Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra

TL;DR

This paper presents a mathematical framework for constructing likelihood functions that incorporate nuisance parameters to account for systematic uncertainties in multisource spectral data analysis.

Contribution

It introduces a general approach to include various types of nuisance parameters in likelihood maximization for spectral fitting.

Findings

Framework accommodates multiple nuisance parameter types.

Enables systematic uncertainty integration into spectral likelihoods.

Applicable to complex multisource spectral analyses.

Abstract

We describe here the general mathematical approach to constructing likelihoods for fitting observed spectra in one or more dimensions with multiple sources, including the effects of systematic uncertainties represented as nuisance parameters, when the likelihood is to be maximized with respect to these parameters. We consider three types of nuisance parameters: simple multiplicative factors, source spectra "morphing" parameters, and parameters representing statistical uncertainties in the predicted source spectra.