  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.
