Limit setting using spacings in the presence of unknown backgrounds

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 dataset.