RooBarlowBeestonLL.cxx

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// @(#)root/roostats:$Id$
// Author: Kyle Cranmer, George Lewis
/*************************************************************************
 * 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::HistFactory::RooBarlowBeestonLL
 * \ingroup HistFactory
//
// Class RooBarlowBeestonLL implements the profile likelihood estimator for
// a given likelihood and set of parameters of interest. The value return by
// RooBarlowBeestonLL is the input likelihood nll minimized w.r.t all nuisance parameters
// (which are all parameters except for those listed in the constructor) minus
// the -log(L) of the best fit. Note that this function is slow to evaluate
// as a MIGRAD minimization step is executed for each function evaluation
*/
 
#include <stdexcept>
#include <cmath>
#include <iostream>
 
#include "RooStats/HistFactory/RooBarlowBeestonLL.h"
#include "RooAbsReal.h"
#include "RooMsgService.h"
#include "RooRealVar.h"
 
#include "RooStats/RooStatsUtils.h"
#include "RooCategory.h"
#include "RooSimultaneous.h"
#include "RooArgList.h"
 
#include "RooStats/HistFactory/ParamHistFunc.h"
#include "RooStats/HistFactory/HistFactoryModelUtils.h"
 
#include <TMath.h>
 
 
 
 
////////////////////////////////////////////////////////////////////////////////
 
RooStats::HistFactory::RooBarlowBeestonLL::RooBarlowBeestonLL(const char *name, const char *title,
                   RooAbsReal& nllIn /*, const RooArgSet& observables*/) :
  RooAbsReal(name,title),
  _nll("input","-log(L) function",this,nllIn)
  //  _obs("paramOfInterest","Parameters of interest",this),
  //  _par("nuisanceParam","Nuisance parameters",this,false,false),
{
  // Constructor of profile likelihood given input likelihood nll w.r.t
  // the given set of variables. The input log likelihood is minimized w.r.t
  // to all other variables of the likelihood at each evaluation and the
  // value of the global log likelihood minimum is always subtracted.
 
  // Determine actual parameters and observables
  /*
  std::unique_ptr<RooArgSet> actualObs{nllIn.getObservables(observables)};
  std::unique_ptr<RooArgSet> actualPars{nllIn.getParameters(observables)};
 
  _obs.add(*actualObs) ;
  _par.add(*actualPars) ;
  */
}
 
 
 
////////////////////////////////////////////////////////////////////////////////
 
RooStats::HistFactory::RooBarlowBeestonLL::RooBarlowBeestonLL(const RooBarlowBeestonLL& other, const char* name) :
  RooAbsReal(other,name),
  _nll("nll",this,other._nll),
  //  _obs("obs",this,other._obs),
  //  _par("par",this,other._par),
  _paramFixed(other._paramFixed)
{
  // Copy constructor
 
  // _paramAbsMin.addClone(other._paramAbsMin) ;
  // _obsAbsMin.addClone(other._obsAbsMin) ;
 
}
 
 
////////////////////////////////////////////////////////////////////////////////
 
void RooStats::HistFactory::RooBarlowBeestonLL::BarlowCache::SetBinCenter() const {
  for (auto const *var : static_range_cast<RooRealVar *>(*bin_center)) {
    RooRealVar* target = static_cast<RooRealVar*>(observables->find(var->GetName())) ;
    target->setVal(var->getVal()) ;
  }
}
 
 
////////////////////////////////////////////////////////////////////////////////
 
void RooStats::HistFactory::RooBarlowBeestonLL::initializeBarlowCache() {
  bool verbose=false;
 
  if(!_data) {
    std::cout << "Error: Must initialize data before initializing cache" << std::endl;
    throw std::runtime_error("Uninitialized Data");
  }
  if(!_pdf) {
    std::cout << "Error: Must initialize model pdf before initializing cache" << std::endl;
    throw std::runtime_error("Uninitialized model pdf");
  }
 
  // Get the data bin values for all channels and bins
  std::map< std::string, std::vector<double> > ChannelBinDataMap;
  getDataValuesForObservables( ChannelBinDataMap, _data, _pdf );
 
  // Get a list of constraint terms
  RooArgList obsTerms;
  RooArgList constraints;
  RooArgSet* obsSet = std::unique_ptr<RooArgSet>{_pdf->getObservables(*_data)}.release();
  FactorizeHistFactoryPdf(*obsSet, *_pdf, obsTerms, constraints);
 
  if( obsTerms.empty() ) {
    std::cout << "Error: Found no observable terms with pdf: " << _pdf->GetName()
         << " using dataset: " << _data->GetName() << std::endl;
    return;
  }
  if( constraints.empty() ) {
    std::cout << "Error: Found no constraint terms with pdf: " << _pdf->GetName()
         << " using dataset: " << _data->GetName() << std::endl;
    return;
  }
 
  // Loop over the channels
  auto simPdf = static_cast<RooSimultaneous*>(_pdf);
  auto channelCat = static_cast<RooCategory const*>(&simPdf->indexCat());
  for (const auto& nameIdx : *channelCat) {
 
    // Warning: channel cat name is not necessarily the same name
    // as the pdf's (for example, if someone does edits)
    RooAbsPdf* channelPdf = simPdf->getPdf(nameIdx.first.c_str());
    std::string channel_name = channelPdf->GetName();
 
    // First, we check if this channel uses Stat Uncertainties:
    RooArgList* gammas = nullptr;
    ParamHistFunc* param_func=nullptr;
    bool hasStatUncert = getStatUncertaintyFromChannel( channelPdf, param_func, gammas );
    if( ! hasStatUncert ) {
      if(verbose) {
   std::cout << "Channel: " << channel_name
        << " doesn't have statistical uncertainties"
        << std::endl;
      }
      continue;
    }
    else {
      if(verbose) std::cout << "Found ParamHistFunc: " << param_func->GetName() << std::endl;
    }
 
    // Now, loop over the bins in this channel
    // To Do: Check that the index convention
    // still works for 2-d (ie matches the
    // convention in ParamHistFunc, etc)
    int num_bins = param_func->numBins();
 
    // Initialize the vector to the number of bins, allowing
    // us to skip gamma's if they are constant
 
    std::vector<BarlowCache> temp_cache( num_bins );
    bool channel_has_stat_uncertainty=false;
 
    for( Int_t bin_index = 0; bin_index < num_bins; ++bin_index ) {
 
      // Create a cache object
      BarlowCache cache;
 
      // Get the gamma for this bin, and skip if it's constant
      RooRealVar* gamma_stat = dynamic_cast<RooRealVar*>(&(param_func->getParameter(bin_index)));
      if(!gamma_stat) throw std::runtime_error("ParamHistFunc contains non-RooRealVar, not supported in RooBarlowBeestonLL");
      if( gamma_stat->isConstant() ) {
   if(verbose) std::cout << "Ignoring constant gamma: " << gamma_stat->GetName() << std::endl;
   continue;
      }
      else {
   cache.hasStatUncert=true;
   channel_has_stat_uncertainty=true;
   cache.gamma = gamma_stat;
   _statUncertParams.insert( gamma_stat->GetName() );
      }
 
      // Store a snapshot of the bin center
      RooArgSet* bin_center = (RooArgSet*) param_func->get( bin_index )->snapshot();
      cache.bin_center = bin_center;
      cache.observables = obsSet;
 
      cache.binVolume = param_func->binVolume(bin_index);
 
      // Delete this part, simply a comment
      RooArgList obs_list( *(cache.bin_center) );
 
      // Get the gamma's constraint term
      RooAbsReal* pois_mean = nullptr;
      RooRealVar* tau = nullptr;
      getStatUncertaintyConstraintTerm( &constraints, gamma_stat, pois_mean, tau );
      if( !tau || !pois_mean ) {
   std::cout << "Failed to find pois mean or tau parameter for " << gamma_stat->GetName() << std::endl;
      }
      else {
   if (verbose) {
      std::cout << "Found pois mean and tau for parameter: " << gamma_stat->GetName() << " tau: " << tau->GetName()
                << " " << tau->getVal() << " pois_mean: " << pois_mean->GetName() << " " << pois_mean->getVal()
                << std::endl;
   }
      }
 
      cache.tau = tau;
      cache.nom_pois_mean = pois_mean;
 
      // Get the RooRealSumPdf
      RooAbsPdf* sum_pdf = getSumPdfFromChannel( channelPdf );
      if( sum_pdf == nullptr )  {
   std::cout << "Failed to find RooRealSumPdf in channel " <<  channel_name
        << ", therefor skipping this channel for analytic uncertainty minimization"
        << std::endl;
   channel_has_stat_uncertainty=false;
   break;
      }
      cache.sumPdf = sum_pdf;
 
      // And set the data value for this bin
      if( ChannelBinDataMap.find(channel_name) == ChannelBinDataMap.end() ) {
   std::cout << "Error: channel with name: " << channel_name
        << " not found in BinDataMap" << std::endl;
   throw std::runtime_error("BinDataMap");
      }
      double nData = ChannelBinDataMap[channel_name].at(bin_index);
      cache.nData = nData;
 
      temp_cache.at(bin_index) = cache;
      //_barlowCache[channel_name].at(bin_index) = cache;
 
    } // End: Loop over bins
 
    if( channel_has_stat_uncertainty ) {
      std::cout << "Adding channel: " << channel_name
      << " to the barlow cache" << std::endl;
      _barlowCache[channel_name] = temp_cache;
    }
 
 
  } // End: Loop over channels
 
 
 
  // Successfully initialized the cache
  // Printing some info
  /*
  std::map< std::string, std::vector< BarlowCache > >::iterator iter_cache;
  for( iter_cache = _barlowCache.begin(); iter_cache != _barlowCache.end(); ++iter_cache ) {
 
    std::string channel_name = (*iter_cache).first;
    std::vector< BarlowCache >& channel_cache = (*iter_cache).second;
 
 
    for( unsigned int i = 0; i < channel_cache.size(); ++i ) {
      BarlowCache& bin_cache = channel_cache.at(i);
 
 
      RooRealVar* gamma = bin_cache.gamma;
      RooRealVar* tau = bin_cache.tau;
      RooAbsReal* pois_mean = bin_cache.nom_pois_mean;
      RooAbsPdf* sum_pdf = (RooAbsPdf*) bin_cache.sumPdf;
      double binVolume = bin_cache.binVolume;
 
 
      if( !bin_cache.hasStatUncert ) {
   std::cout << "Barlow Cache for Channel: " << channel_name
        << " Bin: " << i
        << " NO STAT UNCERT"
        << std::endl;
      }
      else {
      std::cout << "Barlow Cache for Channel: " << channel_name
      << " Bin: " << i
      << " gamma: " << gamma->GetName()
      << " tau: " << tau->GetName()
      << " pois_mean: " << pois_mean->GetName()
      << " sum_pdf: " << sum_pdf->GetName()
      << " binVolume: " << binVolume
      << std::endl;
      }
 
    }
  }
  */
 
}
 
 
////////////////////////////////////////////////////////////////////////////////
 
bool RooStats::HistFactory::RooBarlowBeestonLL::getParameters(const RooArgSet* depList,
                                                              RooArgSet& outputSet,
                                                              bool stripDisconnected) const {
  bool errorInBaseCall = RooAbsArg::getParameters( depList, outputSet, stripDisconnected );
 
  RooArgSet toRemove;
  toRemove.reserve( _statUncertParams.size());
 
  for (auto const& arg : outputSet) {
 
    // If there is a gamma in the name,
    // strip it from the list of dependencies
 
    if( _statUncertParams.find(arg->GetName()) != _statUncertParams.end() ) {
      toRemove.add( *arg );
    }
  }
 
  for( auto& arg : toRemove) outputSet.remove( *arg, true );
 
  return errorInBaseCall || false;
 
}
 
 
/*
////////////////////////////////////////////////////////////////////////////////
 
const RooArgSet& RooStats::HistFactory::RooBarlowBeestonLL::bestFitParams() const
{
  validateAbsMin() ;
  return _paramAbsMin ;
}
 
 
////////////////////////////////////////////////////////////////////////////////
 
const RooArgSet& RooStats::HistFactory::RooBarlowBeestonLL::bestFitObs() const
{
  validateAbsMin() ;
  return _obsAbsMin ;
}
*/
 
 
 
////////////////////////////////////////////////////////////////////////////////
/// Optimized implementation of createProfile for profile likelihoods.
/// Return profile of original function in terms of stated parameters
/// of interest rather than profiling recursively.
 
/*
RooAbsReal* RooStats::HistFactory::RooBarlowBeestonLL::createProfile(const RooArgSet& paramsOfInterest)
{
  return nll().createProfile(paramsOfInterest) ;
}
*/
 
 
/*
void RooStats::HistFactory::RooBarlowBeestonLL::FactorizePdf(const RooArgSet &observables, RooAbsPdf &pdf, RooArgList &obsTerms, RooArgList &constraints) const {
  // utility function to factorize constraint terms from a pdf
  // (from G. Petrucciani)
  const std::type_info & id = typeid(pdf);
  if (id == typeid(RooProdPdf)) {
    RooProdPdf *prod = dynamic_cast<RooProdPdf *>(&pdf);
    RooArgList list(prod->pdfList());
    for (int i = 0, n = list.size(); i < n; ++i) {
      RooAbsPdf *pdfi = (RooAbsPdf *) list.at(i);
      FactorizePdf(observables, *pdfi, obsTerms, constraints);
    }
  } else if (id == typeid(RooSimultaneous) ) {    //|| id == typeid(RooSimultaneousOpt)) {
    RooSimultaneous *sim  = dynamic_cast<RooSimultaneous *>(&pdf);
    std::unique_ptr<RooAbsCategoryLValue> cat{(RooAbsCategoryLValue *) sim->indexCat().Clone()};
    for (int ic = 0, nc = cat->numBins((const char *)0); ic < nc; ++ic) {
      cat->setBin(ic);
      FactorizePdf(observables, *sim->getPdf(cat->getLabel()), obsTerms, constraints);
    }
  } else if (pdf.dependsOn(observables)) {
    if (!obsTerms.contains(pdf)) obsTerms.add(pdf);
  } else {
    if (!constraints.contains(pdf)) constraints.add(pdf);
  }
}
*/
 
 
 
////////////////////////////////////////////////////////////////////////////////
 
double RooStats::HistFactory::RooBarlowBeestonLL::evaluate() const
{
  // Loop over the channels (keys to the map)
  //clock_t time_before_setVal, time_after_setVal;
  //time_before_setVal=clock();
  std::map< std::string, std::vector< BarlowCache > >::iterator iter_cache;
  for( iter_cache = _barlowCache.begin(); iter_cache != _barlowCache.end(); ++iter_cache ) {
 
    std::string channel_name = (*iter_cache).first;
    std::vector< BarlowCache >& channel_cache = (*iter_cache).second;
 
    /* Slower way to find the channel vector:
    // Get the vector of bin uncertainty caches for this channel
    if( _barlowCache.find( channel_name ) == _barlowCache.end() ) {
      std::cout << "Error: channel: " << channel_name
      << " not found in barlow Cache" << std::endl;
      throw std::runtime_error("Channel not in barlow cache");
    }
 
    std::vector< BarlowCache >& channel_cache = _barlowCache[ channel_name ];
    */
 
    // Loop over the bins in the cache
    // Set all gamma's to 0
    for( unsigned int i = 0; i < channel_cache.size(); ++i ) {
      BarlowCache& bin_cache = channel_cache.at(i);
      if( !bin_cache.hasStatUncert ) continue;
      RooRealVar* gamma = bin_cache.gamma;
      gamma->setVal(0.0);
    }
    std::vector< double > nu_b_vec( channel_cache.size() );
    for( unsigned int i = 0; i < channel_cache.size(); ++i ) {
      BarlowCache& bin_cache = channel_cache.at(i);
      if( !bin_cache.hasStatUncert ) continue;
 
      RooAbsPdf* sum_pdf = static_cast<RooAbsPdf*>(bin_cache.sumPdf);
      RooArgSet* obsSet = bin_cache.observables;
      double binVolume = bin_cache.binVolume;
 
      bin_cache.SetBinCenter();
      double nu_b = sum_pdf->getVal(*obsSet)*sum_pdf->expectedEvents(*obsSet)*binVolume;
      nu_b_vec.at(i) = nu_b;
    }
 
    // Loop over the bins in the cache
    // Set all gamma's to 1
    for( unsigned int i = 0; i < channel_cache.size(); ++i ) {
      BarlowCache& bin_cache = channel_cache.at(i);
      if( !bin_cache.hasStatUncert ) continue;
      RooRealVar* gamma = bin_cache.gamma;
      gamma->setVal(1.0);
    }
    std::vector< double > nu_b_stat_vec( channel_cache.size() );
    for( unsigned int i = 0; i < channel_cache.size(); ++i ) {
      BarlowCache& bin_cache = channel_cache.at(i);
      if( !bin_cache.hasStatUncert ) continue;
 
      RooAbsPdf* sum_pdf = static_cast<RooAbsPdf*>(bin_cache.sumPdf);
      RooArgSet* obsSet = bin_cache.observables;
      double binVolume = bin_cache.binVolume;
 
      bin_cache.SetBinCenter();
      double nu_b_stat = sum_pdf->getVal(*obsSet)*sum_pdf->expectedEvents(*obsSet)*binVolume - nu_b_vec.at(i);
      nu_b_stat_vec.at(i) = nu_b_stat;
    }
    //time_after_setVal=clock();
 
    // Done with the first loops.
    // Now evaluating the function
 
    //clock_t time_before_eval, time_after_eval;
 
    // Loop over the bins in the cache
    //time_before_eval=clock();
    for( unsigned int i = 0; i < channel_cache.size(); ++i ) {
 
      BarlowCache& bin_cache = channel_cache.at(i);
 
      if( !bin_cache.hasStatUncert ) {
   //std::cout << "Bin: " << i << " of " << channel_cache.size()
   //   << " in channel: " << channel_name
   //   << " doesn't have stat uncertainties" << std::endl;
   continue;
      }
 
      // Set the observable to the bin center
      bin_cache.SetBinCenter();
 
      // Get the cached objects
      RooRealVar* gamma = bin_cache.gamma;
      RooRealVar* tau = bin_cache.tau;
      RooAbsReal* pois_mean = bin_cache.nom_pois_mean;
      //RooAbsPdf* sum_pdf = (RooAbsPdf*) bin_cache.sumPdf;
      //RooArgSet* obsSet = bin_cache.observables;
      //double binVolume = bin_cache.binVolume;
 
      // Get the values necessary for
      // the analytic minimization
      double nu_b = nu_b_vec.at(i);
      double nu_b_stat = nu_b_stat_vec.at(i);
 
      double tau_val = tau->getVal();
      double nData = bin_cache.nData;
      double m_val = pois_mean->getVal();
 
      // Initialize the minimized value of gamma
      double gamma_hat_hat = 1.0;
 
      // Check that the quadratic term is > 0
      if(nu_b_stat > 0.00000001) {
 
   double A = nu_b_stat*nu_b_stat + tau_val*nu_b_stat;
   double B = nu_b*tau_val + nu_b*nu_b_stat - nData*nu_b_stat - m_val*nu_b_stat;
   double C = -1*m_val*nu_b;
 
   double discrim = B*B-4*A*C;
 
   if( discrim < 0 ) {
     std::cout << "Warning: Discriminant (B*B - 4AC) < 0" << std::endl;
     std::cout << "Warning: Taking B*B - 4*A*C == 0" << std::endl;
     discrim=0;
     //throw std::runtime_error("BarlowBeestonLL::evaluate() : B*B - 4AC < 0");
   }
   if( A <= 0 ) {
     std::cout << "Warning: A <= 0" << std::endl;
     throw std::runtime_error("BarlowBeestonLL::evaluate() : A < 0");
   }
 
   gamma_hat_hat = ( -1*B + std::sqrt(discrim) ) / (2*A);
      }
 
      // If the quadratic term is 0, we simply
      // use a linear equation
      else {
   gamma_hat_hat = m_val/tau_val;
      }
 
      // Check for NAN
      if( TMath::IsNaN(gamma_hat_hat) ) {
   std::cout << "ERROR: gamma hat hat is NAN" << std::endl;
   throw std::runtime_error("BarlowBeestonLL::evaluate() : gamma hat hat is NAN");
      }
 
      if( gamma_hat_hat <= 0 ) {
   std::cout << "WARNING: gamma hat hat <= 0.  Setting to 0" << std::endl;
   gamma_hat_hat = 0;
      }
 
      /*
      std::cout << "n: " << bin_cache.nData << " "
      << "nu_stat: " << nu_b_stat << " "
      << "nu: " << nu_b << " "
      << "tau: " << tau->getVal() << " "
      << "m: " << pois_mean->getVal() << " "
      << "A: " << A << " "
      << "B: " << B << " "
      << "C: " << C << " "
      << "gamma hat hat: " << gamma_hat_hat
      << std::endl;
      */
 
      gamma->setVal( gamma_hat_hat );
 
    }
 
    //time_after_eval=clock();
 
    //float time_setVal = ((float) time_after_setVal - (float) time_before_setVal) / ((float) CLOCKS_PER_SEC);
    //float time_eval   = ((float) time_after_eval - (float) time_before_eval) / ((float) CLOCKS_PER_SEC);
 
    /*
    std::cout << "Barlow timing for channel: " << channel_name
         << " SetVal: " << time_setVal
         << " Eval: " << time_eval
         << std::endl;
    */
  }
 
 
  return _nll;
 
}
 
 
 
/*
////////////////////////////////////////////////////////////////////////////////
/// Check that parameters and likelihood value for 'best fit' are still valid. If not,
/// because the best fit has never been calculated, or because constant parameters have
/// changed value or parameters have changed const/float status, the minimum is recalculated
 
void RooStats::HistFactory::RooBarlowBeestonLL::validateAbsMin() const
{
  // Check if constant status of any of the parameters have changed
  if (_absMinValid) {
    _piter->Reset() ;
    RooAbsArg* par ;
    while((par=(RooAbsArg*)_piter->Next())) {
      if (_paramFixed[par->GetName()] != par->isConstant()) {
   cxcoutI(Minimization) << "RooStats::HistFactory::RooBarlowBeestonLL::evaluate(" << GetName() << ") constant status of parameter " << par->GetName() << " has changed from "
            << (_paramFixed[par->GetName()]?"fixed":"floating") << " to " << (par->isConstant()?"fixed":"floating")
            << ", recalculating absolute minimum" << std::endl ;
   _absMinValid = false ;
   break ;
      }
    }
  }
 
 
  // If we don't have the absolute minimum w.r.t all observables, calculate that first
  if (!_absMinValid) {
 
    cxcoutI(Minimization) << "RooStats::HistFactory::RooBarlowBeestonLL::evaluate(" << GetName() << ") determining minimum likelihood for current configurations w.r.t all observable" << std::endl ;
 
 
    // Save current values of non-marginalized parameters
    std::unique_ptr<RooArgSet> obsStart{(RooArgSet*) _obs.snapshot(false)};
 
    // Start from previous global minimum
    if (_paramAbsMin.size()>0) {
      const_cast<RooSetProxy&>(_par).assignValueOnly(_paramAbsMin) ;
    }
    if (_obsAbsMin.size()>0) {
      const_cast<RooSetProxy&>(_obs).assignValueOnly(_obsAbsMin) ;
    }
 
    // Find minimum with all observables floating
    const_cast<RooSetProxy&>(_obs).setAttribAll("Constant",false) ;
    _minuit->migrad() ;
 
    // Save value and remember
    _absMin = _nll ;
    _absMinValid = true ;
 
    // Save parameter values at abs minimum as well
    _paramAbsMin.removeAll() ;
 
    // Only store non-constant parameters here!
    std::unique_ptr<RooArgSet> tmp{_par.selectByAttrib("Constant",false)};
    _paramAbsMin.addClone(*tmp) ;
 
    _obsAbsMin.addClone(_obs) ;
 
    // Save constant status of all parameters
    _piter->Reset() ;
    RooAbsArg* par ;
    while((par=(RooAbsArg*)_piter->Next())) {
      _paramFixed[par->GetName()] = par->isConstant() ;
    }
 
    if (dologI(Minimization)) {
      cxcoutI(Minimization) << "RooStats::HistFactory::RooBarlowBeestonLL::evaluate(" << GetName() << ") minimum found at (" ;
 
      RooAbsReal* arg ;
      bool first=true ;
      _oiter->Reset() ;
      while ((arg=(RooAbsReal*)_oiter->Next())) {
   ccxcoutI(Minimization) << (first?"":", ") << arg->GetName() << "=" << arg->getVal() ;
   first=false ;
      }
      ccxcoutI(Minimization) << ")" << std::endl ;
    }
 
    // Restore original parameter values
    const_cast<RooSetProxy&>(_obs) = *obsStart ;
 
  }
}
*/