The problem of detecting new signals in the presence of an unknown background is ubiquitous in scientific discoveries and is especially prominent in the physical sciences. Most solutions proposed thus far to address the problem focus on estimating the background distribution and using that estimate to infer the signal. By studying the geometry of the problem, this article demonstrates that estimating the background distribution is somewhat unnecessary for inferring the signal intensity. Instead, it suffices to estimate a single parameter, referred to as the compensator, to account for the incomplete knowledge on the background, substantially simplifying the problem's complexity and enabling proper uncertainty propagation. Such a compensator is shown to govern the conservativeness of the inference, both in the proposed setup and in likelihood-based approaches.

翻译：在科学发现中，特别是在物理科学领域，未知背景下检测新信号的问题普遍存在。迄今为止，大多数提出的解决方案侧重于估计背景分布，并利用该估计推断信号。通过研究该问题的几何结构，本文证明，在推断信号强度时，估计背景分布并非必要。相反，只需估计一个称为补偿器的单一参数，即可弥补对背景认知的不完整性，从而显著简化问题的复杂性并实现合理的不确定性传播。研究表明，无论是在本文提出的框架中还是在基于似然的方法中，该补偿器都主导着推断的保守性。