Rf 3 1 6_Llratioplot¶

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 Monday, January 17, 2022 at 10:01 AM.

In :
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooPolynomial.h"
#include "RooProdPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
In :
%%cpp -d
// This is a workaround to make sure the namespace is used inside functions
using namespace RooFit;

Create 3d pdf and data¶

Create observables

In :
RooRealVar x("x", "x", -5, 5);
RooRealVar y("y", "y", -5, 5);
RooRealVar z("z", "z", -5, 5);
RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University

Create signal pdf gauss(x)gauss(y)gauss(z)

In :
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)

In :
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

In :
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);

Project pdf and data on x¶

Make plain projection of data and pdf on x observable

In :
RooPlot *frame = x.frame(Title("Projection of 3D data and pdf on X"), Bins(40));
data->plotOn(frame);
model.plotOn(frame);
input_line_57:3:1: error: reference to 'data' is ambiguous
data->plotOn(frame);
^
input_line_56:5:13: note: candidate found by name lookup is '__cling_N524::data'
RooDataSet *data = model.generate(RooArgSet(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
^

Define projected signal likelihood ratio¶

Calculate projection of signal and total likelihood on (y,z) observables i.e. integrate signal and composite model over x

In :
RooAbsPdf *sigyz = sig.createProjection(x);
RooAbsPdf *totyz = model.createProjection(x);

Construct the log of the signal / signal+background probability

In :
RooFormulaVar llratio_func("llratio", "log10(@0)-log10(@1)", RooArgList(*sigyz, *totyz));

Plot data with a llratio cut¶

Calculate the llratio value for each event in the dataset

In :
input_line_63:2:2: error: reference to 'data' is ambiguous
^
input_line_56:5:13: note: candidate found by name lookup is '__cling_N524::data'
RooDataSet *data = model.generate(RooArgSet(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

In :
RooDataSet *dataSel = (RooDataSet *)data->reduce(Cut("llratio>0.7"));
input_line_64:2:38: error: reference to 'data' is ambiguous
RooDataSet *dataSel = (RooDataSet *)data->reduce(Cut("llratio>0.7"));
^
input_line_56:5:13: note: candidate found by name lookup is '__cling_N524::data'
RooDataSet *data = model.generate(RooArgSet(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

In :
RooPlot *frame2 = x.frame(Title("Same projection on X with LLratio(y,z)>0.7"), Bins(40));

Plot select data on frame

In :
dataSel->plotOn(frame2);
input_line_67:2:3: error: use of undeclared identifier 'dataSel'
(dataSel->plotOn(((*(class RooPlot **)0x7f3bdc06f670))))
^
Error in <HandleInterpreterException>: Error evaluating expression (dataSel->plotOn(((*(class RooPlot **)0x7f3bdc06f670))))
Execution of your code was aborted.

Make mc projection of pdf with same llratio cut¶

Generate large number of events for mc integration of pdf projection

In :
RooDataSet *mcprojData = model.generate(RooArgSet(x, y, z), 10000);

Calculate ll ratio for each generated event and select mc events with llratio)0.7

In :
RooDataSet *mcprojDataSel = (RooDataSet *)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

In :
model.plotOn(frame2, ProjWData(*mcprojDataSel));

TCanvas *c = new TCanvas("rf316_llratioplot", "rf316_llratioplot", 800, 400);
c->Divide(2);
c->cd(1);
frame->GetYaxis()->SetTitleOffset(1.4);
frame->Draw();
c->cd(2);