Special pdf's: unbinned maximum likelihood fit of an efficiency eff(x) function
to a dataset D(x,cut), where cut is a category encoding a selection, of which the efficiency as function of x should be described by eff(x)
Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, April 17, 2024 at 11:19 AM.
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooFormulaVar.h"
#include "RooProdPdf.h"
#include "RooEfficiency.h"
#include "RooPolynomial.h"
#include "RooCategory.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
Declare variables x,mean,sigma with associated name, title, initial value and allowed range
RooRealVar x("x", "x", -10, 10);
Efficiency function eff(x;a,b)
RooRealVar a("a", "a", 0.4, 0, 1);
RooRealVar b("b", "b", 5);
RooRealVar c("c", "c", -1, -10, 10);
RooFormulaVar effFunc("effFunc", "(1-a)+a*cos((x-c)/b)", RooArgList(a, b, c, x));
Acceptance state cut (1 or 0)
RooCategory cut("cut", "cutr", { {"accept", 1}, {"reject", 0} });
Construct efficiency pdf eff(cut|x)
RooEfficiency effPdf("effPdf", "effPdf", effFunc, cut, "accept");
Construct global shape pdf shape(x) and product model(x,cut) = eff(cut|x)*shape(x) (These are only needed to generate some toy MC here to be used later)
RooPolynomial shapePdf("shapePdf", "shapePdf", x, RooConst(-0.095));
RooProdPdf model("model", "model", shapePdf, Conditional(effPdf, cut));
Generate some toy data from model
std::unique_ptr<RooDataSet> data{model.generate({x, cut}, 10000)};
input_line_56:2:2: warning: 'data' shadows a declaration with the same name in the 'std' namespace; use '::data' to reference this declaration std::unique_ptr<RooDataSet> data{model.generate({x, cut}, 10000)}; ^
Fit conditional efficiency pdf to data
effPdf.fitTo(*data, ConditionalObservables(x), PrintLevel(-1));
input_line_57:2:16: error: reference to 'data' is ambiguous effPdf.fitTo(*data, ConditionalObservables(x), PrintLevel(-1)); ^ input_line_56:2:30: note: candidate found by name lookup is 'data' std::unique_ptr<RooDataSet> data{model.generate({x, cut}, 10000)}; ^ /usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data' data(initializer_list<_Tp> __il) noexcept ^ /usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data' data(_Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data' data(const _Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data' data(_Tp (&__array)[_Nm]) noexcept ^
Plot distribution of all events and accepted fraction of events on frame
RooPlot *frame1 = x.frame(Bins(20), Title("Data (all, accepted)"));
data->plotOn(frame1);
data->plotOn(frame1, Cut("cut==cut::accept"), MarkerColor(kRed), LineColor(kRed));
input_line_58:3:1: error: reference to 'data' is ambiguous data->plotOn(frame1); ^ input_line_56:2:30: note: candidate found by name lookup is 'data' std::unique_ptr<RooDataSet> data{model.generate({x, cut}, 10000)}; ^ /usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data' data(initializer_list<_Tp> __il) noexcept ^ /usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data' data(_Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data' data(const _Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data' data(_Tp (&__array)[_Nm]) noexcept ^ input_line_58:4:1: error: reference to 'data' is ambiguous data->plotOn(frame1, Cut("cut==cut::accept"), MarkerColor(kRed), LineColor(kRed)); ^ input_line_56:2:30: note: candidate found by name lookup is 'data' std::unique_ptr<RooDataSet> data{model.generate({x, cut}, 10000)}; ^ /usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data' data(initializer_list<_Tp> __il) noexcept ^ /usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data' data(_Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data' data(const _Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data' data(_Tp (&__array)[_Nm]) noexcept ^
Plot accept/reject efficiency on data overlay fitted efficiency curve
RooPlot *frame2 = x.frame(Bins(20), Title("Fitted efficiency"));
data->plotOn(frame2, Efficiency(cut)); // needs ROOT version >= 5.21
effFunc.plotOn(frame2, LineColor(kRed));
input_line_59:3:1: error: reference to 'data' is ambiguous data->plotOn(frame2, Efficiency(cut)); // needs ROOT version >= 5.21 ^ input_line_56:2:30: note: candidate found by name lookup is 'data' std::unique_ptr<RooDataSet> data{model.generate({x, cut}, 10000)}; ^ /usr/include/c++/9/bits/range_access.h:318:5: note: candidate found by name lookup is 'std::data' data(initializer_list<_Tp> __il) noexcept ^ /usr/include/c++/9/bits/range_access.h:289:5: note: candidate found by name lookup is 'std::data' data(_Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:299:5: note: candidate found by name lookup is 'std::data' data(const _Container& __cont) noexcept(noexcept(__cont.data())) ^ /usr/include/c++/9/bits/range_access.h:309:5: note: candidate found by name lookup is 'std::data' data(_Tp (&__array)[_Nm]) noexcept ^
Draw all frames on a canvas
TCanvas *ca = new TCanvas("rf701_efficiency", "rf701_efficiency", 800, 400);
ca->Divide(2);
ca->cd(1);
gPad->SetLeftMargin(0.15);
frame1->GetYaxis()->SetTitleOffset(1.6);
frame1->Draw();
ca->cd(2);
gPad->SetLeftMargin(0.15);
frame2->GetYaxis()->SetTitleOffset(1.4);
frame2->Draw();
input_line_61:2:3: error: use of undeclared identifier 'frame1' (frame1->GetYaxis()->SetTitleOffset(1.6000000000000001)) ^ Error in <HandleInterpreterException>: Error evaluating expression (frame1->GetYaxis()->SetTitleOffset(1.6000000000000001)) Execution of your code was aborted.
Draw all canvases
%jsroot on
gROOT->GetListOfCanvases()->Draw()