JTestEffectiveLogLikelihoodRatio.hh

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#ifndef __JCOMPAREHISTOGRAMS__JTESTEFFECTIVELOGLIKELIHOODRATIO__
#define __JCOMPAREHISTOGRAMS__JTESTEFFECTIVELOGLIKELIHOODRATIO__
 
#include <istream>
#include <ostream>
 
#include "JLang/JException.hh"
 
#include "JCompareHistograms/JResultTitle.hh"
#include "JCompareHistograms/JTest_t.hh"
 
#include "TH1.h"
 
 
/**
 * \author bjung
 */
namespace JCOMPAREHISTOGRAMS {
  
  /**
   * Implementation of the effective log-likelihood ratio test.
   * The first histogram is treated as an Asimov dataset corresponding to a given null hypothesis,
   * which is compared to an alternative hypothesis given by the second histogram.   
   *
   * This likelihood in this method is taken from the article:
   * "A binned likelihood for stochastic models"
   * JHEP, Volume 2019, article number 30, (2019),
   * by C.A. Argüelles, A. Schneider and T. Yuan.
   * DOI: 10.1007/JHEP06(2019)030
   */
  class JTestEffectiveLogLikelihoodRatio: 
    public JTest_t
  { 
  public:  
 
    /**
     * Default constructor.
     */
    JTestEffectiveLogLikelihoodRatio() :
      JTest_t("Effective_NLLR", "NLLR"),
      threshold(0.0)
    {}
 
 
    /**
     * Get negative log-likelihood (i.e. \f[-2 \ln\left(\mathcal{L}\right)\f]).
     *
     * \param  k    number of observed events
     * \param  n    model prediction
     * \param  ne   model prediction error
     */
    static double getNLL(const double k,
                         const double n,
                         const double ne)
    {
      using namespace JPP;
      
      static const double epsilon = std::numeric_limits<double>::min();
      
      if (k < 0.0) {
        THROW(JValueOutOfRange, "JTestEffectiveLogLikelihoodRatio::getNLL(): Invalid number of events: " << k);
      }
 
      if (n < 0.0) {
        THROW(JValueOutOfRange, "JTestEffectiveLogLikelihoodRatio::getNLL(): Invalid model prediction: " << n);
      }
            
      double M = epsilon; // Relative bin variance of given model
 
      if (n > 0.0 && ne > 0.0) {
        M = n/ne/ne;
      } else if (n > 0.0) {
        THROW(JDivisionByZero, "JTestEffectiveLogLikelihoodRatio::getNLL(): Invalid effective bin content (bin content error is zero)");
      }
     
      const double N = n*M; // Effective bin content
 
      return -2.0 * ((N + 1) * log(M)         -
                     (k + N + 1) * log(1 + M) +
                     lgamma(k + N + 1)        -
                     lgamma(N + 1)            -
                     lgamma(k + 1));
    }
    
    
    /**
     * Applies a log-likelihood ratio test to the two given histograms.\n
     * The first histogram is treated as an Asimov dataset corresponding to a given null hypothesis.\n
     * The second histogram is treated as the expectation for the alternative hypothesis, to which the null hypothesis is compared.
     * 
     * \param o1    First histogram
     * \param o2    Second histogram
     */
    void test(const TObject* o1, const TObject* o2) override
    {
      using namespace std;
      using namespace JPP;
      
      const TH1* h1 =  dynamic_cast<const TH1*>(o1);
      const TH1* h2 =  dynamic_cast<const TH1*>(o2);
 
      if (h1 == NULL || h2 == NULL) {
        THROW(JValueOutOfRange, "JTestEffectiveLogLikelihood::test(): Could not cast given TObjects to TH1.");
      }
 
      if(h1->GetNbinsX() != h2->GetNbinsX() ||
         h1->GetNbinsY() != h2->GetNbinsY() ||
         h1->GetNbinsZ() != h2->GetNbinsZ()) {
        THROW(JValueOutOfRange, "JTestEffectiveLogLikelihood::test(): Histograms with different binning. The objects: " <<
              h1->GetName() << " and " << h2->GetName() << " can not be compared." << endl);
      }
 
      TH1* h3 = (TH1*) h1->Clone(h1->GetName() == h2->GetName() ?
                                 MAKE_CSTRING(h1->GetName()                            << "_" << testName) :
                                 MAKE_CSTRING(h1->GetName() << "_VS_" << h2->GetName() << "_" << testName));
 
      h3->Reset();
 
      double LnLratio = 0.0;
 
      for (int i=1 ; i <= h1->GetNbinsX() ; ++i) {
        for (int j=1 ; j <= h1->GetNbinsY() ; ++j) {
          for (int k=1 ; k <= h1->GetNbinsZ() ; ++k) {
 
            const double n1 = h1->GetBinContent(i,j,k);
            const double n2 = h2->GetBinContent(i,j,k);
 
            const double e1 = h1->GetBinError(i,j,k);
            const double e2 = h2->GetBinError(i,j,k);
            
            double contribution = 0.0;
            
            if        (n1 > 0.0) {
              contribution = (getNLL(n1, n2, e2) -
                              getNLL(n1, n1, e1));
            } else if (n2 > 0.0) {
              contribution =  getNLL(n1, n2, e2);
            } // Skip bins with zero data and zero prediction
 
            h3->SetBinContent(i,j,k, contribution);
            
            LnLratio += contribution;
          }
        }
      }
 
      const bool passed = (LnLratio < threshold);
 
      const JResultTitle title(testName, resultType, passed, LnLratio);
 
      h3->SetTitle(title.getTitle().c_str());
      h3->GetYaxis()->SetTitle(resultType.c_str());
 
      const JTestResult r (testName,
                           JRootObjectID(MAKE_STRING(h1->GetDirectory()->GetPath() << h1->GetName())),
                           JRootObjectID(MAKE_STRING(h2->GetDirectory()->GetPath() << h1->GetName())),
                           resultType, LnLratio, threshold, h3, passed);
      
      this->push_back(r);
    }
 
 
    /**
     * Read test parameters from input.
     *
     * \param  in            input stream
     * \return               input stream
     */
    std::istream& read(std::istream& in) override
    {
      using namespace JPP;
      
      in >> threshold;
 
      if (!(threshold > 0.0)) {
        THROW(JValueOutOfRange, "JTestEffectiveLogLikelihoodRatio::read(): Given chi-square threshold " << threshold << " is invalid");
      }
       
      return in;
    }
  
  private:
    
    double threshold;  //!< threshold chi-square to decide if test is passed.
  };
}
  
#endif