rf403_weightedevts.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///  'DATA AND CATEGORIES' RooFit tutorial macro #403
///
///  Using weights in unbinned datasets
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke 


#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooFormulaVar.h"
#include "RooGenericPdf.h"
#include "RooPolynomial.h"
#include "RooChi2Var.h"
#include "RooMinimizer.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooFitResult.h"
using namespace RooFit ;


void rf403_weightedevts()
{
   // C r e a t e   o b s e r v a b l e   a n d   u n w e i g h t e d   d a t a s e t 
   // -------------------------------------------------------------------------------

   // Declare observable
   RooRealVar x("x","x",-10,10) ;
   x.setBins(40) ;

   // Construction a uniform pdf
   RooPolynomial p0("px","px",x) ;

   // Sample 1000 events from pdf
   RooDataSet* data = p0.generate(x,1000) ;

   

   // 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) ;

   // Dataset d is now a dataset with two observable (x,w) with 1000 entries
   data->Print() ;

   // 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()) ;

   // Dataset d is now a dataset with one observable (x) with 1000 entries and a sum of weights of ~430K
   wdata.Print() ;



   // U n b i n n e d   M L   f i t   t o   w e i g h t e d   d a t a 
   // ---------------------------------------------------------------

   // Construction quadratic polynomial pdf for fitting
   RooRealVar a0("a0","a0",1) ;
   RooRealVar a1("a1","a1",0,-1,1) ;
   RooRealVar a2("a2","a2",1,0,10) ;
   RooPolynomial p2("p2","p2",x,RooArgList(a0,a1,a2),0) ;

   // Fit quadratic polynomial to weighted data

   // NOTE: A plain Maximum likelihood fit to weighted data does in general 
   //       NOT result in correct error estimates, unless individual
   //       event weights represent Poisson statistics themselves.
   //       
   // Fit with 'wrong' errors
   RooFitResult* r_ml_wgt = p2.fitTo(wdata,Save()) ;
   
   // A first order correction to estimated parameter errors in an 
   // (unbinned) ML fit can be obtained by calculating the
   // covariance matrix as
   //
   //    V' = V C-1 V
   //
   // where V is the covariance matrix calculated from a fit
   // to -logL = - sum [ w_i log f(x_i) ] and C is the covariance
   // matrix calculated from -logL' = -sum [ w_i^2 log f(x_i) ] 
   // (i.e. the weights are applied squared)
   //
   // A fit in this mode can be performed as follows:

   RooFitResult* r_ml_wgt_corr = p2.fitTo(wdata,Save(),SumW2Error(kTRUE)) ;



   // P l o t   w e i g h e d   d a t a   a n d   f i t   r e s u l t 
   // ---------------------------------------------------------------

   // Construct plot frame
   RooPlot* frame = x.frame(Title("Unbinned ML fit, binned chi^2 fit to weighted data")) ;

   // Plot data using sum-of-weights-squared error rather than Poisson errors
   wdata.plotOn(frame,DataError(RooAbsData::SumW2)) ;

   // Overlay result of 2nd order polynomial fit to weighted data
   p2.plotOn(frame) ;



   // ML Fit of pdf to equivalent unweighted dataset
   // -----------------------------------------------------------------------------------------
   
   // Construct a pdf with the same shape as p0 after weighting
   RooGenericPdf genPdf("genPdf","x*x+10",x) ;

   // Sample a dataset with the same number of events as data
   RooDataSet* data2 = genPdf.generate(x,1000) ;

   // Sample a dataset with the same number of weights as data
   RooDataSet* data3 = genPdf.generate(x,43000) ;

   // Fit the 2nd order polynomial to both unweighted datasets and save the results for comparison
   RooFitResult* r_ml_unw10 = p2.fitTo(*data2,Save()) ;
   RooFitResult* r_ml_unw43 = p2.fitTo(*data3,Save()) ;


   // C h i 2   f i t   o f   p d f   t o   b i n n e d   w e i g h t e d   d a t a s e t
   // ------------------------------------------------------------------------------------

   // Construct binned clone of unbinned weighted dataset
   RooDataHist* binnedData = wdata.binnedClone() ;
   binnedData->Print("v") ;

   // Perform chi2 fit to binned weighted dataset using sum-of-weights errors
   // 
   // NB: Within the usual approximations of a chi2 fit, a chi2 fit to weighted
   // data using sum-of-weights-squared errors does give correct error
   // estimates
   RooChi2Var chi2("chi2","chi2",p2,*binnedData,DataError(RooAbsData::SumW2)) ;
   RooMinimizer m(chi2) ;
   m.migrad() ;
   m.hesse() ;

   // Plot chi^2 fit result on frame as well
   RooFitResult* r_chi2_wgt = m.save() ;
   p2.plotOn(frame,LineStyle(kDashed),LineColor(kRed)) ;



   // C o m p a r e   f i t   r e s u l t s   o f   c h i 2 , M L   f i t s   t o   ( u n ) w e i g h t e d   d a t a 
   // ---------------------------------------------------------------------------------------------------------------

   // Note that ML fit on 1Kevt of weighted data is closer to result of ML fit on 43Kevt of unweighted data 
   // than to 1Kevt of unweighted data, whereas the reference chi^2 fit with SumW2 error gives a result closer to
   // that of an unbinned ML fit to 1Kevt of unweighted data. 

   cout << "==> ML Fit results on 1K unweighted events" << endl ;
   r_ml_unw10->Print() ;
   cout << "==> ML Fit results on 43K unweighted events" << endl ;
   r_ml_unw43->Print() ;
   cout << "==> ML Fit results on 1K weighted events with a summed weight of 43K" << endl ;
   r_ml_wgt->Print() ;
   cout << "==> Corrected ML Fit results on 1K weighted events with a summed weight of 43K" << endl ;
   r_ml_wgt_corr->Print() ;
   cout << "==> Chi2 Fit results on 1K weighted events with a summed weight of 43K" << endl ;
   r_chi2_wgt->Print() ;


   new TCanvas("rf403_weightedevts","rf403_weightedevts",600,600) ;
   gPad->SetLeftMargin(0.15) ; frame->GetYaxis()->SetTitleOffset(1.8) ; frame->Draw() ;


}