Multidimensional models: using the likelihood ratio technique to construct a signal enhanced one-dimensional projection of a multi-dimensional pdf
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 11:18 AM.
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooPolynomial.h"
#include "RooAddPdf.h"
#include "RooProdPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
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, 0.0, 1.0);
RooGaussian gy("gy", "gy", y, 0.0, 1.0);
RooGaussian gz("gz", "gz", z, 0.0, 1.0);
RooProdPdf sig("sig", "sig", RooArgSet(gx, gy, gz));
Create background pdf poly(x)poly(y)poly(z)
RooPolynomial px("px", "px", x, RooArgSet(-0.1, 0.004));
RooPolynomial py("py", "py", y, RooArgSet(0.1, -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);
std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)};
input_line_51:5:1: 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, y, z}, 20000)}; ^
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);
input_line_52:3:1: error: reference to 'data' is ambiguous data->plotOn(frame); ^ input_line_51:5:29: note: candidate found by name lookup is 'data' std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)}; ^ /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 ^
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));
Calculate the llratio value for each event in the dataset
data->addColumn(llratio_func);
input_line_58:2:2: error: reference to 'data' is ambiguous data->addColumn(llratio_func); ^ input_line_51:5:29: note: candidate found by name lookup is 'data' std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)}; ^ /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 ^
Extract the subset of data with large signal likelihood
std::unique_ptr<RooAbsData> dataSel{data->reduce(Cut("llratio>0.7"))};
input_line_59:2:38: error: reference to 'data' is ambiguous std::unique_ptr<RooAbsData> dataSel{data->reduce(Cut("llratio>0.7"))}; ^ input_line_51:5:29: note: candidate found by name lookup is 'data' std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)}; ^ /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 ^
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);
input_line_62:2:3: error: use of undeclared identifier 'dataSel' (dataSel->plotOn(((*(RooPlot **)0x7fa06c003000)))) ^ Error in <HandleInterpreterException>: Error evaluating expression (dataSel->plotOn(((*(RooPlot **)0x7fa06c003000)))) Execution of your code was aborted.
Generate large number of events for MC integration of pdf projection
std::unique_ptr<RooDataSet> mcprojData{model.generate({x, y, z}, 10000)};
Calculate LL ratio for each generated event and select MC events with llratio)0.7
mcprojData->addColumn(llratio_func);
std::unique_ptr<RooAbsData> mcprojDataSel{mcprojData->reduce(Cut("llratio>0.7"))};
[#1] INFO:InputArguments -- The formula llratio>0.7 claims to use the variables (x,y,z,llratio) but only (llratio) seem to be in use. inputs: 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();
input_line_69:2:3: error: use of undeclared identifier 'frame' (frame->GetYaxis()->SetTitleOffset(1.3999999999999999)) ^ Error in <HandleInterpreterException>: Error evaluating expression (frame->GetYaxis()->SetTitleOffset(1.3999999999999999)) Execution of your code was aborted.
Draw all canvases
%jsroot on
gROOT->GetListOfCanvases()->Draw()