# Gaussian Uncertainty on a variable of PDF

Hi all,

I am trying to prepare my PDF model for CLs machinery and I am facing a problem including gaussian uncertainty on a variable.

Since I want to use as POI the Branching ratio I am “transforming” the signal events with a constant into Branching ratio. My goal is to have an error on that constant term with a gaussian (mean value the nominal one and sigma to be editable by the user).
I have:
PDF : BRconv * sig_pdf + Nbkg * bkg_pdf
sig_pdf = Gaus(M|m,s)
bkg_pdf = Cheb(M|a20,a21)
BRconv = BR * SES
where SES is the constant term
and BR my POI.

I attach also the relevant code.
GausCheb_BRConv_Model.C (4.44 KB)
Thank you in advance,
Kostas

Hi,

Looking at your code, I see you have already defined a Gaussian pdf for the “SES” variable (gErrSES).
You would need to then multiply your model pdf by this constraint term that will be added in the likelihood function when doing the statistical calculations.
You should then define a full model as a product of your original model and the gaussian constraint.
In addition you need to define “SES” as a nuisance parameter and “SESMean” as a global observable, that can be varied in the frequentist calculations in RooStats. You should do:

``````w->factory("PROD::fullModel(model,gErrSES)");
// define also SESMean with a min and max range to make it vary when doing toys generation
w->var("SESMean")->setMin(f-5*sf);
w->var("SESMean")->setMax(f+5*sf);
w->var("SESMean")->setConstant();
// then later after defining the ModelConfig
mc->setPdf(*w->pdf("fullModel"));
/// define set of nuisance parameters
w->defineSet("nuisParams","a20,a21,"SES"");
mc->SetGlobalObservables(*w->var("SESMean"));``````

You can also find a similar example in

twiki.cern.ch/twiki/bin/view/Ro … isson_Coun

Best Regards

Lorenzo