Compensator-Based Inference for Signal Detection Under Unknown Background

TL;DR

This paper introduces a new inference method for detecting signals amidst unknown backgrounds, focusing on estimating a single compensator parameter rather than the entire background distribution, simplifying analysis.

Contribution

The study demonstrates that estimating a single compensator parameter suffices for signal inference, reducing complexity compared to traditional background distribution estimation.

Findings

Estimating the compensator parameter effectively accounts for background uncertainty.

The approach simplifies the inference process and improves uncertainty propagation.

The compensator governs the conservativeness of the inference.

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.