rf707_kernelestimation.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook
/// Speecial p.d.f.'s: using non-parametric (multi-dimensional) kernel estimation p.d.f.s
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke

#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooPolynomial.h"
#include "RooKeysPdf.h"
#include "RooNDKeysPdf.h"
#include "RooProdPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
#include "RooPlot.h"
using namespace RooFit;

void rf707_kernelestimation()
{
   // C r e a t e   l o w   s t a t s   1 - D   d a t a s e t
   // -------------------------------------------------------

   // Create a toy pdf for sampling
   RooRealVar x("x", "x", 0, 20);
   RooPolynomial p("p", "p", x, RooArgList(RooConst(0.01), RooConst(-0.01), RooConst(0.0004)));

   // Sample 500 events from p
   RooDataSet *data1 = p.generate(x, 200);

   // C r e a t e   1 - D   k e r n e l   e s t i m a t i o n   p d f
   // ---------------------------------------------------------------

   // Create adaptive kernel estimation pdf. In this configuration the input data
   // is mirrored over the boundaries to minimize edge effects in distribution
   // that do not fall to zero towards the edges
   RooKeysPdf kest1("kest1", "kest1", x, *data1, RooKeysPdf::MirrorBoth);

   // An adaptive kernel estimation pdf on the same data without mirroring option
   // for comparison
   RooKeysPdf kest2("kest2", "kest2", x, *data1, RooKeysPdf::NoMirror);

   // Adaptive kernel estimation pdf with increased bandwidth scale factor
   // (promotes smoothness over detail preservation)
   RooKeysPdf kest3("kest1", "kest1", x, *data1, RooKeysPdf::MirrorBoth, 2);

   // Plot kernel estimation pdfs with and without mirroring over data
   RooPlot *frame = x.frame(Title("Adaptive kernel estimation pdf with and w/o mirroring"), Bins(20));
   data1->plotOn(frame);
   kest1.plotOn(frame);
   kest2.plotOn(frame, LineStyle(kDashed), LineColor(kRed));

   // Plot kernel estimation pdfs with regular and increased bandwidth
   RooPlot *frame2 = x.frame(Title("Adaptive kernel estimation pdf with regular, increased bandwidth"));
   kest1.plotOn(frame2);
   kest3.plotOn(frame2, LineColor(kMagenta));

   // C r e a t e   l o w   s t a t s   2 - D   d a t a s e t
   // -------------------------------------------------------

   // Construct a 2D toy pdf for sampling
   RooRealVar y("y", "y", 0, 20);
   RooPolynomial py("py", "py", y, RooArgList(RooConst(0.01), RooConst(0.01), RooConst(-0.0004)));
   RooProdPdf pxy("pxy", "pxy", RooArgSet(p, py));
   RooDataSet *data2 = pxy.generate(RooArgSet(x, y), 1000);

   // C r e a t e   2 - D   k e r n e l   e s t i m a t i o n   p d f
   // ---------------------------------------------------------------

   // Create 2D adaptive kernel estimation pdf with mirroring
   RooNDKeysPdf kest4("kest4", "kest4", RooArgSet(x, y), *data2, "am");

   // Create 2D adaptive kernel estimation pdf with mirroring and double bandwidth
   RooNDKeysPdf kest5("kest5", "kest5", RooArgSet(x, y), *data2, "am", 2);

   // Create a histogram of the data
   TH1 *hh_data = data2->createHistogram("hh_data", x, Binning(10), YVar(y, Binning(10)));

   // Create histogram of the 2d kernel estimation pdfs
   TH1 *hh_pdf = kest4.createHistogram("hh_pdf", x, Binning(25), YVar(y, Binning(25)));
   TH1 *hh_pdf2 = kest5.createHistogram("hh_pdf2", x, Binning(25), YVar(y, Binning(25)));
   hh_pdf->SetLineColor(kBlue);
   hh_pdf2->SetLineColor(kMagenta);

   TCanvas *c = new TCanvas("rf707_kernelestimation", "rf707_kernelestimation", 800, 800);
   c->Divide(2, 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(1.8);
   frame2->Draw();
   c->cd(3);
   gPad->SetLeftMargin(0.15);
   hh_data->GetZaxis()->SetTitleOffset(1.4);
   hh_data->Draw("lego");
   c->cd(4);
   gPad->SetLeftMargin(0.20);
   hh_pdf->GetZaxis()->SetTitleOffset(2.4);
   hh_pdf->Draw("surf");
   hh_pdf2->Draw("surfsame");
}