/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///
/// Validation and MC studies:
/// RooMCStudy - using separate fit and generator models, using the chi^2 calculator model
/// Running a biased fit model against an optimal fit.
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \date 07/2008
/// \author Wouter Verkerke

#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "RooMCStudy.h"
#include "RooChi2MCSModule.h"
#include "RooPlot.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
#include "TDirectory.h"
#include "TLegend.h"

using namespace RooFit;

void rf802_mcstudy_addons()
{

   // C r e a t e   m o d e l
   // -----------------------

   // Observables, parameters
   RooRealVar x("x", "x", -10, 10);
   x.setBins(10);
   RooRealVar mean("mean", "mean of gaussian", 0, -2., 1.8);
   RooRealVar sigma("sigma", "width of gaussian", 5, 1, 10);

   // Create Gaussian pdf
   RooGaussian gauss("gauss", "gaussian PDF", x, mean, sigma);

   // C r e a t e   m a n a g e r  w i t h   c h i ^ 2   a d d - o n   m o d u l e
   // ----------------------------------------------------------------------------

   // Create study manager for binned likelihood fits of a Gaussian pdf in 10 bins
   RooMCStudy *mcs = new RooMCStudy(gauss, x, Silence(), Binned());

   // Add chi^2 calculator module to mcs
   RooChi2MCSModule chi2mod;
   mcs->addModule(chi2mod);

   // Generate 1000 samples of 1000 events
   mcs->generateAndFit(2000, 1000);

   // Fill histograms with distributions chi2 and prob(chi2,ndf) that
   // are calculated by RooChiMCSModule
   TH1 *hist_chi2 = mcs->fitParDataSet().createHistogram("chi2");
   hist_chi2->SetTitle("#chi^{2} values of all toy runs;#chi^{2}");
   TH1 *hist_prob = mcs->fitParDataSet().createHistogram("prob");
   hist_prob->SetTitle("Corresponding #chi^{2} probability;Prob(#chi^{2},ndof)");


   // C r e a t e   m a n a g e r  w i t h   s e p a r a t e   f i t   m o d e l
   // ----------------------------------------------------------------------------

   // Create alternate pdf with shifted mean
   RooRealVar mean2("mean2", "mean of gaussian 2", 2.);
   RooGaussian gauss2("gauss2", "gaussian PDF2", x, mean2, sigma);

   // Create study manager with separate generation and fit model. This configuration
   // is set up to generate biased fits as the fit and generator model have different means,
   // and the mean parameter is limited to [-2., 1.8], so it just misses the optimal
   // mean value of 2 in the data.
   RooMCStudy *mcs2 = new RooMCStudy(gauss2, x, FitModel(gauss), Silence(), Binned());

   // Add chi^2 calculator module to mcs
   RooChi2MCSModule chi2mod2;
   mcs2->addModule(chi2mod2);

   // Generate 1000 samples of 1000 events
   mcs2->generateAndFit(2000, 1000);

   // Request a the pull plot of mean. The pulls will be one-sided because
   // `mean` is limited to 1.8.
   // Note that RooFit will have trouble to compute the pulls because the parameters
   // are called `mean` in the fit, but `mean2` in the generator model. It is not obvious
   // that these are related. RooFit will nevertheless compute pulls, but complain that
   // this is risky.
   auto pullMeanFrame = mcs2->plotPull(mean);

   // Fill histograms with distributions chi2 and prob(chi2,ndf) that
   // are calculated by RooChiMCSModule
   TH1 *hist2_chi2 = mcs2->fitParDataSet().createHistogram("chi2");
   TH1 *hist2_prob = mcs2->fitParDataSet().createHistogram("prob");
   hist2_chi2->SetLineColor(kRed);
   hist2_prob->SetLineColor(kRed);

   TLegend leg;
   leg.AddEntry(hist_chi2, "Optimal fit", "L");
   leg.AddEntry(hist2_chi2, "Biased fit", "L");
   leg.SetBorderSize(0);
   leg.SetFillStyle(0);

   TCanvas *c = new TCanvas("rf802_mcstudy_addons", "rf802_mcstudy_addons", 800, 400);
   c->Divide(3);
   c->cd(1);
   gPad->SetLeftMargin(0.15);
   hist_chi2->GetYaxis()->SetTitleOffset(1.4);
   hist_chi2->Draw();
   hist2_chi2->Draw("esame");
   leg.DrawClone();
   c->cd(2);
   gPad->SetLeftMargin(0.15);
   hist_prob->GetYaxis()->SetTitleOffset(1.4);
   hist_prob->Draw();
   hist2_prob->Draw("esame");
   c->cd(3);
   pullMeanFrame->Draw();


   // Make RooMCStudy object available on command line after
   // macro finishes
   gDirectory->Add(mcs);
}