////////////////////////////////////////////////////////////////////////// // // 'DATA AND CATEGORIES' RooFit tutorial macro #403 // // Using weights in unbinned datasets // // // // 07/2008 - Wouter Verkerke // ///////////////////////////////////////////////////////////////////////// #ifndef __CINT__ #include "RooGlobalFunc.h" #endif #include "RooRealVar.h" #include "RooDataSet.h" #include "RooDataHist.h" #include "RooGaussian.h" #include "RooFormulaVar.h" #include "RooGenericPdf.h" #include "RooPolynomial.h" #include "RooChi2Var.h" #include "RooMinuit.h" #include "TCanvas.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 d in interpret w as event weight rather than as observable data->setWeightVar(*w) ; // Dataset d is now a dataset with one observable (x) with 1000 entries and a sum of weights of ~430K data->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(*data,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(*data,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 data->plotOn(frame,DataError(RooAbsData::SumW2)) ; // Overlay result of 2nd order polynomial fit to weighted data p2.plotOn(frame) ; // M L F i t o f p d f t o e q u i v a l e n t u n w e i g h t e d d a t a s e t // ----------------------------------------------------------------------------------------- // 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 = data->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)) ; RooMinuit 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) ; frame->Draw() ; }