Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra

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.Comment: Presented at PHYSTAT 2011, CERN, Geneva, Switzerland, January 2011, to be published in a CERN Yellow Repor