MCMCIntervalPlot.cxx

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// @(#)root/roostats:$Id$
// Authors: Kevin Belasco        17/06/2009
// Authors: Kyle Cranmer         17/06/2009
/*************************************************************************
 * Project: RooStats                                                     *
 * Package: RooFit/RooStats                                              *
 *************************************************************************
 * Copyright (C) 1995-2008, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
/** \class RooStats::MCMCIntervalPlot
    \ingroup Roostats
 
This class provides simple and straightforward utilities to plot a MCMCInterval
object.  Basic use only requires a few lines once you have an MCMCInterval*:
 
~~~ {.cpp}
      MCMCIntervalPlot plot(*interval);
      plot.Draw();
~~~
 
The standard Draw() function will currently draw the confidence interval
range with bars if 1-D and a contour if 2-D.  The MCMC posterior will also be
plotted for the 1-D case.
 
*/
 
#include "RooStats/MCMCIntervalPlot.h"
#include "RooStats/MCMCInterval.h"
#include "RooStats/MarkovChain.h"
 
#include "TLine.h"
#include "TGraph.h"
#include "RooRealVar.h"
#include "RooPlot.h"
#include "TH2.h"
#include "TH1F.h"
#include "RooArgList.h"
#include "TAxis.h"
#include "RooGlobalFunc.h"
 
#include <iostream>
 
// Extra draw commands
//static const char* POSTERIOR_HIST = "posterior_hist";
//static const char* POSTERIOR_KEYS_PDF = "posterior_keys_pdf";
//static const char* POSTERIOR_KEYS_PRODUCT = "posterior_keys_product";
//static const char* HIST_INTERVAL = "hist_interval";
//static const char* KEYS_PDF_INTERVAL = "keys_pdf_interval";
//static const char* TAIL_FRACTION_INTERVAL = "tail_fraction_interval";
//static const char* OPTION_SEP = ":";
 
ClassImp(RooStats::MCMCIntervalPlot);
 
using std::endl;
using namespace RooStats;
 
////////////////////////////////////////////////////////////////////////////////
 
MCMCIntervalPlot::MCMCIntervalPlot() {}
 
////////////////////////////////////////////////////////////////////////////////
 
MCMCIntervalPlot::MCMCIntervalPlot(MCMCInterval &interval)
{
   SetMCMCInterval(interval);
}
 
////////////////////////////////////////////////////////////////////////////////
 
MCMCIntervalPlot::~MCMCIntervalPlot()
{
   delete fParameters;
   // kbelasco: why does deleting fPosteriorHist remove the graphics
   // but deleting TGraphs doesn't?
   //delete fPosteriorHist;
   // can we delete fNLLHist and fWeightHist?
   //delete fNLLHist;
   //delete fWeightHist;
 
   // kbelasco: should we delete fPosteriorKeysPdf and fPosteriorKeysProduct?
   delete fPosteriorKeysPdf;
   delete fPosteriorKeysProduct;
 
   delete fWalk;
   delete fBurnIn;
   delete fFirst;
   delete fParamGraph;
   delete fNLLGraph;
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::SetMCMCInterval(MCMCInterval& interval)
{
   fInterval = &interval;
   fDimension = fInterval->GetDimension();
   fParameters = fInterval->GetParameters();
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::Draw(const Option_t* options)
{
   DrawInterval(options);
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawPosterior(const Option_t* options)
{
   if (fInterval->GetUseKeys()) {
      DrawPosteriorKeysPdf(options);
   } else {
      DrawPosteriorHist(options);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
 
void* MCMCIntervalPlot::DrawPosteriorHist(const Option_t* /*options*/,
      const char* title, bool scale)
{
   if (fPosteriorHist == nullptr)
      fPosteriorHist = fInterval->GetPosteriorHist();
 
   if (fPosteriorHist == nullptr) {
      coutE(InputArguments) << "MCMCIntervalPlot::DrawPosteriorHist: "
         << "Couldn't get posterior histogram." << endl;
      return nullptr;
   }
 
   // kbelasco: annoying hack because histogram drawing fails when it sees
   // an un-recognized option like POSTERIOR_HIST, etc.
   //const Option_t* myOpt = nullptr;
 
   //TString tmpOpt(options);
   //if (tmpOpt.Contains("same"))
   //   myOpt = "same";
 
   // scale so highest bin has height 1
   if (scale) {
      fPosteriorHist->Scale(1 / fPosteriorHist->GetBinContent(fPosteriorHist->GetMaximumBin()));
   }
 
   TString ourTitle(GetTitle());
   if (ourTitle.CompareTo("") == 0) {
      if (title)
         fPosteriorHist->SetTitle(title);
   } else
      fPosteriorHist->SetTitle(GetTitle());
 
   //fPosteriorHist->Draw(myOpt);
 
   return (void*)fPosteriorHist;
}
 
////////////////////////////////////////////////////////////////////////////////
 
void* MCMCIntervalPlot::DrawPosteriorKeysPdf(const Option_t* options)
{
   if (fPosteriorKeysPdf == nullptr)
      fPosteriorKeysPdf = fInterval->GetPosteriorKeysPdf();
 
   if (fPosteriorKeysPdf == nullptr) {
      coutE(InputArguments) << "MCMCIntervalPlot::DrawPosteriorKeysPdf: "
         << "Couldn't get posterior Keys PDF." << endl;
      return nullptr;
   }
 
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   if (fDimension == 1) {
      RooRealVar* v = static_cast<RooRealVar*>(fParameters->first());
      RooPlot* frame = v->frame();
      if (frame == nullptr) {
         coutE(InputArguments) << "MCMCIntervalPlot::DrawPosteriorKeysPdf: "
                               << "Invalid parameter" << endl;
         return nullptr;
      }
      if (isEmpty) {
         frame->SetTitle(("Posterior Keys PDF for " + std::string(v->GetName())).c_str());
      } else {
         frame->SetTitle(GetTitle());
      }
      //fPosteriorKeysPdf->plotOn(frame);
      //fPosteriorKeysPdf->plotOn(frame,
      //      RooFit::Normalization(1, RooAbsReal::Raw));
      //frame->Draw(options);
      return (void*)frame;
   } else if (fDimension == 2) {
      RooArgList* axes = fInterval->GetAxes();
      RooRealVar* xVar = static_cast<RooRealVar*>(axes->at(0));
      RooRealVar* yVar = static_cast<RooRealVar*>(axes->at(1));
      TH2F* keysHist = static_cast<TH2F*>(fPosteriorKeysPdf->createHistogram(
            "keysPlot2D", *xVar, RooFit::YVar(*yVar), RooFit::Scaling(false)));
      if (isEmpty) {
         keysHist->SetTitle(
               Form("MCMC histogram of posterior Keys PDF for %s, %s",
                  axes->at(0)->GetName(), axes->at(1)->GetName()));
      } else {
         keysHist->SetTitle(GetTitle());
      }
 
      keysHist->Draw(options);
      delete axes;
      return nullptr;
   }
   return nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawInterval(const Option_t* options)
{
   switch (fInterval->GetIntervalType()) {
      case MCMCInterval::kShortest:
         DrawShortestInterval(options);
         break;
      case MCMCInterval::kTailFraction:
         DrawTailFractionInterval(options);
         break;
      default:
         coutE(InputArguments) << "MCMCIntervalPlot::DrawInterval(): " <<
            "Interval type not supported" << endl;
         break;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawShortestInterval(const Option_t* options)
{
   if (fInterval->GetUseKeys()) {
         DrawKeysPdfInterval(options);
   } else {
         DrawHistInterval(options);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawKeysPdfInterval(const Option_t* options)
{
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   if (fDimension == 1) {
      // Draw the posterior keys PDF as well so the user can see where the
      // limit bars line up
      // fDimension == 1, so we know we will receive a RooPlot
      RooPlot* frame = reinterpret_cast<RooPlot*>(DrawPosteriorKeysPdf(options));
 
      //double height = 1;
      //double height = 2.0 * fInterval->GetKeysPdfCutoff();
      double height = fInterval->GetKeysMax();
 
      RooRealVar* p = static_cast<RooRealVar*>(fParameters->first());
      double ul = fInterval->UpperLimitByKeys(*p);
      double ll = fInterval->LowerLimitByKeys(*p);
 
      if (frame != nullptr && fPosteriorKeysPdf != nullptr) {
         // draw shading in interval
         if (isEmpty) {
            frame->SetTitle(nullptr);
         } else {
            frame->SetTitle(GetTitle());
         }
         frame->GetYaxis()->SetTitle(("Posterior for parameter " + std::string(p->GetName())).c_str());
         fPosteriorKeysPdf->plotOn(frame,
               RooFit::Normalization(1, RooAbsReal::Raw),
               RooFit::Range(ll, ul, false),
               RooFit::VLines(),
               RooFit::DrawOption("F"),
               RooFit::MoveToBack(),
               RooFit::FillColor(fShadeColor));
 
         // hack - this is drawn twice now:
         // once by DrawPosteriorKeysPdf (which also configures things and sets
         // the title), and once again here so the shading shows up behind.
         fPosteriorKeysPdf->plotOn(frame,
               RooFit::Normalization(1, RooAbsReal::Raw));
      }
      if (frame) {
   frame->Draw(options);
      }
 
      TLine* llLine = new TLine(ll, 0, ll, height);
      TLine* ulLine = new TLine(ul, 0, ul, height);
      llLine->SetLineColor(fLineColor);
      ulLine->SetLineColor(fLineColor);
      llLine->SetLineWidth(fLineWidth);
      ulLine->SetLineWidth(fLineWidth);
      llLine->Draw(options);
      ulLine->Draw(options);
   } else if (fDimension == 2) {
      if (fPosteriorKeysPdf == nullptr)
         fPosteriorKeysPdf = fInterval->GetPosteriorKeysPdf();
 
      if (fPosteriorKeysPdf == nullptr) {
         coutE(InputArguments) << "MCMCIntervalPlot::DrawKeysPdfInterval: "
            << "Couldn't get posterior Keys PDF." << endl;
         return;
      }
 
      RooArgList* axes = fInterval->GetAxes();
      RooRealVar* xVar = static_cast<RooRealVar*>(axes->at(0));
      RooRealVar* yVar = static_cast<RooRealVar*>(axes->at(1));
      TH2F* contHist = static_cast<TH2F*>(fPosteriorKeysPdf->createHistogram(
          "keysContour2D", *xVar, RooFit::YVar(*yVar), RooFit::Scaling(false)));
      //if (isEmpty)
      //   contHist->SetTitle(Form("MCMC Keys conf. interval for %s, %s",
      //            axes->at(0)->GetName(), axes->at(1)->GetName()));
      //else
      //   contHist->SetTitle(GetTitle());
      if (!isEmpty) {
         contHist->SetTitle(GetTitle());
      } else {
         contHist->SetTitle(nullptr);
      }
 
      contHist->SetStats(false);
 
      TString tmpOpt(options);
      if (!tmpOpt.Contains("CONT2")) tmpOpt.Append("CONT2");
 
      double cutoff = fInterval->GetKeysPdfCutoff();
      contHist->SetContour(1, &cutoff);
      contHist->SetLineColor(fLineColor);
      contHist->SetLineWidth(fLineWidth);
      contHist->Draw(tmpOpt.Data());
      delete axes;
   } else {
      coutE(InputArguments) << "MCMCIntervalPlot::DrawKeysPdfInterval: "
         << " Sorry: " << fDimension << "-D plots not currently supported" << endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawHistInterval(const Option_t* options)
{
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   if (fDimension == 1) {
      // draw lower and upper limits
      RooRealVar* p = static_cast<RooRealVar*>(fParameters->first());
      double ul = fInterval->UpperLimitByHist(*p);
      double ll = fInterval->LowerLimitByHist(*p);
 
      // Draw the posterior histogram as well so the user can see where the
      // limit bars line up
      // fDimension == 1, so we know will get a TH1F*
      TH1F* hist = reinterpret_cast<TH1F*>(DrawPosteriorHist(options, nullptr, false));
      if (hist == nullptr) return;
      if (isEmpty) {
         hist->SetTitle(nullptr);
      } else {
         hist->SetTitle(GetTitle());
      }
      hist->GetYaxis()->SetTitle(("Posterior for parameter " + std::string(p->GetName())).c_str());
      hist->SetStats(false);
      TH1F* copy = static_cast<TH1F*>(hist->Clone((std::string(hist->GetTitle()) + "_copy").c_str()));
      double histCutoff = fInterval->GetHistCutoff();
 
      Int_t i;
      Int_t nBins = copy->GetNbinsX();
      double height;
      for (i = 1; i <= nBins; i++) {
         // remove bins with height < cutoff
         height = copy->GetBinContent(i);
         if (height < histCutoff) {
            copy->SetBinContent(i, 0);
            copy->SetBinError(i, 0);
         }
      }
 
      hist->Scale(1/hist->GetBinContent(hist->GetMaximumBin()));
      copy->Scale(1/copy->GetBinContent(hist->GetMaximumBin()));
 
      copy->SetFillStyle(1001);
      copy->SetFillColor(fShadeColor);
      hist->Draw(options);
      // to show the interval area
      copy->Draw("HIST SAME");
 
      fPosteriorHistHistCopy = copy;
 
      TLine* llLine = new TLine(ll, 0, ll, 1);
      TLine* ulLine = new TLine(ul, 0, ul, 1);
      llLine->SetLineColor(fLineColor);
      ulLine->SetLineColor(fLineColor);
      llLine->SetLineWidth(fLineWidth);
      ulLine->SetLineWidth(fLineWidth);
      llLine->Draw(options);
      ulLine->Draw(options);
 
   } else if (fDimension == 2) {
      if (fPosteriorHist == nullptr)
         fPosteriorHist = fInterval->GetPosteriorHist();
 
      if (fPosteriorHist == nullptr) {
         coutE(InputArguments) << "MCMCIntervalPlot::DrawHistInterval: "
            << "Couldn't get posterior histogram." << endl;
         return;
      }
 
      RooArgList* axes = fInterval->GetAxes();
      //if (isEmpty)
      //   fPosteriorHist->SetTitle(
      //         Form("MCMC histogram conf. interval for %s, %s",
      //            axes->at(0)->GetName(), axes->at(1)->GetName()));
      //else
      //   fPosteriorHist->SetTitle(GetTitle());
      if (!isEmpty) {
         fPosteriorHist->SetTitle(GetTitle());
      } else {
         fPosteriorHist->SetTitle(nullptr);
      }
      delete axes;
 
      fPosteriorHist->SetStats(false);
 
      TString tmpOpt(options);
      if (!tmpOpt.Contains("CONT2")) tmpOpt.Append("CONT2");
 
      double cutoff = fInterval->GetHistCutoff();
      fPosteriorHist->SetContour(1, &cutoff);
      fPosteriorHist->SetLineColor(fLineColor);
      fPosteriorHist->SetLineWidth(fLineWidth);
      fPosteriorHist->Draw(tmpOpt.Data());
   } else {
      coutE(InputArguments) << "MCMCIntervalPlot::DrawHistInterval: "
         << " Sorry: " << fDimension << "-D plots not currently supported" << endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawTailFractionInterval(const Option_t* options)
{
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   if (fDimension == 1) {
      // Draw the posterior histogram as well so the user can see where the
      // limit bars line up
      RooRealVar* p = static_cast<RooRealVar*>(fParameters->first());
      double ul = fInterval->UpperLimitTailFraction(*p);
      double ll = fInterval->LowerLimitTailFraction(*p);
 
      TH1F* hist = reinterpret_cast<TH1F*>(DrawPosteriorHist(options, nullptr, false));
      if (hist == nullptr) return;
      if (isEmpty) {
         hist->SetTitle(nullptr);
      } else {
         hist->SetTitle(GetTitle());
      }
      hist->GetYaxis()->SetTitle(Form("Posterior for parameter %s",
               p->GetName()));
      hist->SetStats(false);
      TH1F* copy = static_cast<TH1F*>(hist->Clone(Form("%s_copy", hist->GetTitle())));
 
      Int_t i;
      Int_t nBins = copy->GetNbinsX();
      double center;
      for (i = 1; i <= nBins; i++) {
         // remove bins outside interval
         center = copy->GetBinCenter(i);
         if (center < ll || center > ul) {
            copy->SetBinContent(i, 0);
            copy->SetBinError(i, 0);
         }
      }
 
      hist->Scale(1/hist->GetBinContent(hist->GetMaximumBin()));
      copy->Scale(1/copy->GetBinContent(hist->GetMaximumBin()));
 
      copy->SetFillStyle(1001);
      copy->SetFillColor(fShadeColor);
      hist->Draw(options);
      copy->Draw("hist same");
 
      // draw lower and upper limits
      TLine* llLine = new TLine(ll, 0, ll, 1);
      TLine* ulLine = new TLine(ul, 0, ul, 1);
      llLine->SetLineColor(fLineColor);
      ulLine->SetLineColor(fLineColor);
      llLine->SetLineWidth(fLineWidth);
      ulLine->SetLineWidth(fLineWidth);
      llLine->Draw(options);
      ulLine->Draw(options);
   } else {
      coutE(InputArguments) << "MCMCIntervalPlot::DrawTailFractionInterval: "
         << " Sorry: " << fDimension << "-D plots not currently supported"
         << endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
 
void* MCMCIntervalPlot::DrawPosteriorKeysProduct(const Option_t* options)
{
   if (fPosteriorKeysProduct == nullptr)
      fPosteriorKeysProduct = fInterval->GetPosteriorKeysProduct();
 
   if (fPosteriorKeysProduct == nullptr) {
      coutE(InputArguments) << "MCMCIntervalPlot::DrawPosteriorKeysProduct: "
         << "Couldn't get posterior Keys product." << endl;
      return nullptr;
   }
 
   RooArgList* axes = fInterval->GetAxes();
 
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   if (fDimension == 1) {
      RooPlot* frame = (static_cast<RooRealVar*>(fParameters->first()))->frame();
      if (!frame) return nullptr;
      if (isEmpty) {
         frame->SetTitle(Form("Posterior Keys PDF * Heaviside product for %s",
                  axes->at(0)->GetName()));
      } else {
         frame->SetTitle(GetTitle());
      }
      //fPosteriorKeysProduct->plotOn(frame);
      fPosteriorKeysProduct->plotOn(frame,
            RooFit::Normalization(1, RooAbsReal::Raw));
      frame->Draw(options);
      return (void*)frame;
   } else if (fDimension == 2) {
      RooRealVar* xVar = static_cast<RooRealVar*>(axes->at(0));
      RooRealVar* yVar = static_cast<RooRealVar*>(axes->at(1));
      TH2F* productHist = static_cast<TH2F*>(fPosteriorKeysProduct->createHistogram(
            "prodPlot2D", *xVar, RooFit::YVar(*yVar), RooFit::Scaling(false)));
      if (isEmpty) {
         productHist->SetTitle(
               Form("MCMC Posterior Keys Product Hist. for %s, %s",
                  axes->at(0)->GetName(), axes->at(1)->GetName()));
      } else {
         productHist->SetTitle(GetTitle());
      }
      productHist->Draw(options);
      return nullptr;
   }
   delete axes;
   return nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawChainScatter(RooRealVar& xVar, RooRealVar& yVar)
{
   const MarkovChain* markovChain = fInterval->GetChain();
 
   Int_t size = markovChain->Size();
   Int_t burnInSteps;
   if (fShowBurnIn) {
      burnInSteps = fInterval->GetNumBurnInSteps();
   } else {
      burnInSteps = 0;
   }
 
   double* x = new double[size - burnInSteps];
   double* y = new double[size - burnInSteps];
   double* burnInX = nullptr;
   double* burnInY = nullptr;
   if (burnInSteps > 0) {
      burnInX = new double[burnInSteps];
      burnInY = new double[burnInSteps];
   }
   double firstX;
   double firstY;
 
   for (Int_t i = burnInSteps; i < size; i++) {
      x[i - burnInSteps] = markovChain->Get(i)->getRealValue(xVar.GetName());
      y[i - burnInSteps] = markovChain->Get(i)->getRealValue(yVar.GetName());
   }
 
   for (Int_t i = 0; i < burnInSteps; i++) {
      burnInX[i] = markovChain->Get(i)->getRealValue(xVar.GetName());
      burnInY[i] = markovChain->Get(i)->getRealValue(yVar.GetName());
   }
 
   firstX = markovChain->Get(0)->getRealValue(xVar.GetName());
   firstY = markovChain->Get(0)->getRealValue(yVar.GetName());
 
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   TGraph* walk = new TGraph(size - burnInSteps, x, y);
   if (isEmpty) {
      walk->SetTitle(Form("2-D Scatter Plot of Markov chain for %s, %s",
               xVar.GetName(), yVar.GetName()));
   } else {
      walk->SetTitle(GetTitle());
   }
   // kbelasco: figure out how to set TGraph variable ranges
   walk->GetXaxis()->Set(xVar.numBins(), xVar.getMin(), xVar.getMax());
   walk->GetXaxis()->SetTitle(xVar.GetName());
   walk->GetYaxis()->Set(yVar.numBins(), yVar.getMin(), yVar.getMax());
   walk->GetYaxis()->SetTitle(yVar.GetName());
   walk->SetLineColor(kGray);
   walk->SetMarkerStyle(6);
   walk->SetMarkerColor(kViolet);
   walk->Draw("A,L,P,same");
 
   TGraph* burnIn = nullptr;
   if (burnInX != nullptr && burnInY != nullptr) {
      burnIn = new TGraph(burnInSteps - 1, burnInX, burnInY);
      burnIn->SetLineColor(kPink);
      burnIn->SetMarkerStyle(6);
      burnIn->SetMarkerColor(kPink);
      burnIn->Draw("L,P,same");
   }
 
   TGraph* first = new TGraph(1, &firstX, &firstY);
   first->SetLineColor(kGreen);
   first->SetMarkerStyle(3);
   first->SetMarkerSize(2);
   first->SetMarkerColor(kGreen);
   first->Draw("L,P,same");
 
   //walkCanvas->Update();
   delete [] x;
   delete [] y;
   if (burnInX != nullptr) delete [] burnInX;
   if (burnInY != nullptr) delete [] burnInY;
   //delete walk;
   //delete burnIn;
   //delete first;
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawParameterVsTime(RooRealVar& param)
{
   const MarkovChain* markovChain = fInterval->GetChain();
   Int_t size = markovChain->Size();
   Int_t numEntries = 2 * size;
   double* value = new double[numEntries];
   double* time = new double[numEntries];
   double val;
   Int_t weight;
   Int_t t = 0;
   for (Int_t i = 0; i < size; i++) {
      val = markovChain->Get(i)->getRealValue(param.GetName());
      weight = (Int_t)markovChain->Weight();
      value[2*i] = val;
      value[2*i + 1] = val;
      time[2*i] = t;
      t += weight;
      time[2*i + 1] = t;
   }
 
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   TGraph* paramGraph = new TGraph(numEntries, time, value);
   if (isEmpty) {
      paramGraph->SetTitle(Form("%s vs. time in Markov chain",param.GetName()));
   } else {
      paramGraph->SetTitle(GetTitle());
   }
   paramGraph->GetXaxis()->SetTitle("Time (discrete steps)");
   paramGraph->GetYaxis()->SetTitle(param.GetName());
   //paramGraph->SetLineColor(fLineColor);
   paramGraph->Draw("A,L,same");
   delete [] value;
   delete [] time;
   //gPad->Update();
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawNLLVsTime()
{
   const MarkovChain* markovChain = fInterval->GetChain();
   Int_t size = markovChain->Size();
   Int_t numEntries = 2 * size;
   double* nllValue = new double[numEntries];
   double* time = new double[numEntries];
   double nll;
   Int_t weight;
   Int_t t = 0;
   for (Int_t i = 0; i < size; i++) {
      nll = markovChain->NLL(i);
      weight = (Int_t)markovChain->Weight();
      nllValue[2*i] = nll;
      nllValue[2*i + 1] = nll;
      time[2*i] = t;
      t += weight;
      time[2*i + 1] = t;
   }
 
   TString title(GetTitle());
   bool isEmpty = (title.CompareTo("") == 0);
 
   TGraph* nllGraph = new TGraph(numEntries, time, nllValue);
   if (isEmpty) {
      nllGraph->SetTitle("NLL value vs. time in Markov chain");
   } else {
      nllGraph->SetTitle(GetTitle());
   }
   nllGraph->GetXaxis()->SetTitle("Time (discrete steps)");
   nllGraph->GetYaxis()->SetTitle("NLL (-log(likelihood))");
   //nllGraph->SetLineColor(fLineColor);
   nllGraph->Draw("A,L,same");
   //gPad->Update();
   delete [] nllValue;
   delete [] time;
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawNLLHist(const Option_t* options)
{
   if (fNLLHist == nullptr) {
      const MarkovChain* markovChain = fInterval->GetChain();
      // find the max NLL value
      double maxNLL = 0;
      Int_t size = markovChain->Size();
      for (Int_t i = 0; i < size; i++) {
         if (markovChain->NLL(i) > maxNLL)
            maxNLL = markovChain->NLL(i);
      }
      RooRealVar* nllVar = fInterval->GetNLLVar();
      fNLLHist = new TH1F("mcmc_nll_hist", "MCMC NLL Histogram",
            nllVar->getBins(), 0, maxNLL);
      TString title(GetTitle());
      bool isEmpty = (title.CompareTo("") == 0);
      if (!isEmpty)
         fNLLHist->SetTitle(GetTitle());
      fNLLHist->GetXaxis()->SetTitle("-log(likelihood)");
      for (Int_t i = 0; i < size; i++)
         fNLLHist->Fill(markovChain->NLL(i), markovChain->Weight());
   }
   fNLLHist->Draw(options);
}
 
////////////////////////////////////////////////////////////////////////////////
 
void MCMCIntervalPlot::DrawWeightHist(const Option_t* options)
{
   if (fWeightHist == nullptr) {
      const MarkovChain* markovChain = fInterval->GetChain();
      // find the max weight value
      double maxWeight = 0;
      Int_t size = markovChain->Size();
      for (Int_t i = 0; i < size; i++) {
         if (markovChain->Weight(i) > maxWeight)
            maxWeight = markovChain->Weight(i);
      }
      fWeightHist = new TH1F("mcmc_weight_hist", "MCMC Weight Histogram",
            (Int_t)(maxWeight + 1), 0, maxWeight * 1.02);
      for (Int_t i = 0; i < size; i++)
         fWeightHist->Fill(markovChain->Weight(i));
   }
   fWeightHist->Draw(options);
}
 
/*
/////////////////////////////////////////////////////////////////////
  // 3-d plot of the parameter points
  dataCanvas->cd(2);
  // also plot the points in the markov chain
  RooDataSet* markovChainData = ((MCMCInterval*)mcmcint)->GetChainAsDataSet();
 
  TTree& chain =  ((RooTreeDataStore*) markovChainData->store())->tree();
  chain.SetMarkerStyle(6);
  chain.SetMarkerColor(kRed);
  chain.Draw("s:ratioSigEff:ratioBkgEff","","box"); // 3-d box proportional to posterior
 
  // the points used in the profile construction
  TTree& parameterScan =  ((RooTreeDataStore*) fc.GetPointsToScan()->store())->tree();
  parameterScan.SetMarkerStyle(24);
  parameterScan.Draw("s:ratioSigEff:ratioBkgEff","","same");
 
  chain.SetMarkerStyle(6);
  chain.SetMarkerColor(kRed);
  //chain.Draw("s:ratioSigEff:ratioBkgEff", "_MarkovChain_local_nll","box");
  //chain.Draw("_MarkovChain_local_nll");
////////////////////////////////////////////////////////////////////
*/