A Test for the Presence of a Signal, with Multiple Channels and Marked Poisson

TL;DR

This paper introduces a likelihood ratio-based statistical test for detecting signals in complex scenarios involving multiple channels and marked Poisson distributions, demonstrating strong performance through extensive studies.

Contribution

It develops a new hypothesis test tailored for multi-channel and marked Poisson data, extending previous methods and validating its effectiveness through performance evaluations.

Findings

Test performs well in tail regions

Effective with multiple channels

Works with marked Poisson distributions

Abstract

We describe a statistical hypothesis test for the presence of a signal based on the likelihood ratio statistic. We derive the test for a special case of interest. We study extensions of the test to cases where there are multiple channels and to marked Poisson distributions. We show the results of a number of performance studies which indicate that the test works very well, even far out in the tails of the distribution and with multiple channels and marked Poisson.