rs_bernsteinCorrection.C File Reference

Detailed Description

'Bernstein Correction' RooStats tutorial macro

This tutorial shows usage of a the BernsteinCorrection utility in RooStats. The idea is that one has a distribution coming either from data or Monte Carlo (called "reality" in the macro) and a nominal model that is not sufficiently flexible to take into account the real distribution. One wants to take into account the systematic associated with this imperfect modeling by augmenting the nominal model with some correction term (in this case a polynomial). The BernsteinCorrection utility will import into your workspace a corrected model given by nominal(x) * poly_N(x), where poly_N is an n-th order polynomial in the Bernstein basis. The degree N of the polynomial is chosen by specifying the tolerance one has in adding an extra term to the polynomial. The Bernstein basis is nice because it only has positive-definite terms and works well with PDFs. Finally, the macro makes a plot of:

• the data (drawn from 'reality'),
• the best fit of the nominal model (blue)
• and the best fit corrected model.

Processing /mnt/build/workspace/root-makedoc-v610/rootspi/rdoc/src/v6-10-00-patches/tutorials/roostats/rs_bernsteinCorrection.C...

#include "RooDataSet.h"
#include "RooRealVar.h"
#include "RooConstVar.h"
#include "RooBernstein.h"
#include "TCanvas.h"
#include "RooAbsPdf.h"
#include "RooFit.h"
#include "RooFitResult.h"
#include "RooPlot.h"
#include <string>
#include <vector>
#include <stdio.h>
#include <sstream>
#include <iostream>

#include "RooProdPdf.h"
#include "RooAddPdf.h"
#include "RooGaussian.h"
#include "RooNLLVar.h"
#include "RooMinuit.h"
#include "RooProfileLL.h"
#include "RooWorkspace.h"

#include "RooStats/BernsteinCorrection.h"

// use this order for safety on library loading
using namespace RooFit;
using namespace RooStats;


//____________________________________
void rs_bernsteinCorrection(){

   // set range of observable
   Double_t lowRange = -1, highRange =5;

   // make a RooRealVar for the observable
   RooRealVar x("x", "x", lowRange, highRange);

   // true model
   RooGaussian narrow("narrow","",x,RooConst(0.), RooConst(.8));
   RooGaussian wide("wide","",x,RooConst(0.), RooConst(2.));
   RooAddPdf reality("reality","",RooArgList(narrow, wide), RooConst(0.8));

   RooDataSet* data = reality.generate(x,1000);

   // nominal model
   RooRealVar sigma("sigma","",1.,0,10);
   RooGaussian nominal("nominal","",x,RooConst(0.), sigma);

   RooWorkspace* wks = new RooWorkspace("myWorksspace");

   wks->import(*data, Rename("data"));
   wks->import(nominal);

   // use Minuit2
   ROOT::Math::MinimizerOptions::SetDefaultMinimizer("Minuit2");

   // The tolerance sets the probability to add an unnecessary term.
   // lower tolerance will add fewer terms, while higher tolerance
   // will add more terms and provide a more flexible function.
   Double_t tolerance = 0.05;
   BernsteinCorrection bernsteinCorrection(tolerance);
   Int_t degree = bernsteinCorrection.ImportCorrectedPdf(wks,"nominal","x","data");

   if (degree < 0) {
      Error("rs_bernsteinCorrection","Bernstein correction failed ! ");
      return;
   }

   cout << " Correction based on Bernstein Poly of degree " << degree << endl;


   RooPlot* frame = x.frame();
   data->plotOn(frame);
   // plot the best fit nominal model in blue
   TString minimType =  ROOT::Math::MinimizerOptions::DefaultMinimizerType();
   nominal.fitTo(*data,PrintLevel(0),Minimizer(minimType));
   nominal.plotOn(frame);

   // plot the best fit corrected model in red
   RooAbsPdf* corrected = wks->pdf("corrected");
   if (!corrected) return;

   // fit corrected model
   corrected->fitTo(*data,PrintLevel(0),Minimizer(minimType) );
   corrected->plotOn(frame,LineColor(kRed));

   // plot the correction term (* norm constant) in dashed green
   // should make norm constant just be 1, not depend on binning of data
   RooAbsPdf* poly = wks->pdf("poly");
   if (poly)
   poly->plotOn(frame,LineColor(kGreen), LineStyle(kDashed));

   // this is a switch to check the sampling distribution
   // of -2 log LR for two comparisons:
   // the first is for n-1 vs. n degree polynomial corrections
   // the second is for n vs. n+1 degree polynomial corrections
   // Here we choose n to be the one chosen by the tolerance
   // criterion above, eg. n = "degree" in the code.
   // Setting this to true is takes about 10 min.
   bool checkSamplingDist = true;
   int numToyMC = 20;  // increase this value for sensible results

   TCanvas* c1 = new TCanvas();
   if(checkSamplingDist) {
      c1->Divide(1,2);
      c1->cd(1);
   }
   frame->Draw();
   gPad->Update();

   if(checkSamplingDist) {
      // check sampling dist
      ROOT::Math::MinimizerOptions::SetDefaultPrintLevel(-1);
      TH1F* samplingDist = new TH1F("samplingDist","",20,0,10);
      TH1F* samplingDistExtra = new TH1F("samplingDistExtra","",20,0,10);
      bernsteinCorrection.CreateQSamplingDist(wks,"nominal","x","data",samplingDist, samplingDistExtra, degree,numToyMC);

      c1->cd(2);
      samplingDistExtra->SetLineColor(kRed);
      samplingDistExtra->Draw();
      samplingDist->Draw("same");
   }
}

Author

Kyle Cranmer

Definition in file rs_bernsteinCorrection.C.