Finding upper limits on the rate of events from a proposed process in the presence of unknown backgrounds is an often encountered problem in the search for rare processes. Methods based on unusually large "gaps", or spacings, in the event distribution allow to set limits on the rate of the proposed signal distribution. In this paper, we present two novel spacings-based methods: the "Sum of sorted spacings" and the "Product of complementary spacings" as tests and compare these to existing tests on synthetic data as well as on a published data set.

翻译：在寻找稀有过程时，常遇到一个问题：在未知背景存在的情况下，如何对拟议过程的事件发生率设定上限。基于事件分布中异常大的“间隙”（即间隔）的方法，可对拟议信号分布的速率设定限值。本文提出两种新颖的基于间隔的方法：即“排序间隔之和”与“互补间隔之积”，作为检验手段，并将其与现有检验方法在合成数据及已公开发布的数据集上进行比较。