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algomez |
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#include <iostream>
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#include <cmath>
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#include <cassert>
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#include <sstream>
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#include <TGraph.h>
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#include <TFile.h>
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#include <TH1D.h>
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#include <TCanvas.h>
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#include <TF1.h>
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#include <TMath.h>
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#include <TROOT.h>
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#include "binneddata.hh"
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#include "fit.hh"
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#include "statistics.hh"
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////////////////////////////////////////////////////////////////////////////////
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// magic numbers
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////////////////////////////////////////////////////////////////////////////////
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// number of pseudoexperiments
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const int NPES=0;
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// number of samples of nuisance parameters for Bayesian MC integration
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const int NSAMPLES=2E5;
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// alpha (1-alpha=confidence interval)
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const double ALPHA=0.05;
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// left side tail
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const double LEFTSIDETAIL=0.0;
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// output file name
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const char* OUTPUTFILE="stats.root";
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// input file name
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const char* INPUTFILE="dijet_mass_HT_fat_1p010fbm1.txt";
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// histogram binning
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const int NBINS=34;
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double BOUNDARIES[NBINS] = { 838,
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890, 944, 1000, 1058, 1118, 1181, 1246, 1313, 1383,
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1455, 1530, 1607, 1687, 1770, 1856, 1945, 2037, 2132,
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2231, 2332, 2438, 2546, 2659, 2775, 2895, 3019, 3147,
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3275, 3403, 3531, 3659, 3787, 3915 };
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// parameters
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double SIGMASS=0;
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const int NPARS=8;
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const int POIINDEX=0; // which parameter is "of interest"
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const char* PAR_NAMES[8] = { "xs", "lumi", "jes", "jer", "bkg norm", "p1", "p2", "p3" };
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const double PAR_GUESSES[8] = { 0.1, 1010., 1.0, 1.0, 5.6E-2, 7.4, 6.3, 0.2 };
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const double PAR_MIN[8] = { 0.0, 0.0, 0.0, 0.0, 0., 0.0, 0.0, 0.0 };
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const double PAR_MAX[8] = { 1.E6, 5000., 2.0, 2.0, 10.0, 100.0, 100.0, 10.0 };
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const double PAR_ERR[8] = { 0.01, 40.4, 0.04, 0.10, 1.E-3, 1.0, 1.0, 0.1 };
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const int PAR_TYPE[8] = { 1, 1, 1, 1, 0, 0, 0, 0 }; // 1 = signal, 0 = background
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const int PAR_NUIS[8] = { 0, 0, 0, 0, 0, 0, 0, 0 }; // 1 = nuisance parameter, 0 = not varied (the POI is not a nuisance parameter)
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TH1D* HIST=0; // signal histogram
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TH1D* HISTCDF=0; // signal CDF
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////////////////////////////////////////////////////////////////////////////////
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// function definition (not really used; only the integral is used)
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////////////////////////////////////////////////////////////////////////////////
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double FCN(double *x, double *par)
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{
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double invmass=x[0];
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double xs=par[0];
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double lumi=par[1];
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double jes=par[2];
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double jer=par[3];
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double norm=par[4];
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double p1=par[5];
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double p2=par[6];
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double p3=par[7];
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double bkg = norm*pow(1.0-invmass/7000.0,p1)/pow(invmass/7000.0,p2+p3*log(invmass/7000.0));
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double mass=jes*(jer*(invmass-SIGMASS)+SIGMASS);
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int bin=HIST->GetXaxis()->FindBin(mass);
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double sig = xs*lumi*HIST->GetBinContent(bin);
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return bkg+sig;
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}
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////////////////////////////////////////////////////////////////////////////////
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// function integral
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////////////////////////////////////////////////////////////////////////////////
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double INTEGRAL(double *x0, double *xf, double *par)
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{
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double xs=par[0];
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double lumi=par[1];
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double jes=par[2];
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double jer=par[3];
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double norm=par[4];
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double p1=par[5];
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double p2=par[6];
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double p3=par[7];
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// uses Simpson's 3/8th rule to compute the background integral over a short interval
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// also use a power series expansion to determine the intermediate intervals since the pow() call is expensive
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double dx=(xf[0]-x0[0])/3./7000.;
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double x=x0[0]/7000.0;
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double logx=log(x);
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double a=pow(1-x,p1)/pow(x,p2+p3*logx);
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double b=dx*a/x/(x-1)*(p2+p1*x-p2*x-2*p3*(x-1)*logx);
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double c=0.5*dx*dx*a*( (p1-1)*p1/(x-1)/(x-1) - 2*p1*(p2+2*p3*logx)/(x-1)/x + (p2+p2*p2-2*p3+2*p3*logx*(1+2*p2+2*p3*logx))/x/x );
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double d=0.166666667*dx*dx*dx*a*( (p1-2)*(p1-1)*p1/(x-1)/(x-1)/(x-1) - 3*(p1-1)*p1*(p2+2*p3*logx)/(x-1)/(x-1)/x - (1+p2+2*p3*logx)*(p2*(2+p2) - 6*p3 + 4*p3*logx*(1+p2*p3*logx))/x/x/x + 3*p1*(p2+p2*p2-2*p3+2*p3*logx*(1+2*p2+2*p3*logx))/(x-1)/x/x );
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double bkg=(xf[0]-x0[0])*norm*(a+0.375*(b+c+d)+0.375*(2*b+4*c+8*d)+0.125*(3*b+9*c+27*d));
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if(xs==0.0) return bkg;
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double xprimef=jes*(jer*(xf[0]-SIGMASS)+SIGMASS);
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double xprime0=jes*(jer*(x0[0]-SIGMASS)+SIGMASS);
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int bin1=HISTCDF->GetXaxis()->FindBin(xprimef);
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int bin2=HISTCDF->GetXaxis()->FindBin(xprime0);
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if(bin1<1) bin1=1;
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if(bin1>HISTCDF->GetNbinsX()) bin1=HISTCDF->GetNbinsX();
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if(bin2<1) bin1=1;
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if(bin2>HISTCDF->GetNbinsX()) bin2=HISTCDF->GetNbinsX();
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double sig=xs*lumi*(HISTCDF->GetBinContent(bin1)-HISTCDF->GetBinContent(bin2));
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return bkg+sig;
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}
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////////////////////////////////////////////////////////////////////////////////
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// main function
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////////////////////////////////////////////////////////////////////////////////
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int main(int argc, char* argv[])
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{
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if(argc<=1) {
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std::cout << "Usage: stats signalmass" << std::endl;
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return 0;
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}
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// setup the signal histogram
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TFile* histfile=new TFile("Test_Resonance_Shapes.root");
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histfile->cd();
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SIGMASS = std::atof(argv[1]);
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int masspoint = static_cast<int>(SIGMASS);
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std::ostringstream histname, cdfname;
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histname << "h_qstar_" << masspoint;
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cdfname << "h_qstar_" << masspoint << "_cdf";
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HIST=dynamic_cast<TH1D*>(gROOT->FindObject(histname.str().c_str()));
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HISTCDF=dynamic_cast<TH1D*>(gROOT->FindObject(cdfname.str().c_str()));
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assert(HIST && HISTCDF && SIGMASS>0);
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HIST->Scale(5.); // proper normalization
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// create the output file
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TFile* rootfile=new TFile(OUTPUTFILE, "RECREATE"); rootfile->cd();
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// get the data
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TH1D* data=getData(INPUTFILE, "data_0", NBINS-1, BOUNDARIES);
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// setup an initial fitter to perform a background-only fit
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Fitter initfit(data, INTEGRAL);
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for(int i=0; i<NPARS; i++) initfit.defineParameter(i, PAR_NAMES[i], PAR_GUESSES[i], PAR_ERR[i], PAR_MIN[i], PAR_MAX[i], PAR_NUIS[i]);
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// do an initial background-only fit, first
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for(int i=0; i<NPARS; i++) if(PAR_TYPE[i]==1) initfit.fixParameter(i);
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initfit.setParameter(POIINDEX, 0.0); // set the POI value to 0
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initfit.doFit();
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initfit.calcPull("pull_bkg_init")->Write();
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initfit.calcDiff("diff_bkg_init")->Write();
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initfit.write("fit_bkg_init");
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// setup the limit values
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double observedLowerBound, observedUpperBound;
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std::vector<double> expectedLowerBounds;
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std::vector<double> expectedUpperBounds;
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// perform the PEs (0 = data)
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for(int pe=0; pe<=NPES; ++pe) {
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std::cout << "*********** pe=" << pe << " ***********" << std::endl;
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std::ostringstream pestr;
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pestr << "_" << pe;
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// setup the fitter with the input from the background-only fit
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TH1D* hist = (pe==0) ? data : initfit.makePseudoData((std::string("data")+pestr.str()).c_str());
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Fitter fit(hist, INTEGRAL);
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fit.setPOIIndex(POIINDEX);
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fit.setPrintLevel(0);
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for(int i=0; i<NPARS; i++) fit.defineParameter(i, PAR_NAMES[i], initfit.getParameter(i), PAR_ERR[i], PAR_MIN[i], PAR_MAX[i], PAR_NUIS[i]);
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// perform a background-only fit
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for(int i=0; i<NPARS; i++) if(PAR_TYPE[i]==1) fit.fixParameter(i);
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fit.setParameter(POIINDEX, 0.0); // set the POI value to 0
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fit.doFit();
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fit.calcPull((std::string("pull_bkg")+pestr.str()).c_str())->Write();
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fit.calcDiff((std::string("diff_bkg")+pestr.str()).c_str())->Write();
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fit.write((std::string("fit_bkg")+pestr.str()).c_str());
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// fix the ranges for the background parameters before calculating the posterior
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for(int i=0; i<NPARS; i++) {
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if(PAR_TYPE[i]==0 && PAR_NUIS[i]==1) {
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double val, err;
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fit.getParameter(i, val, err);
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fit.setParLimits(i, val-err, val+err);
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}
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}
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observedLowerBound=0.;
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observedUpperBound=fit.calculateUpperBoundWithCLs(NSAMPLES, ALPHA);
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// put the ranges back in place
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for(int i=0; i<NPARS; i++) {
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if(PAR_TYPE[i]==0 && PAR_NUIS[i]==1) {
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fit.setParLimits(i, PAR_MIN[i], PAR_MAX[i]);
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}
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}
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// evaluate the limit
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/* std::pair<double, double> bounds=evaluateInterval(post, ALPHA, LEFTSIDETAIL);
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if(pe==0) {
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observedLowerBound=bounds.first;
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observedUpperBound=bounds.second;
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} else {
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expectedLowerBounds.push_back(bounds.first);
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expectedUpperBounds.push_back(bounds.second);
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}*/
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}
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////////////////////////////////////////////////////////////////////////////////
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// print the results
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////////////////////////////////////////////////////////////////////////////////
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std::cout << "**********************************************************************" << std::endl;
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for(unsigned int i=0; i<expectedLowerBounds.size(); i++)
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std::cout << "expected bound(" << (i+1) << ") = [ " << expectedLowerBounds[i] << " , " << expectedUpperBounds[i] << " ]" << std::endl;
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std::cout << "\nobserved bound = [ " << observedLowerBound << " , " << observedUpperBound << " ]" << std::endl;
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if(LEFTSIDETAIL>0.0 && NPES>0) {
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std::cout << "\n***** expected lower bounds *****" << std::endl;
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double median;
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std::pair<double, double> onesigma;
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std::pair<double, double> twosigma;
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getQuantiles(expectedLowerBounds, median, onesigma, twosigma);
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std::cout << "median: " << median << std::endl;
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std::cout << "+/-1 sigma band: [ " << onesigma.first << " , " << onesigma.second << " ] " << std::endl;
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std::cout << "+/-2 sigma band: [ " << twosigma.first << " , " << twosigma.second << " ] " << std::endl;
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}
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if(LEFTSIDETAIL<1.0 && NPES>0) {
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std::cout << "\n***** expected upper bounds *****" << std::endl;
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double median;
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std::pair<double, double> onesigma;
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std::pair<double, double> twosigma;
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getQuantiles(expectedUpperBounds, median, onesigma, twosigma);
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std::cout << "median: " << median << std::endl;
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std::cout << "+/-1 sigma band: [ " << onesigma.first << " , " << onesigma.second << " ] " << std::endl;
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std::cout << "+/-2 sigma band: [ " << twosigma.first << " , " << twosigma.second << " ] " << std::endl;
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}
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// close the output file
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rootfile->Close();
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return 0;
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}
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