subjective beliefs on outcomes of interest, y, conditional on predictors, x. Bayesian prediction is well-calibrated when the model is true, but the predictive intervals may exhibit poor empirical coverage when the model is misspecified, under the so called calM-open perspective. In contrast, conformal inference provides finite sample frequentist guarantees on predictive confidence intervals without the requirement of model fidelity. Using 'add-one-in' importance sampling, we show that conformal Bayesian predictive intervals are efficiently obtained from re-weighted posterior samples of model parameters. Our approach contrasts with existing conformal methods that require expensive refitting of models or data-splitting to achieve computational efficiency. We demonstrate the utility on a range of examples including extensions to partially exchangeable settings such as hierarchical models.