Review: A new method for estimation and use of systematic errors in Poisson regression

TL;DR

This paper reviews a novel method for incorporating systematic errors into Poisson regression, especially for astronomical spectra, by generalizing the Cash statistic to better model uncertainties and assess fit quality.

Contribution

It introduces a generalized approach to include systematic errors in Poisson likelihood, enhancing modeling simplicity and simultaneous evaluation of systematics and fit quality.

Findings

The method allows simultaneous estimation of systematic errors and goodness of fit.

It simplifies modeling by extending the Cash statistic to account for systematics.

Applicable to astronomical spectra analysis and potentially other Poisson data contexts.

Abstract

A new method for including systematic errors in the regression with Poisson data is reviewed in this contribution, with emphasis on applications to astronomical spectra. The method consists of generalizing the usual Poisson log-likelihood, known as the Cash statistic $C_{min}$, and its associated likelihood-ratio statistic $\Delta C$, to include the presence of systematic sources of uncertainty. Advantages of this new method include its modeling simplicity and its ability to assess both the level of systematics and the goodness of fit at the same time, including for a nested model component.