Efficient representations of upper limits and confidence intervals for experimental data

Upper limits and confidence intervals are a convenient way to present experimental results. With modern experiments producing more and more data, it is often necessary to reduce the volume of the results for convenient distribution. A common approach is to take a maximum over a set of upper limits, which yields an upper limit valid for the entire set. This, however, can result in significant sensitivity loss, because we discard more constraining data. In this paper we introduce functional upper limits and confidence intervals that allow to summarize results with small relaxation of constraints. A toy example and an application to upper limits in all-sky continuous gravitational wave searches are worked out.
Comment: Expanded version with a toy example. Author preferred equation formatting