# Optimal Conformal Prediction for Small Areas

arXiv: https://arxiv.org/abs/2204.08122 · HTML: https://mlsanity.com/paper/2204.08122/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2022.

## Built on by (most cited first, 5 of 5)

- [Prediction-Powered Inference Across Many Tasks for AI Evaluation & Social Science Research](https://mlsanity.com/paper/2605.29249/) (2026)
- [Design-based conformal prediction](https://mlsanity.com/paper/2303.01422/) (2023)
- [Conformalized Regression for Continuous Bounded Outcomes](https://mlsanity.com/paper/2507.14023/) (2025)
- [Probabilistic Conformal Coverage Guarantees in Small-Data Settings](https://mlsanity.com/paper/2509.15349/) (2025)
- [Robust Bayes-Assisted Conformal Prediction](https://mlsanity.com/paper/2607.04236/) (2026)

## Abstract (arXiv)

Existing inferential methods for small area data involve a trade-off between maintaining area-level frequentist coverage rates and improving inferential precision via the incorporation of indirect information. In this article, we propose a method to obtain an area-level prediction region for a future observation which mitigates this trade-off. The proposed method takes a conformal prediction approach in which the conformity measure is the posterior predictive density of a working model that incorporates indirect information. The resulting prediction region has guaranteed frequentist coverage regardless of the working model, and, if the working model assumptions are accurate, the region has minimum expected volume compared to other regions with the same coverage rate. When constructed under a normal working model, we prove such a prediction region is an interval and construct an efficient algorithm to obtain the exact interval. We illustrate the performance of our method through simulation studies and an application to EPA radon survey data.