🤖 AI Summary
This work addresses the challenge of signal detection in high-dimensional binned Poisson count data with unknown background by extending the compensator inference framework—originally developed for unbinned settings—to the binned data context for the first time. By introducing a single compensator parameter within a mixture model to govern inference conservativeness, the method circumvents the need for direct estimation of potentially misspecified background component densities. Consequently, it achieves robust signal detection without explicitly modeling the background distribution, effectively controlling the false positive rate while enhancing detection power. This approach offers a computationally efficient and statistically reliable solution for identifying sparse signals in high-dimensional count data, with direct applicability to modern physics and astronomical experiments where background uncertainty is a critical concern.
📝 Abstract
The problem of signal detection under an unknown background can be framed as one of inferring the weight of a mixture model with one misspecified component. Banerjee and Algeri (2026) show that, for this problem, the conservativeness of the inference is entirely determined by one single parameter, called the compensator. They demonstrate that, when the data are independent and identically distributed, an inferential approach based on the compensator circumvents the need to estimate the density of the misspecified component and the associated challenges. The main purpose of this manuscript is to broaden the scope of such an approach and extend it to the case in which, as is often encountered in modern experiments in physics and astronomy, the data consist of Poisson counts observed over a large number of bins.