Optimal Conformal Prediction for Small Areas

TL;DR

This paper introduces a conformal prediction method for small area data that guarantees coverage and minimizes volume when the model is correct, improving inference by balancing coverage and precision.

Contribution

It proposes a novel conformal prediction approach using posterior predictive density to achieve guaranteed coverage and minimal volume under correct model assumptions.

Findings

Guarantees frequentist coverage regardless of the working model.

Achieves minimum expected volume when the model assumptions are correct.

Demonstrates effectiveness through simulations and EPA radon data application.

Abstract

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.