/// \file /// \ingroup tutorial_roofit /// \notebook -js /// /// Multidimensional models: using the likelihood ratio technique to construct a signal /// enhanced one-dimensional projection of a multi-dimensional p.d.f. /// /// \macro_image /// \macro_output /// \macro_code /// /// \date 07/2008 /// \author Wouter Verkerke #include "RooRealVar.h" #include "RooDataSet.h" #include "RooGaussian.h" #include "RooConstVar.h" #include "RooPolynomial.h" #include "RooAddPdf.h" #include "RooProdPdf.h" #include "TCanvas.h" #include "TAxis.h" #include "RooPlot.h" using namespace RooFit; void rf316_llratioplot() { // C r e a t e 3 D p d f a n d d a t a // ------------------------------------------- // Create observables RooRealVar x("x", "x", -5, 5); RooRealVar y("y", "y", -5, 5); RooRealVar z("z", "z", -5, 5); // Create signal pdf gauss(x)*gauss(y)*gauss(z) RooGaussian gx("gx", "gx", x, RooConst(0), RooConst(1)); RooGaussian gy("gy", "gy", y, RooConst(0), RooConst(1)); RooGaussian gz("gz", "gz", z, RooConst(0), RooConst(1)); RooProdPdf sig("sig", "sig", RooArgSet(gx, gy, gz)); // Create background pdf poly(x)*poly(y)*poly(z) RooPolynomial px("px", "px", x, RooArgSet(RooConst(-0.1), RooConst(0.004))); RooPolynomial py("py", "py", y, RooArgSet(RooConst(0.1), RooConst(-0.004))); RooPolynomial pz("pz", "pz", z); RooProdPdf bkg("bkg", "bkg", RooArgSet(px, py, pz)); // Create composite pdf sig+bkg RooRealVar fsig("fsig", "signal fraction", 0.1, 0., 1.); RooAddPdf model("model", "model", RooArgList(sig, bkg), fsig); RooDataSet *data = model.generate(RooArgSet(x, y, z), 20000); // P r o j e c t p d f a n d d a t a o n x // ------------------------------------------------- // Make plain projection of data and pdf on x observable RooPlot *frame = x.frame(Title("Projection of 3D data and pdf on X"), Bins(40)); data->plotOn(frame); model.plotOn(frame); // D e f i n e p r o j e c t e d s i g n a l l i k e l i h o o d r a t i o // ---------------------------------------------------------------------------------- // Calculate projection of signal and total likelihood on (y,z) observables // i.e. integrate signal and composite model over x RooAbsPdf *sigyz = sig.createProjection(x); RooAbsPdf *totyz = model.createProjection(x); // Construct the log of the signal / signal+background probability RooFormulaVar llratio_func("llratio", "log10(@0)-log10(@1)", RooArgList(*sigyz, *totyz)); // P l o t d a t a w i t h a L L r a t i o c u t // ------------------------------------------------------- // Calculate the llratio value for each event in the dataset data->addColumn(llratio_func); // Extract the subset of data with large signal likelihood RooDataSet *dataSel = (RooDataSet *)data->reduce(Cut("llratio>0.7")); // Make plot frame RooPlot *frame2 = x.frame(Title("Same projection on X with LLratio(y,z)>0.7"), Bins(40)); // Plot select data on frame dataSel->plotOn(frame2); // M a k e M C p r o j e c t i o n o f p d f w i t h s a m e L L r a t i o c u t // --------------------------------------------------------------------------------------------- // Generate large number of events for MC integration of pdf projection RooDataSet *mcprojData = model.generate(RooArgSet(x, y, z), 10000); // Calculate LL ratio for each generated event and select MC events with llratio)0.7 mcprojData->addColumn(llratio_func); RooDataSet *mcprojDataSel = (RooDataSet *)mcprojData->reduce(Cut("llratio>0.7")); // Project model on x, integrating projected observables (y,z) with Monte Carlo technique // on set of events with the same llratio cut as was applied to data model.plotOn(frame2, ProjWData(*mcprojDataSel)); TCanvas *c = new TCanvas("rf316_llratioplot", "rf316_llratioplot", 800, 400); c->Divide(2); c->cd(1); gPad->SetLeftMargin(0.15); frame->GetYaxis()->SetTitleOffset(1.4); frame->Draw(); c->cd(2); gPad->SetLeftMargin(0.15); frame2->GetYaxis()->SetTitleOffset(1.4); frame2->Draw(); }