🤖 AI Summary
In signal detection tasks within physical sciences and related fields, background interference is often unknown and highly complex. This work proposes a geometrically motivated, single-parameter approach termed the “compensator,” which enables effective inference of signal strength without requiring a full model of the background distribution. Grounded in geometric analysis and statistical inference, the method operates within a likelihood-based framework, substantially reducing computational complexity while naturally accounting for the source of inferential conservatism. The resulting detection mechanism is both more parsimonious and robust, offering a principled means to quantify the reliability of inferences under background uncertainty.
📝 Abstract
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.