Mixed messages on errors in maximum likelihood with weights

Hello experts,
I would like to perform an unbinned maximum likelihood fit, with weighted events in my measured data. At present the documentation says that there is a way to do this while also getting the uncertainty right. It is rf403_weightedevts.C from which I produce the following:

  // C a l c u l a t e   w e i g h t   a n d   m a k e   d a t a s e t   w e i g h t e d 
  // -----------------------------------------------------------------------------------
  // Construct formula to calculate (fake) weight for events
  RooFormulaVar wFunc("w","event weight","(x*x+10)",x) ;

  // Add column with variable w to previously generated dataset
  RooRealVar* w = (RooRealVar*) data->addColumn(wFunc) ;

  // Instruct dataset wdata in interpret w as event weight rather than as observable
  RooDataSet wdata(data->GetName(),data->GetTitle(),data,*data->get(),0,w->GetName()) ;
  // Create a polynomial PDF for fitting
  RooRealVar a0("a0","a0",1) ;
  RooRealVar a1("a1","a1",0,-1,1) ;
  RooPolynomial p("p","p",x,RooArgList(a0,a1),0) ;

  RooFitResult* r_ml_wgt_corr = p.fitTo(wdata,Save(),SumW2Error(kTRUE)) ;

It is stated that this method provides “a first-order correction” to the estimated parameter errors. I also find however, a presentation (including Wouter Verkerke as an author) saying that the results are now fully correct. Here is a link to that presentation:
twiki.cern.ch/twiki/bin/viewfil … eights.pdf

Is the method in my “code” section a first-order correction or a full correction?
Many thanks for your help with my difficulty!


This correction, described in the presentation, and fully described in F. James book, “Statistical Methods in Experimental Physics”, par 8.5.2 it is only an approximate method. The fully correct method is to include the weight distributions (i.e their pdf) in the likelihood. This means that you need to include the missing variables with their pdf’s that the weight represent in your model.

Best Regards