Model for hypotest with signal AND background uncertainties

Roofit and RooStats
#1

Hello,

I’m trying to use RooStats for my analysis, and some of the tutorials seem to come
tantalizingly close to what I’m doing, but I can’t seem to put the pieces together.
I’m pretty new to all this and the factory interface is a total mystery to me.

Currently I have from code I inherited:

  1. A RooHistPdf to define my signal pdf as a function of one observable, a particle mass.
  TH1* signalShape=(TH1*)(signalfile->Get(finalVarHist)->Clone("ss"));
  RooWorkspace w("myw");
  w.factory("mwr[520,2000]"); // observable is called mwr
  w.defineSet("obs","mwr");
  RooDataHist signals("signals","signals",RooArgList(*w.var("mwr")),signalShape) ;
  RooHistPdf signalPdf("sig_pdf","sig_pdf",RooArgList(*w.var("mwr")),signals);
  w.import(signalPdf);
  1. The signal yield as the sole parameter of interest
  w.defineSet("poi","sig_yield");
  1. Background fits to exponentials for two background processes ttbar and z+jets
  sprintf(temp,"Exponential::bkg_tt(mwr,%f)", tt_expfit_p1);  w.factory(temp);
  sprintf(temp,"Exponential::bkg_zj(mwr,%f)", zj_expfit_p1);  w.factory(temp);
  1. Background yields as nuisance parameters that have lognormal priors.
    sprintf(temp,"Lognormal::tt_xsec(tt_est[%f],tt_yield,%f)",tt_yield_mc,tt_yield_ferror); w.factory(temp);
    sprintf(temp,"Lognormal::zj_xsec(zj_est[%f],zj_yield,%f)",zj_yield_mc,zj_yield_ferror); w.factory(temp);
    w.var("tt_yield")->setVal(tt_yield_mc);
    w.var("zj_yield")->setVal(zj_yield_mc);
  1. Setting up to do the CLs method (showing the s+b model part):
  w.factory(
"SUM::main_pdf(sig_yield[20,0,3000]*sig_pdf,tt_yield[0.1,1e-5,10]*bkg_tt,zj_yield[0.1,1e-5,10]*bkg_zj)");
    w.factory("PROD::control_pdf(tt_xsec,zj_xsec)");
    w.factory("PROD::main_with_control(main_pdf,control_pdf)");

  ModelConfig sb_model("S+B_model", &w); // signal+background, alternative hypothesis
  sb_model.SetPdf(w.pdf("main_with_control"));
  sb_model.SetParametersOfInterest(*w.set("poi"));
  sb_model.SetNuisanceParameters(*w.set("nuis")); 
...

(Don’t know how much further I need to show…some of what you see may be associated
with dead code, but I can’t tell for sure.)
To this picture I want to add the uncertainty to the total signal yield as a nuisance parameter.

I tried doing this with the signal yield directly but ended up with disaster.
It was suggested to me to use the signal efficiency as a nuisance parameter instead,
but once again, the workspace factory interface has me flummoxed, it all seems like magic.

Any tips, please? Thanks,
-Phil D.