BCEngineMCMC.cxx

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/*
 * Copyright (C) 2008, Daniel Kollar and Kevin Kroeninger.
 * All rights reserved.
 *
 * For the licensing terms see doc/COPYING.
 */

// ---------------------------------------------------------

#include "BAT/BCEngineMCMC.h"

#include "BAT/BCParameter.h"
#include "BAT/BCDataPoint.h"
#include "BAT/BCLog.h"

#include <TH1D.h>
#include <TH2D.h>
#include <TTree.h>
#include <TRandom3.h>
#include <TPrincipal.h>

#include <iostream>

#include <math.h>


#define DEBUG 0

// ---------------------------------------------------------

BCEngineMCMC::BCEngineMCMC()
{
   // default settings
   fMCMCNParameters          = 0;
   fMCMCFlagWriteChainToFile = false;
   fMCMCFlagPreRun           = false;
   fMCMCEfficiencyMin        = 0.15;
   fMCMCEfficiencyMax        = 0.50;

   this -> MCMCSetValuesDefault();

// fMCMCRelativePrecisionMode = 1e-3;

   // set pointer to control histograms to NULL
// for (int i = 0; i < int(fMCMCH1Marginalized.size()); ++i)
//    fMCMCH1Marginalized[i] = 0;

// for (int i = 0; i < int(fMCMCH2Marginalized.size()); ++i)
//    fMCMCH2Marginalized[i] = 0;

// fMCMCH1RValue = 0;
// fMCMCH1Efficiency = 0;

   // initialize random number generator
   fMCMCRandom = new TRandom3(0);

   // initialize
// this -> MCMCInitialize();
}

// ---------------------------------------------------------

BCEngineMCMC::BCEngineMCMC(int n)
{
   // set number of chains to n
   fMCMCNChains = n;

   // call default constructor
   BCEngineMCMC();
}

// ---------------------------------------------------------

BCEngineMCMC::~BCEngineMCMC()
{
   // delete random number generator
   if (fMCMCRandom) delete fMCMCRandom;

   // delete PCA object
   if (fMCMCPCA) delete fMCMCPCA;

   // delete constrol histograms and plots
   for (int i = 0; i < int(fMCMCH1Marginalized.size()); ++i)
      if (fMCMCH1Marginalized[i])
         delete fMCMCH1Marginalized[i];

   fMCMCH1Marginalized.clear();

   for (int i = 0; i < int(fMCMCH2Marginalized.size()); ++i)
      if (fMCMCH2Marginalized[i])
         delete fMCMCH2Marginalized[i];

   fMCMCH2Marginalized.clear();

// if (fMCMCH1RValue) delete fMCMCH1RValue;
// if (fMCMCH1Efficiency) delete fMCMCH1Efficiency;
}

// ---------------------------------------------------------

BCEngineMCMC::BCEngineMCMC(const BCEngineMCMC & enginemcmc)
{
   enginemcmc.Copy(*this);
}

// ---------------------------------------------------------

BCEngineMCMC & BCEngineMCMC::operator = (const BCEngineMCMC & enginemcmc)
{
   if (this != &enginemcmc)
      enginemcmc.Copy(* this);

   return * this;
}

// --------------------------------------------------------

TH2D * BCEngineMCMC::MCMCGetH2Marginalized(int index1, int index2)
{
   int counter = 0;
   int index = 0;

   // search for correct combination
   for(int i = 0; i < fMCMCNParameters; i++)
      for (int j = 0; j < i; ++j)
      {
         if(j == index1 && i == index2)
            index = counter;
         counter++;
      }

   return fMCMCH2Marginalized[index];
}

// --------------------------------------------------------

std::vector <double> BCEngineMCMC::MCMCGetMaximumPoint(int i)
{
   // create a new vector with the lenght of fMCMCNParameters
   std::vector <double> x;

   // check if i is in range
   if (i < 0 || i >= fMCMCNChains)
      return x;

   // copy the point in the ith chain into the temporary vector
   for (int j = 0; j < fMCMCNParameters; ++j)
   x.push_back(fMCMCMaximumPoints.at(i * fMCMCNParameters + j));

   return x;
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCSetNChains(int n)
{
   fMCMCNChains = n;

   // re-initialize
   this -> MCMCInitialize();
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCSetInitialPosition(int chain, std::vector<double> x0)
{
   // check consistency
   if (chain >= fMCMCNChains)
   {
      fMCMCInitialPosition.clear();
      return;
   }

   if (int(x0.size()) == fMCMCNParameters)
   {
      fMCMCInitialPosition.clear();
      for (int j = 0; j < fMCMCNChains; ++j)
         for (int i = 0; i < fMCMCNParameters; ++i)
            fMCMCInitialPosition.push_back(x0.at(i));
   }
   else
      return;

   bool flagin = true;
   for (int j = 0; j < fMCMCNChains; ++j)
      for (int i = 0; i < fMCMCNParameters; ++i)
         if (fMCMCInitialPosition[j * fMCMCNParameters + i] < fMCMCBoundaryMin[i] ||
               fMCMCInitialPosition[j * fMCMCNParameters + i] > fMCMCBoundaryMax[i])
            flagin = false;

   if (flagin == false)
   {
      fMCMCInitialPosition.clear();
      return;
   }
   // copy this intial position into the particular Markov chain
   else
      for (int i = 0; i < fMCMCNParameters; ++i)
         fMCMCInitialPosition[chain * fMCMCNParameters + i] = x0.at(i);

   // use this intial position for the Markov chain
   this -> MCMCSetFlagInitialPosition(2);
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCSetInitialPosition(std::vector<double> x0)
{
   for (int i = 0; i < fMCMCNChains; ++i)
      this -> MCMCSetInitialPosition(i, x0);
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCSetInitialPositions(std::vector<double> x0s)
{
   if (int(fMCMCInitialPosition.size()) != (fMCMCNChains * fMCMCNParameters))
      return;

   if (int(x0s.size()) != (fMCMCNChains * fMCMCNParameters))
      return;

   // copy these intial positions into the Markov chains
   for (int i = 0; i < (fMCMCNChains * fMCMCNParameters); ++i)
      fMCMCInitialPosition[i] = x0s.at(i);

   // use these intial positions for the Markov chain
   this -> MCMCSetFlagInitialPosition(2);
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCSetMarkovChainTrees(std::vector <TTree *> trees)
{
// clear vector
   fMCMCTrees.clear();

   // copy tree
   for (int i = 0; i < int(trees.size()); ++i)
      fMCMCTrees.push_back(trees[i]);
}

// --------------------------------------------------------

void BCEngineMCMC::Copy(BCEngineMCMC & enginemcmc) const
{}

// --------------------------------------------------------

void BCEngineMCMC::MCMCTrialFunction(std::vector <double> &x)
{
   // use uniform distribution for now
   for (int i = 0; i < fMCMCNParameters; ++i)
      x[i] = fMCMCTrialFunctionScale * 2.0 * (0.5 - fMCMCRandom -> Rndm());
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCTrialFunctionSingle(int ichain, int iparameter, std::vector <double> &x)
{
   // no check of range for performance reasons

   // use uniform distribution
   x[iparameter] = fMCMCTrialFunctionScaleFactor[ichain * fMCMCNParameters + iparameter] * 2.0 * (0.5 - fMCMCRandom -> Rndm());
}

// --------------------------------------------------------

double BCEngineMCMC::MCMCTrialFunctionIndependent(std::vector <double> &xnew, std::vector <double> &xold, bool newpoint)
{
   // use uniform distribution for now
   if (newpoint)
      for (int i = 0; i < fMCMCNParameters; ++i)
         xnew[i] = fMCMCRandom -> Rndm() * (fMCMCBoundaryMax.at(i) - fMCMCBoundaryMin.at(i));

   double prob = 1.0;
   for (int i = 0; i < fMCMCNParameters; ++i)
      prob /= fMCMCBoundaryMax.at(i) - fMCMCBoundaryMin.at(i);

   return prob;
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCTrialFunctionAuto(std::vector <double> &x)
{
   // use uniform distribution for now
   for (int i = 0; i < fMCMCNParameters; ++i)
      x[i] = fMCMCRandom -> Gaus(fMCMCPCAMean[i], sqrt(fMCMCPCAVariance[i]));
}

// --------------------------------------------------------

std::vector <double> BCEngineMCMC::MCMCGetTrialFunctionScaleFactor(int ichain)
{
   // create a new vector with the length of fMCMCNParameters
   std::vector <double> x;

   // check if ichain is in range
   if (ichain < 0 || ichain >= fMCMCNChains)
      return x;

   // copy the scale factors into the temporary vector
   for (int j = 0; j < fMCMCNParameters; ++j)
      x.push_back(fMCMCTrialFunctionScaleFactor.at(ichain * fMCMCNParameters + j));

   return x;
}

// --------------------------------------------------------

double BCEngineMCMC::MCMCGetTrialFunctionScaleFactor(int ichain, int ipar)
{
   // check if ichain is in range
   if (ichain < 0 || ichain >= fMCMCNChains)
      return 0;

   // check if ipar is in range
   if (ipar < 0 || ipar >= fMCMCNParameters)
      return 0;

   // return component of ipar point in the ichain chain
   return fMCMCTrialFunctionScaleFactor.at(ichain *  fMCMCNChains + ipar);
}

// --------------------------------------------------------

std::vector <double> BCEngineMCMC::MCMCGetx(int ichain)
{
   // create a new vector with the length of fMCMCNParameters
   std::vector <double> x;

   // check if ichain is in range
   if (ichain < 0 || ichain >= fMCMCNChains)
      return x;

   // copy the point in the ichain chain into the temporary vector
   for (int j = 0; j < fMCMCNParameters; ++j)
      x.push_back(fMCMCx.at(ichain * fMCMCNParameters + j));

   return x;
}

// --------------------------------------------------------

double BCEngineMCMC::MCMCGetx(int ichain, int ipar)
{
   // check if ichain is in range
   if (ichain < 0 || ichain >= fMCMCNChains)
      return 0;

   // check if ipar is in range
   if (ipar < 0 || ipar >= fMCMCNParameters)
      return 0;

   // return component of jth point in the ith chain
   return fMCMCx.at(ichain *  fMCMCNParameters + ipar);
}

// --------------------------------------------------------

double BCEngineMCMC::MCMCGetLogProbx(int ichain)
{
   // check if ichain is in range
   if (ichain < 0 || ichain >= fMCMCNChains)
      return -1;

   // return log of the probability at the current point in the ith chain
   return fMCMCLogProbx.at(ichain);
}

// --------------------------------------------------------

bool BCEngineMCMC::MCMCGetProposalPointMetropolis(int chain, std::vector <double> &x, bool pca)
{
   // get unscaled random point. this point might not be in the correct volume.
   this -> MCMCTrialFunction(x);

   // shift the point to the old point (x0) and scale it.
   if (pca == false)
   {
      // get a proposal point from the trial function and scale it
      for (int i = 0; i < fMCMCNParameters; ++i)
         x[i] = fMCMCx[chain * fMCMCNParameters + i] + x[i] * (fMCMCBoundaryMax.at(i) - fMCMCBoundaryMin.at(i));
   }
   else
   {
      // create temporary points in x and p space
      double * newp = new double[fMCMCNParameters];
      double * newx = new double[fMCMCNParameters];

      for (int i = 0; i < fMCMCNParameters; i++)
      {
         newp[i] = 0.;
         newx[i] = 0.;
      }

      // get a new trial point
      this -> MCMCTrialFunctionAuto(x);

      // get the old point in x space
      for (int i = 0; i < fMCMCNParameters; i++)
         newx[i] = fMCMCx[chain * fMCMCNParameters + i];

      // transform the old point into p space
      fMCMCPCA -> X2P(newx, newp);

      // add new trial point to old point
      for (int i = 0; i < fMCMCNParameters; i++)
         newp[i] += fMCMCTrialFunctionScale * x[i];

      // transform new point back to x space
//    fMCMCPCA -> P2X(newp, newx, fMCMCNParameters);
      fMCMCPCA -> P2X(newp, newx, fMCMCNDimensionsPCA);

      // copy point into vector
      for (int i = 0; i < fMCMCNParameters; ++i)
         x[i] = newx[i];

      delete [] newp;
      delete [] newx;
   }

   // check if the point is in the correct volume.
   for (int i = 0; i < fMCMCNParameters; ++i)
      if ((x[i] < fMCMCBoundaryMin[i]) || (x[i] > fMCMCBoundaryMax[i]))
         return false;

   return true;
}
// --------------------------------------------------------

bool BCEngineMCMC::MCMCGetProposalPointMetropolis(int chain, int parameter, std::vector <double> &x, bool pca)
{
   // get unscaled random point in the dimension of the chosen
   // parameter. this point might not be in the correct volume.
   this -> MCMCTrialFunctionSingle(chain, parameter, x);

   // shift the point to the old point (x0) and scale it.
   if (pca == false)
   {
      // copy the old point into the new
      for (int i = 0; i < fMCMCNParameters; ++i)
         if (i != parameter)
            x[i] = fMCMCx[chain * fMCMCNParameters + i];

      // modify the parameter under study
      x[parameter] = fMCMCx[chain * fMCMCNParameters + parameter] + x[parameter] * (fMCMCBoundaryMax.at(parameter) - fMCMCBoundaryMin.at(parameter));
   }
   else
   {
      // create temporary points in x and p space
      double * newp = new double[fMCMCNParameters];
      double * newx = new double[fMCMCNParameters];

      for (int i = 0; i < fMCMCNParameters; i++)
      {
         newp[i] = 0.;
         newx[i] = 0.;
      }

      // get the old point in x space
      for (int i = 0; i < fMCMCNParameters; i++)
         newx[i] = fMCMCx[chain * fMCMCNParameters + i];

      // transform the old point into p space
      fMCMCPCA -> X2P(newx, newp);

      // add new trial point to old point
      newp[parameter] += x[parameter] * sqrt(fMCMCPCAVariance[parameter]);

      // transform new point back to x space
//    fMCMCPCA -> P2X(newp, newx, fMCMCNParameters);
      fMCMCPCA -> P2X(newp, newx, fMCMCNDimensionsPCA);

      // copy point into vector
      for (int i = 0; i < fMCMCNParameters; ++i)
         x[i] = newx[i];

      delete [] newp;
      delete [] newx;
   }

   // check if the point is in the correct volume.
   for (int i = 0; i < fMCMCNParameters; ++i)
      if ((x[i] < fMCMCBoundaryMin[i]) || (x[i] > fMCMCBoundaryMax[i]))
         return false;

   return true;
}

// --------------------------------------------------------

bool BCEngineMCMC::MCMCGetProposalPointMetropolisHastings(int chain, std::vector <double> &xnew, std::vector <double> &xold)
{
   // get a scaled random point.
   this -> MCMCTrialFunctionIndependent(xnew, xold, true);

   // check if the point is in the correct volume.
   for (int i = 0; i < fMCMCNParameters; ++i)
      if ((xnew[i] < fMCMCBoundaryMin[i]) || (xnew[i] > fMCMCBoundaryMax[i]))
         return false;

   return true;
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCGetNewPointPCA()
{
   // get random point in allowed parameter space
   for (int i = 0; i < fMCMCNParameters; ++i)
      fMCMCx[i] = fMCMCBoundaryMin.at(i) + (fMCMCBoundaryMax.at(i) - fMCMCBoundaryMin.at(i)) * 2.0 * (0.5 - fMCMCRandom -> Rndm());
}

// --------------------------------------------------------

bool BCEngineMCMC::MCMCGetNewPointMetropolis(int chain, int parameter, bool pca)
{
   // calculate index
   int index = chain * fMCMCNParameters;

   // get proposal point
   int counter = 0;

   while (!this -> MCMCGetProposalPointMetropolis(chain, parameter, fMCMCxLocal, pca) && counter < 1000)
      counter++;

   // calculate probabilities of the old and new points
   double p0 = fMCMCLogProbx[chain];
   double p1 = this -> LogEval(fMCMCxLocal);

   // flag for accept
   bool accept = false;

   // if the new point is more probable, keep it ...
   if (p1 >= p0)
      accept = true;
   // ... or else throw dice.
   else
   {
      double r = log(fMCMCRandom -> Rndm());

      if(r < p1 - p0)
         accept = true;
   }

   // fill the new point
   if(accept)
   {
      // increase counter
      fMCMCNTrialsTrue[chain * fMCMCNParameters + parameter]++;

      // copy the point
      for(int i = 0; i < fMCMCNParameters; ++i)
      {
         // save the point
         fMCMCx[index + i] = fMCMCxLocal[i];

         // save the probability of the point
         fMCMCLogProbx[chain] = p1;
      }
   }
   else
   {
      // increase counter
      fMCMCNTrialsFalse[chain * fMCMCNParameters + parameter]++;
   }

   // increase counter
   fMCMCNIterations[chain]++;

   return accept;
}

// --------------------------------------------------------

bool BCEngineMCMC::MCMCGetNewPointMetropolis(int chain, bool pca)
{
   // calculate index
   int index = chain * fMCMCNParameters;

   // get proposal point
   int counter = 0;

   while (!this -> MCMCGetProposalPointMetropolis(chain, fMCMCxLocal, pca) && counter < 1000)
      counter++;

   // calculate probabilities of the old and new points
   double p0 = fMCMCLogProbx[chain];
   double p1 = this -> LogEval(fMCMCxLocal);

   // flag for accept
   bool accept = false;

   // if the new point is more probable, keep it ...
   if (p1 >= p0)
      accept = true;

   // ... or else throw dice.
   else
   {
      double r = log(fMCMCRandom -> Rndm());

      if(r < p1 - p0)
         accept = true;
   }

   // fill the new point
   if(accept)
   {
      // increase counter
      for (int i = 0; i < fMCMCNParameters; ++i)
         fMCMCNTrialsTrue[chain * fMCMCNParameters + i]++;

      // copy the point
      for(int i = 0; i < fMCMCNParameters; ++i)
      {
         // save the point
         fMCMCx[index + i] = fMCMCxLocal[i];

         // save the probability of the point
         fMCMCLogProbx[chain] = p1;
      }
   }
   else
   {
      // increase counter
      for (int i = 0; i < fMCMCNParameters; ++i)
         fMCMCNTrialsFalse[chain * fMCMCNParameters + i]++;
   }

   // increase counter
   fMCMCNIterations[chain]++;

   return accept;
}

// --------------------------------------------------------

bool BCEngineMCMC::MCMCGetNewPointMetropolisHastings(int chain)
{
   // calculate index
   int index = chain * fMCMCNParameters;

   // save old point
   std::vector <double> xold;
   for (int i = 0; i < fMCMCNParameters; ++i)
      xold.push_back(fMCMCxLocal.at(i));

   // get proposal point
   int counter = 0;
   while (!this -> MCMCGetProposalPointMetropolisHastings(chain, fMCMCxLocal, xold) && counter < 1000)
      counter++;

   // calculate probabilities of the old and new points
   double p0 = fMCMCLogProbx[chain] + log(this -> MCMCTrialFunctionIndependent(xold, fMCMCxLocal, false));
   double p1 = this -> LogEval(fMCMCxLocal) + log(this -> MCMCTrialFunctionIndependent(xold, fMCMCxLocal, false));

   // flag for accept
   bool accept = false;

   // if the new point is more probable, keep it ...
   if (p1 >= p0)
      accept = true;
   // ... or else throw dice.
   else
   {
      if( log(fMCMCRandom -> Rndm()) < p1 - p0)
         accept = true;
   }

   // fill the new point
   if(accept)
   {
      // increase counter
      for (int i = 0; i < fMCMCNParameters; ++i)
         fMCMCNTrialsTrue[chain * fMCMCNParameters + i]++;

      // copy the point
      for(int i = 0; i < fMCMCNParameters; ++i)
      {
         // save the point
         fMCMCx[index + i] = fMCMCxLocal[i];

         // save the probability of the point
         fMCMCLogProbx[chain] = p1;
      }
   }
   else
   {
      // increase counter
      for (int i = 0; i < fMCMCNParameters; ++i)
         fMCMCNTrialsFalse[chain * fMCMCNParameters + i]++;
   }

   // increase counter
   fMCMCNIterations[chain]++;

   return accept;
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCUpdateStatisticsModeConvergence()
{
   double * mode_minimum = new double[fMCMCNParameters];
   double * mode_maximum = new double[fMCMCNParameters];
   double * mode_average = new double[fMCMCNParameters];

   // set initial values
   for (int j = 0; j < fMCMCNParameters; ++j)
   {
      mode_minimum[j] = fMCMCMaximumPoints[j];
      mode_maximum[j] = fMCMCMaximumPoints[j];
      mode_average[j] = 0;
   }

   // calculate the maximum difference in each dimension
   for (int i = 0; i < fMCMCNChains; ++i)
      for (int j = 0; j < fMCMCNParameters; ++j)
      {
         if (fMCMCMaximumPoints[i * fMCMCNParameters + j] < mode_minimum[j])
            mode_minimum[j] = fMCMCMaximumPoints[i * fMCMCNParameters + j];

         if (fMCMCMaximumPoints[i * fMCMCNParameters + j] > mode_maximum[j])
            mode_maximum[j] = fMCMCMaximumPoints[i * fMCMCNParameters + j];

         mode_average[j] += fMCMCMaximumPoints[i * fMCMCNParameters + j] / double(fMCMCNChains);
      }

   for (int j = 0; j < fMCMCNParameters; ++j)
      fMCMCNumericalPrecisionModeValues[j] = (mode_maximum[j] - mode_minimum[j]);
//    fMCMCRelativePrecisionModeValues[j] = (mode_maximum[j] - mode_minimum[j]) / mode_average[j];

   delete [] mode_minimum;
   delete [] mode_maximum;
   delete [] mode_average;
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCUpdateStatisticsCheckMaximum()
{
   // loop over all chains
   for (int i = 0; i < fMCMCNChains; ++i)
   {
      if (fMCMCLogProbx[i] > fMCMCMaximumLogProb[i] || fMCMCNIterations[i] == 1)
      {
         fMCMCMaximumLogProb[i] = fMCMCLogProbx[i];
         for (int j = 0; j < fMCMCNParameters; ++j)
            fMCMCMaximumPoints[i * fMCMCNParameters + j] = fMCMCx[i * fMCMCNParameters + j];
      }
   }
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCUpdateStatisticsFillHistograms()
{
   // loop over chains
   for (int i = 0; i < fMCMCNChains; ++i)
   {
      // fill each 1-dimensional histogram
      for (int j = 0; j < fMCMCNParameters; ++j)
         fMCMCH1Marginalized[j] -> Fill(fMCMCx[i * fMCMCNParameters + j]);

      // fill each 2-dimensional histogram
      int counter = 0;

      for (int j = 0; j < fMCMCNParameters; ++j)
         for (int k = 0; k < j; ++k)
         {
            fMCMCH2Marginalized[counter] -> Fill(
                  fMCMCx[i * fMCMCNParameters + k],
                  fMCMCx[i * fMCMCNParameters + j]);
            counter ++;
         }
   }
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCUpdateStatisticsTestConvergenceAllChains()
{
  // calculate number of entries in this part of the chain   
  int npoints = fMCMCNTrialsTrue[0] + fMCMCNTrialsFalse[0]; 

  // do not evaluate the convergence criterion if the numbers of
  // elements is too small.
   //  if (npoints < fMCMCNIterationsPreRunMin) 
   //    {
   //      fMCMCNIterationsConvergenceGlobal = -1;      
   //      return; 
   //    }
  
  if (fMCMCNChains > 1 && npoints > 1)
    {
      // define flag for convergence       
      bool flag_convergence = true; 
      
      // loop over parameters       
      for (int iparameters = 0; iparameters < fMCMCNParameters; ++iparameters)
            {
               double sum = 0; 
               double sum2 = 0; 
               double sumv = 0; 
     
               // loop over chains              
               for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
                  {
                     // get parameter index
                     int index = ichains * fMCMCNParameters + iparameters; 
                     
                     // calculate mean value of each parameter in the chain for this part                      
                     fMCMCMeanx[index] += (fMCMCx[index] - fMCMCMeanx[index]) / double(npoints);   
                     
                     // calculate variance of each chain for this part                    
                     fMCMCVariancex[index] = (1.0 - 1/double(npoints)) * fMCMCVariancex[index] 
                        + (fMCMCx[index] - fMCMCMeanx[index]) * (fMCMCx[index] - fMCMCMeanx[index]) / double(npoints - 1); 
                     
                     sum  += fMCMCMeanx[index]; 
                     sum2 += fMCMCMeanx[index] * fMCMCMeanx[index]; 
                     sumv += fMCMCVariancex[index]; 
                  }
               
               // calculate r-value for each parameter               
               double mean = sum / double(fMCMCNChains); 
               double B = (sum2 / double(fMCMCNChains) - mean * mean) * double(fMCMCNChains) / double(fMCMCNChains-1) * double(npoints); 
               double W = sumv * double(npoints) / double(npoints - 1) / double(fMCMCNChains); 
               
               double r = 100.0; 
               
               if (W > 0)
                  {
                     r = sqrt( ( (1-1/double(npoints)) * W + 1/double(npoints) * B ) / W); 
                     
                     fMCMCRValueParameters[iparameters] = r; 
                  }
               // debugKK
               //             std::cout << " here : " << W << " " << fMCMCRValueParameters[iparameters] << std::endl; 
               
               // set flag to false if convergence criterion is not fulfilled for the parameter                
               if (! ((fMCMCRValueParameters[iparameters]-1.0) < fMCMCRValueParametersCriterion))
                  flag_convergence = false; 
            }
      
      // convergence criterion applied on the log-likelihood         
      double sum = 0; 
      double sum2 = 0; 
      double sumv = 0; 
      
      // loop over chains       
      for (int i = 0; i < fMCMCNChains; ++i)
            {
               // calculate mean value of each chain for this part               
               fMCMCMean[i] += (fMCMCLogProbx[i] - fMCMCMean[i]) / double(npoints); 
               
               // calculate variance of each chain for this part              
               if (npoints > 1) 
                  fMCMCVariance[i] = (1.0 - 1/double(npoints)) * fMCMCVariance[i] 
                     + (fMCMCLogProbx[i] - fMCMCMean[i]) * (fMCMCLogProbx[i] - fMCMCMean[i]) / double(npoints - 1); 
               
               sum  += fMCMCMean[i]; 
               sum2 += fMCMCMean[i] * fMCMCMean[i]; ; 
               sumv += fMCMCVariance[i]; 
            }
      
      // calculate r-value for log-likelihood   
      double mean = sum / double(fMCMCNChains); 
      double B = (sum2 / double(fMCMCNChains) - mean * mean) * double(fMCMCNChains) / double(fMCMCNChains-1) * double(npoints); 
      double W = sumv * double(npoints) / double(npoints - 1) / double(fMCMCNChains);       
      double r = 100.0; 
      
      if (W > 0)
            {
               r = sqrt( ( (1-1/double(npoints)) * W + 1/double(npoints) * B ) / W); 
               
               fMCMCRValue = r; 
            }
         
      // set flag to false if convergence criterion is not fulfilled for the log-likelihood        
      if (! ((fMCMCRValue-1.0) < fMCMCRValueCriterion))
            flag_convergence = false; 
      
      // remember number of iterations needed to converge       
      if (fMCMCNIterationsConvergenceGlobal == -1 && flag_convergence == true)
            fMCMCNIterationsConvergenceGlobal = fMCMCNIterations[0] / fMCMCNParameters; 
    }
  
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCUpdateStatisticsWriteChains()
{
   // loop over all chains
   for (int i = 0; i < fMCMCNChains; ++i)
      fMCMCTrees[i] -> Fill();
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCUpdateStatistics()
{
   // check if maximum is reached
   this -> MCMCUpdateStatisticsCheckMaximum();

   // fill histograms of marginalized distributions
   this -> MCMCUpdateStatisticsFillHistograms();

   // test convergence of single Markov chains
   //  --> not implemented yet

   // test convergence of all Markov chains
   // debugKK -> this will be called explicitly
   // this -> MCMCUpdateStatisticsTestConvergenceAllChains();

   // fill Markov chains
   if (fMCMCFlagWriteChainToFile)
      this -> MCMCUpdateStatisticsWriteChains();
}

// --------------------------------------------------------

double BCEngineMCMC::LogEval(std::vector <double> parameters)
{
   // test function for now
   // this will be overloaded by the user
   return 0.0;
}

// --------------------------------------------------------

int BCEngineMCMC::MCMCMetropolisPreRun()
{
   // print on screen
   BCLog::Out(BCLog::summary, BCLog::summary, "Pre-run Metropolis MCMC...");

   // initialize Markov chain
   this -> MCMCInitialize();
   this -> MCMCInitializeMarkovChains();

   // helper variable containing number of digits in the number of parameters
   int ndigits = (int)log10(fMCMCNParameters) +1;
   if(ndigits<4)
      ndigits=4;

   // perform burn-in run
   if (fMCMCNIterationsBurnIn > 0)
      BCLog::Out(BCLog::detail, BCLog::detail,
            Form(" --> Start burn-in run with %i iterations", fMCMCNIterationsBurnIn));

   // if the flag is set then run over the parameters one after the other.
   if (fMCMCFlagOrderParameters)
   {
      for (int i = 0; i < fMCMCNIterationsBurnIn; ++i)
         for (int j = 0; j < fMCMCNChains; ++j)
            for (int k = 0; k < fMCMCNParameters; ++k)
               this -> MCMCGetNewPointMetropolis(j, k, false);
   }
   // if the flag is not set then run over the parameters at the same time.
   else
   {
      for (int i = 0; i < fMCMCNIterationsBurnIn; ++i)
      {
         // loop over chains
         for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
            // get new point
            this -> MCMCGetNewPointMetropolis(ichains, false);
      }
   }

   // reset run statistics
   this -> MCMCResetRunStatistics();
   fMCMCNIterationsConvergenceGlobal = -1;

   // define data buffer for pca run
   double * dataall = 0;
   double * sum = 0;
   double * sum2 = 0;

   // allocate memory if pca is switched on
   if (fMCMCFlagPCA)
   {
      BCLog::Out(BCLog::detail, BCLog::detail, " --> PCA switched on");

      // create new TPrincipal
      fMCMCPCA = new TPrincipal(fMCMCNParameters, "D");

      // create buffer of sampled points
      dataall = new double[fMCMCNParameters * fMCMCNIterationsPCA];

      // create buffer for the sum and the sum of the squares
      sum = new double[fMCMCNParameters];
      sum2 = new double[fMCMCNParameters];

      // reset the buffers
      for (int i = 0; i < fMCMCNParameters; ++i)
      {
         sum[i]  = 0.0;
         sum2[i] = 0.0;
      }

      if (fMCMCFlagPCATruncate == true)
      {
         fMCMCNDimensionsPCA = 0;

         const double * ma = fMCMCPCA -> GetEigenValues() -> GetMatrixArray();

         for (int i = 0; i < fMCMCNParameters; ++i)
            if (ma[i]/ma[0] > fMCMCPCAMinimumRatio)
               fMCMCNDimensionsPCA++;

         BCLog::Out(BCLog::detail, BCLog::detail,
               Form(" --> Use %i out of %i dimensions", fMCMCNDimensionsPCA, fMCMCNParameters));
      }
      else
         fMCMCNDimensionsPCA = fMCMCNParameters;
   }
   else
      BCLog::Out(BCLog::detail, BCLog::detail, " --> No PCA run");

   // reset run statistics
   this -> MCMCResetRunStatistics();
   fMCMCNIterationsConvergenceGlobal = -1;

   // perform run
   BCLog::Out(BCLog::summary, BCLog::summary,
         Form(" --> Perform MCMC pre-run with %i chains, each with maximum %i iterations", fMCMCNChains, fMCMCNIterationsMax));

   bool tempflag_writetofile = fMCMCFlagWriteChainToFile;

   // don't write to file during pre run
   fMCMCFlagWriteChainToFile = false;

   int counter = 0;
   int counterupdate = 0;
   bool convergence = false;
   bool flagefficiency = false;

   std::vector <double> efficiency;

   for (int i = 0; i < fMCMCNParameters; ++i)
      for (int j = 0; j < fMCMCNChains; ++j)
         efficiency.push_back(0.);

   if (fMCMCFlagPCA)
   {
      fMCMCNIterationsPreRunMin = fMCMCNIterationsPCA;
      fMCMCNIterationsMax = fMCMCNIterationsPCA;
   }

   // run chain
   while (counter < fMCMCNIterationsPreRunMin || (counter < fMCMCNIterationsMax && !(convergence && flagefficiency)))
   {
      // set convergence to false by default
      convergence = false;

      // debugKK
      fMCMCNIterationsConvergenceGlobal = -1; 

      // if the flag is set then run over the parameters one after the other.
      if (fMCMCFlagOrderParameters)
      {
         // loop over parameters
         for (int iparameters = 0; iparameters < fMCMCNParameters; ++iparameters)
         {
            // loop over chains
            for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
            {
               this -> MCMCGetNewPointMetropolis(ichains, iparameters, false);

               // save point for finding the eigenvalues
               if (fMCMCFlagPCA)
               {
                  // create buffer for the new point
                  double * data = new double[fMCMCNParameters];

                  // copy the current point
                  for (int j = 0; j < fMCMCNParameters; ++j)
                  {
                     data[j] = fMCMCx[j];
                     dataall[ichains * fMCMCNParameters + j] = fMCMCx[j];
                  }

                  // add point to PCA object
                  fMCMCPCA -> AddRow(data);

                  // delete buffer
                  delete [] data;

               } // end if fMCMCPCAflag
            } // end loop over chains

            // search for global maximum
            this -> MCMCUpdateStatisticsCheckMaximum();

            // check convergence status
            // debugKK
            //          this -> MCMCUpdateStatisticsTestConvergenceAllChains();

         } // end loop over parameters
      } // end if fMCMCFlagOrderParameters

      // if the flag is not set then run over the parameters at the same time.
      else
      {
         // loop over chains
         for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
            // get new point
            this -> MCMCGetNewPointMetropolis(ichains, false);

         // save point for finding the eigenvalues
         if (fMCMCFlagPCA)
         {
            // create buffer for the new point
            double * data = new double[fMCMCNParameters];

            // copy the current point
            for (int j = 0; j < fMCMCNParameters; ++j)
            {
               // loop over chains
               for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
               {
                  data[j] = fMCMCx[j];
                  dataall[ichains * fMCMCNParameters + j] = fMCMCx[j];
               }
            }

            // add point to PCA object
            fMCMCPCA -> AddRow(data);

            // delete buffer
            delete [] data;
         }

         // search for global maximum
         this -> MCMCUpdateStatisticsCheckMaximum();

         // check convergence status
         // debugKK
         //       this -> MCMCUpdateStatisticsTestConvergenceAllChains();
      }

      //-------------------------------------------
      // update scale factors and check convergence 
      //-------------------------------------------
      if (counterupdate % (fMCMCNIterationsUpdate*(fMCMCNParameters+1)) == 0 && counterupdate > 0 && counter >= fMCMCNIterationsPreRunMin)
      {
         // prompt status
         BCLog::Out(BCLog::detail, BCLog::detail,
               Form(" --> Iteration %i", fMCMCNIterations[0] / fMCMCNParameters));

         bool rvalues_ok = true;
         static bool has_converged = false;

         // -----------------------------
         // check convergence status
         // -----------------------------
         // debugKK
         fMCMCNIterationsConvergenceGlobal = -1; 

         this -> MCMCUpdateStatisticsTestConvergenceAllChains();

         // debugKK
         //       std::cout << " HERE " << fMCMCRValueParameters[0] << fMCMCNTrialsTrue[0] << " " << fMCMCNTrialsFalse[0] << std::endl; 

         // check convergence
         if (fMCMCNIterationsConvergenceGlobal > 0)
            convergence = true;
         
         // print convergence status: 
         if (convergence && fMCMCNChains > 1)
            BCLog::Out(BCLog::detail, BCLog::detail,
                            Form("     * Convergence status: Set of %i Markov chains converged within %i iterations.", fMCMCNChains, fMCMCNIterationsConvergenceGlobal));
         else if (!convergence && fMCMCNChains > 1)
            {
               BCLog::Out(BCLog::detail, BCLog::detail,
                            Form("     * Convergence status: Set of %i Markov chains did not converge after %i iterations.", fMCMCNChains, counter));
               
               BCLog::Out(BCLog::detail, BCLog::detail, "       - R-Values:");
               for (int iparameter = 0; iparameter < fMCMCNParameters; ++iparameter)
                  {
                     if(fabs(fMCMCRValueParameters[iparameter]-1.) < fMCMCRValueParametersCriterion)
                        BCLog::Out(BCLog::detail, BCLog::detail,
                                        Form( TString::Format("         parameter %%%di :  %%.06f",ndigits), iparameter, fMCMCRValueParameters.at(iparameter)));
                     else
                        {
                           BCLog::Out(BCLog::detail, BCLog::detail,
                                           Form( TString::Format("         parameter %%%di :  %%.06f <--",ndigits), iparameter, fMCMCRValueParameters.at(iparameter)));
                           rvalues_ok = false;
                        }
                  }
               if(fabs(fMCMCRValue-1.) < fMCMCRValueCriterion)
                  BCLog::Out(BCLog::detail, BCLog::detail, Form("         log-likelihood :  %.06f", fMCMCRValue));
               else
                  {
                     BCLog::Out(BCLog::detail, BCLog::detail, Form("         log-likelihood :  %.06f <--", fMCMCRValue));
                     rvalues_ok = false;
                  }
            }

         if(!has_converged)
            if(rvalues_ok)
               has_converged = true;

         // -----------------------------
         // check efficiency status
         // -----------------------------

         // set flag
         flagefficiency = true;

         bool flagprintefficiency = true; 

         // loop over chains
         for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
         {
            // loop over parameters
            for (int iparameter = 0; iparameter < fMCMCNParameters; ++iparameter)
            {
               // global index of the parameter (throughout all the chains)
               int ipc = ichains * fMCMCNParameters + iparameter;

               // calculate efficiency
               efficiency[ipc] = double(fMCMCNTrialsTrue[ipc]) / double(fMCMCNTrialsTrue[ipc] + fMCMCNTrialsFalse[ipc]);

               // adjust scale factors if efficiency is too low
               if (efficiency[ipc] < fMCMCEfficiencyMin && fMCMCTrialFunctionScaleFactor[ipc] > .01)
               {
                  if (flagprintefficiency)
                     {
                        BCLog::Out(BCLog::detail, BCLog::detail,
                                        Form("     * Efficiency status: Efficiencies not within pre-defined range."));
                        BCLog::Out(BCLog::detail, BCLog::detail, 
                                        Form("       - Efficiencies:"));
                        flagprintefficiency = false; 
                     }

                  double fscale=2.;
                  if(has_converged && fMCMCEfficiencyMin/efficiency[ipc] > 2.)
                     fscale = 4.;
                  fMCMCTrialFunctionScaleFactor[ipc] /= fscale;

                  BCLog::Out(BCLog::detail, BCLog::detail,
                        Form("         Efficiency of parameter %i dropped below %.2lf%% (eps = %.2lf%%) in chain %i. Set scale to %.4g",
                              iparameter, 100. * fMCMCEfficiencyMin, 100. * efficiency[ipc], ichains, fMCMCTrialFunctionScaleFactor[ipc]));
               }

               // adjust scale factors if efficiency is too high
               else if (efficiency[ipc] > fMCMCEfficiencyMax && (fMCMCTrialFunctionScaleFactor[ipc] < 1. || (fMCMCFlagPCA && fMCMCTrialFunctionScaleFactor[ipc] < 10.)))
               {
                  if (flagprintefficiency)
                     {
                        BCLog::Out(BCLog::detail, BCLog::detail,
                                        Form("   * Efficiency status: Efficiencies not within pre-defined ranges."));
                        BCLog::Out(BCLog::detail, BCLog::detail, 
                                        Form("     - Efficiencies:"));
                        flagprintefficiency = false; 
                     }

                  fMCMCTrialFunctionScaleFactor[ipc] *= 2.;

                  BCLog::Out(BCLog::detail, BCLog::detail,
                                  Form("         Efficiency of parameter %i above %.2lf%% (eps = %.2lf%%) in chain %i. Set scale to %.4g",
                                          iparameter, 100.0 * fMCMCEfficiencyMax, 100.0 * efficiency[ipc], ichains, fMCMCTrialFunctionScaleFactor[ipc]));
               }

               // check flag
               if ((efficiency[ipc] < fMCMCEfficiencyMin && fMCMCTrialFunctionScaleFactor[ipc] > .01)
                     || (efficiency[ipc] > fMCMCEfficiencyMax && fMCMCTrialFunctionScaleFactor[ipc] < 1.))
                  flagefficiency = false;

               // reset counters
               counterupdate = 0;
               fMCMCNTrialsTrue[ipc] = 0;
               fMCMCNTrialsFalse[ipc] = 0;
            } // end of running over all parameters 

            // reset counters
            fMCMCMean[ichains] = 0;
            fMCMCVariance[ichains] = 0;
         } // end of running over all chains 
         
         // print to scrren 
         if (flagefficiency)
            BCLog::Out(BCLog::detail, BCLog::detail,
                            Form("     * Efficiency status: Efficiencies within pre-defined ranges.")); 
         
      } // end if update scale factors and check convergence

      // increase counter
      counter++;
      counterupdate++;

      // debugKK
//       // check convergence
//       if (fMCMCNIterationsConvergenceGlobal > 0)
//          convergence = true;
   } // end of running 

   // ---------------
   // after chain ran
   // ---------------

   // define convergence status
   if (fMCMCNIterationsConvergenceGlobal > 0)
      fMCMCFlagConvergenceGlobal = true;
   else
      fMCMCFlagConvergenceGlobal = false;

   // print convergence status
   if (fMCMCFlagConvergenceGlobal && fMCMCNChains > 1 && !flagefficiency)
      BCLog::Out(BCLog::summary, BCLog::summary,
            Form(" --> Set of %i Markov chains converged within %i iterations but could not adjust scales.", fMCMCNChains, fMCMCNIterationsConvergenceGlobal));

   else if (fMCMCFlagConvergenceGlobal && fMCMCNChains > 1 && flagefficiency)
      BCLog::Out(BCLog::summary, BCLog::summary,
            Form(" --> Set of %i Markov chains converged within %i iterations and could adjust scales.", fMCMCNChains, fMCMCNIterationsConvergenceGlobal));

   else if (!fMCMCFlagConvergenceGlobal && (fMCMCNChains > 1) && flagefficiency)
      BCLog::Out(BCLog::summary, BCLog::summary,
             Form(" --> Set of %i Markov chains did not converge within %i iterations.", fMCMCNChains, fMCMCNIterationsMax));

   else if (!fMCMCFlagConvergenceGlobal && (fMCMCNChains > 1) && !flagefficiency)
      BCLog::Out(BCLog::summary, BCLog::summary,
             Form(" --> Set of %i Markov chains did not converge within %i iterations and could not adjust scales.", fMCMCNChains, fMCMCNIterationsMax));

   else if(fMCMCNChains == 1)
      BCLog::Out(BCLog::summary, BCLog::summary,
             " --> No convergence criterion for a single chain defined.");

   else
      BCLog::Out(BCLog::summary, BCLog::summary,
            " --> Only one Markov chain. No global convergence criterion defined.");

   BCLog::Out(BCLog::summary, BCLog::summary,
         Form(" --> Markov chains ran for %i iterations.", counter));


   // print efficiencies
   std::vector <double> efficiencies;

   for (int i = 0; i < fMCMCNParameters; ++i)
      efficiencies.push_back(0.);

   BCLog::Out(BCLog::detail, BCLog::detail, " --> Average efficiencies:");
   for (int i = 0; i < fMCMCNParameters; ++i)
   {
      for (int j = 0; j < fMCMCNChains; ++j)
         efficiencies[i] += efficiency[j * fMCMCNParameters + i] / double(fMCMCNChains);

      BCLog::Out(BCLog::detail, BCLog::detail,
            Form( TString::Format(" -->      parameter %%%di :  %%.02f%%%%",ndigits), i, 100. * efficiencies[i]));
   }


   // print scale factors
   std::vector <double> scalefactors;

   for (int i = 0; i < fMCMCNParameters; ++i)
      scalefactors.push_back(0.0);

   BCLog::Out(BCLog::detail, BCLog::detail, " --> Average scale factors:");
   for (int i = 0; i < fMCMCNParameters; ++i)
   {
      for (int j = 0; j < fMCMCNChains; ++j)
         scalefactors[i] += fMCMCTrialFunctionScaleFactor[j * fMCMCNParameters + i] / double(fMCMCNChains);

      BCLog::Out(BCLog::detail, BCLog::detail,
            Form( TString::Format(" -->      parameter %%%di :  %%.02f%%%%",ndigits), i, 100. * scalefactors[i]));
   }


   // perform PCA analysis
   if (fMCMCFlagPCA)
   {

      // calculate eigenvalues and vectors
      fMCMCPCA -> MakePrincipals();

      // re-run over data points to gain a measure for the spread of the variables
      for (int i = 0; i < fMCMCNIterationsPCA; ++i)
      {
         double * data = new double[fMCMCNParameters];
         double * p    = new double[fMCMCNParameters];

         for (int j = 0; j < fMCMCNParameters; ++j)
            data[j] = dataall[i * fMCMCNParameters + j];

         fMCMCPCA -> X2P(data, p);

         for (int j = 0; j < fMCMCNParameters; ++j)
         {
            sum[j]  += p[j];
            sum2[j] += p[j] * p[j];
         }

         delete [] data;
         delete [] p;
      }

      delete [] dataall;

      fMCMCPCAMean.clear();
      fMCMCPCAVariance.clear();

      // calculate mean and variance
      for (int j = 0; j < fMCMCNParameters; ++j)
      {
         fMCMCPCAMean.push_back(sum[j] / double(fMCMCNIterationsPCA) / double(fMCMCNChains));
         fMCMCPCAVariance.push_back(sum2[j] / double(fMCMCNIterationsPCA) / double(fMCMCNChains) - fMCMCPCAMean[j] * fMCMCPCAMean[j]);
      }

      // check if all eigenvalues are found
      int neigenvalues = fMCMCPCA -> GetEigenValues() -> GetNoElements();

      const double * eigenv = fMCMCPCA -> GetEigenValues() -> GetMatrixArray();

      bool flageigenvalues = true;

      for (int i = 0; i < neigenvalues; ++i)
         if (isnan(eigenv[i]))
            flageigenvalues = false;

      // print on screen
      if (flageigenvalues)
         BCLog::Out(BCLog::detail, BCLog::detail, " --> PCA : All eigenvalues ok.");
      else
      {
         BCLog::Out(BCLog::detail, BCLog::detail, " --> PCA : Not all eigenvalues ok. Don't use PCA.");
         fMCMCFlagPCA = false;
      }

      // reset scale factors
      for (int i = 0; i < fMCMCNParameters; ++i)
         for (int j = 0; j < fMCMCNChains; ++j)
            fMCMCTrialFunctionScaleFactor[j * fMCMCNParameters + i] = 1.0;

      if (DEBUG)
      {
         fMCMCPCA -> Print("MSEV");

         for (int j = 0; j < fMCMCNParameters; ++j)
            std::cout << fMCMCPCAMean.at(j) << " " << sqrt(fMCMCPCAVariance.at(j)) << std::endl;
      }

   }

   // fill efficiency plot
   // for (int i = 0; i < fMCMCNParameters; ++i)
   //    fMCMCH1Efficiency -> SetBinContent(i + 1, efficiencies[i]);

   // reset flag
   fMCMCFlagWriteChainToFile = tempflag_writetofile;

   // set flag
   fMCMCFlagPreRun = true;

   return 1;

}

// --------------------------------------------------------

int BCEngineMCMC::MCMCMetropolis()
{
   // check if prerun has been performed
   if (!fMCMCFlagPreRun)
      this -> MCMCMetropolisPreRun();

   // print to screen
   BCLog::Out(BCLog::summary, BCLog::summary, "Run Metropolis MCMC...");

   if (fMCMCFlagPCA)
      BCLog::Out(BCLog::detail, BCLog::detail, " --> PCA switched on");

   // reset run statistics
   this -> MCMCResetRunStatistics();

   // perform run
   BCLog::Out(BCLog::summary, BCLog::summary,
         Form(" --> Perform MCMC run with %i chains, each with %i iterations.", fMCMCNChains, fMCMCNIterationsRun));

// int counterupdate = 0;
// bool convergence = false;
// bool flagefficiency = false;

// std::vector <double> efficiency;

// for (int i = 0; i < fMCMCNParameters; ++i)
//    for (int j = 0; j < fMCMCNChains; ++j)
//       efficiency.push_back(0.0);

   int nwrite = fMCMCNIterationsRun/10;
   if(nwrite < 100)
      nwrite=100;
   else if(nwrite < 500)
      nwrite=1000;
   else if(nwrite < 10000)
      nwrite=1000;
   else
      nwrite=10000;

   // start the run
   for (int iiterations = 0; iiterations < fMCMCNIterationsRun; ++iiterations)
   {
      if ( (iiterations+1)%nwrite == 0 )
         BCLog::Out(BCLog::detail, BCLog::detail,
               Form(" --> iteration number %i (%.2f%%)", iiterations+1, (double)(iiterations+1)/(double)fMCMCNIterationsRun*100.));

      // if the flag is set then run over the parameters one after the other.
      if (fMCMCFlagOrderParameters)
      {
         // loop over parameters
         for (int iparameters = 0; iparameters < fMCMCNParameters; ++iparameters)
            {
               // loop over chains
               for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
                  this -> MCMCGetNewPointMetropolis(ichains, iparameters, fMCMCFlagPCA);

               // update statistics
               this -> MCMCUpdateStatistics();

               // do anything interface
               this -> MCMCIterationInterface();
            } // end loop over all parameters
      }
      // if the flag is not set then run over the parameters at the same time.
      else
      {
         // loop over chains
         for (int ichains = 0; ichains < fMCMCNChains; ++ichains)
            // get new point
            this -> MCMCGetNewPointMetropolis(ichains, false);

         // update statistics
         this -> MCMCUpdateStatistics();

         // do anything interface
         this -> MCMCIterationInterface();
      }
   } // end run

   // print convergence status
   BCLog::Out(BCLog::summary, BCLog::summary,
         Form(" --> Markov chains ran for %i iterations.", fMCMCNIterationsRun));

   // print modes

   // find global maximum
   double probmax = fMCMCMaximumLogProb.at(0);
   int probmaxindex = 0;

   // loop over all chains and find the maximum point
   for (int i = 1; i < fMCMCNChains; ++i)
   if (fMCMCMaximumLogProb.at(i) > probmax)
   {
      probmax = fMCMCMaximumLogProb.at(i);
      probmaxindex = i;
   }

   BCLog::Out(BCLog::detail, BCLog::detail, " --> Global mode from MCMC:");
   int ndigits = (int) log10(fMCMCNParameters);
   for (int i = 0; i < fMCMCNParameters; ++i)
      BCLog::Out(BCLog::detail, BCLog::detail,
            Form( TString::Format(" -->      parameter %%%di:   %%.4g", ndigits+1),
                  i, fMCMCMaximumPoints[probmaxindex * fMCMCNParameters + i]));

   // set flag
   fMCMCFlagPreRun = false;

   return 1;
}

// --------------------------------------------------------

int BCEngineMCMC::MCMCMetropolisHastings()
{
   BCLog::Out(BCLog::summary, BCLog::summary, "Run Metropolis-Hastings MCMC.");

   // initialize Markov chain
   this -> MCMCInitializeMarkovChains();

   // perform burn-in run
   BCLog::Out(BCLog::detail, BCLog::detail, Form(" --> Start burn-in run with %i iterations.", fMCMCNIterationsBurnIn));
   for (int i = 0; i < fMCMCNIterationsBurnIn; ++i)
      for (int j = 0; j < fMCMCNChains; ++j)
         this -> MCMCGetNewPointMetropolisHastings(j);

   // reset run statistics
   this -> MCMCResetRunStatistics();

   // perform run
   BCLog::Out(BCLog::detail, BCLog::detail, Form(" --> Perform MCMC run with %i iterations.", fMCMCNIterationsMax));
   for (int i = 0; i < fMCMCNIterationsMax; ++i)
   {
      for (int j = 0; j < fMCMCNChains; ++j)
         // get new point and increase counters
         this -> MCMCGetNewPointMetropolisHastings(j);

      // update statistics
      this -> MCMCUpdateStatistics();

      // call user interface
      this -> MCMCIterationInterface();
   }

   if (fMCMCNIterationsConvergenceGlobal > 0)
      BCLog::Out(BCLog::detail, BCLog::detail,
            Form(" --> Set of %i Markov chains converged within %i iterations.", fMCMCNChains, fMCMCNIterationsConvergenceGlobal));
   else
      BCLog::Out(BCLog::detail, BCLog::detail,
            Form(" --> Set of %i Markov chains did not converge within %i iterations.", fMCMCNChains, fMCMCNIterationsMax));

   // debug
   if (DEBUG)
   {
      for (int i = 0; i < fMCMCNChains; ++i)
      {
         std::cout << i << " " << fMCMCMaximumLogProb[i] << std::endl;
         for (int j = 0; j < fMCMCNParameters; ++j)
            std::cout << fMCMCMaximumPoints[i * fMCMCNParameters + j] << " ";
         std::cout << std::endl;
      }
   }

   return 1;
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCResetRunStatistics()
{
   // debugKK -> this is set explicitly
   // fMCMCNIterationsConvergenceGlobal = -1;

   for (int j = 0; j < fMCMCNChains; ++j)
   {
      fMCMCNIterations[j]  = 0;
      fMCMCNTrialsTrue[j]  = 0;
      fMCMCNTrialsFalse[j] = 0;
      fMCMCMean[j]         = 0;
      fMCMCVariance[j]     = 0;

      for (int k = 0; k < fMCMCNParameters; ++k)
      {
         fMCMCNTrialsTrue[j * fMCMCNParameters + k]  = 0;
         fMCMCNTrialsFalse[j * fMCMCNParameters + k] = 0;
      }
   }

   // reset marginalized distributions
   for (int i = 0; i < int(fMCMCH1Marginalized.size()); ++i)
      fMCMCH1Marginalized[i] -> Reset();

   for (int i = 0; i < int(fMCMCH2Marginalized.size()); ++i)
      fMCMCH2Marginalized[i] -> Reset();

// if (fMCMCH1RValue)
//   fMCMCH1RValue -> Reset();

// if (fMCMCH1Efficiency)
//   fMCMCH1Efficiency -> Reset();

   fMCMCRValue = 100;
}

// --------------------------------------------------------

int BCEngineMCMC::MCMCAddParameter(double min, double max)
{
   // add the boundaries to the corresponding vectors
   fMCMCBoundaryMin.push_back(min);
   fMCMCBoundaryMax.push_back(max);

   // increase the number of parameters by one
   fMCMCNParameters++;

   // return the number of parameters
   return fMCMCNParameters;
}

// --------------------------------------------------------

void BCEngineMCMC::MCMCInitializeMarkovChains()
{
   // evaluate function at the starting point
   std::vector <double> x0;

   for (int j = 0; j < fMCMCNChains; ++j)
   {
      x0.clear();
      for (int i = 0; i < fMCMCNParameters; ++i)
         x0.push_back(fMCMCx[j * fMCMCNParameters + i]);
      fMCMCLogProbx[j] = this -> LogEval(x0);
   }

   x0.clear();
}

// --------------------------------------------------------

int BCEngineMCMC::MCMCInitialize()
{
   // reset variables
   fMCMCNIterations.clear();
   fMCMCNIterationsConvergenceLocal.clear();
   fMCMCNTrialsTrue.clear();
   fMCMCNTrialsFalse.clear();
   fMCMCTrialFunctionScaleFactor.clear();
   fMCMCMean.clear();
   fMCMCVariance.clear();
   fMCMCMeanx.clear();
   fMCMCVariancex.clear();
   fMCMCx.clear();
   fMCMCLogProbx.clear();
   fMCMCMaximumPoints.clear();
   fMCMCMaximumLogProb.clear();
// fMCMCRelativePrecisionModeValues.clear();
   fMCMCNumericalPrecisionModeValues.clear();
   fMCMCNIterationsConvergenceGlobal = -1;
   fMCMCFlagConvergenceGlobal = false;
   fMCMCRValueParameters.clear();

   for (int i = 0; i < int(fMCMCH1Marginalized.size()); ++i)
      if (fMCMCH1Marginalized[i])
         delete fMCMCH1Marginalized[i];

   for (int i = 0; i < int(fMCMCH2Marginalized.size()); ++i)
      if (fMCMCH2Marginalized[i])
         delete fMCMCH2Marginalized[i];

   // clear plots
   fMCMCH1Marginalized.clear();
   fMCMCH2Marginalized.clear();

// if (fMCMCH1RValue)
//    delete fMCMCH1RValue;

// if (fMCMCH1Efficiency)
//    delete fMCMCH1Efficiency;

// free memory for vectors
   fMCMCNIterationsConvergenceLocal.assign(fMCMCNChains, -1);
   fMCMCNIterations.assign(fMCMCNChains, 0);
   fMCMCMean.assign(fMCMCNChains, 0);
   fMCMCVariance.assign(fMCMCNChains, 0);
   fMCMCLogProbx.assign(fMCMCNChains, -1.0);
   fMCMCMaximumLogProb.assign(fMCMCNChains, -1.0);

   fMCMCNumericalPrecisionModeValues.assign(fMCMCNParameters, 0.0);

   fMCMCNTrialsTrue.assign(fMCMCNChains * fMCMCNParameters, 0);
   fMCMCNTrialsFalse.assign(fMCMCNChains * fMCMCNParameters, 0);
   fMCMCMaximumPoints.assign(fMCMCNChains * fMCMCNParameters, 0.);
   fMCMCMeanx.assign(fMCMCNChains * fMCMCNParameters, 0);
   fMCMCVariancex.assign(fMCMCNChains * fMCMCNParameters, 0);

   fMCMCRValueParameters.assign(fMCMCNParameters, 0.);

   if (fMCMCTrialFunctionScaleFactorStart.size() == 0)
      fMCMCTrialFunctionScaleFactor.assign(fMCMCNChains * fMCMCNParameters, 1.0);
   else
      for (int i = 0; i < fMCMCNChains; ++i)
         for (int j = 0; j < fMCMCNParameters; ++j)
            fMCMCTrialFunctionScaleFactor.push_back(fMCMCTrialFunctionScaleFactorStart.at(j));

   // set initial position
   for (int j = 0; j < fMCMCNChains; ++j)
      for (int i = 0; i < fMCMCNParameters; ++i)
         switch(fMCMCFlagInitialPosition)
         {
            // use the center of the region
            case 0 :
               fMCMCx.push_back(fMCMCBoundaryMin[i] + .5 * (fMCMCBoundaryMax[i] - fMCMCBoundaryMin[i]));
               break;
            // use a random variable in the valid region
            case 1 :
               fMCMCx.push_back(fMCMCBoundaryMin[i] + fMCMCRandom -> Rndm() * (fMCMCBoundaryMax[i] - fMCMCBoundaryMin[i]));
               break;
            // use user-defined value
            case 2 :
               if (int(fMCMCInitialPosition.size()) == fMCMCNParameters * fMCMCNChains)
                  fMCMCx.push_back(fMCMCInitialPosition[j * fMCMCNParameters + i]);
               else
                  fMCMCx.push_back(fMCMCBoundaryMin[i] + .5 * (fMCMCBoundaryMax[i] - fMCMCBoundaryMin[i]));
               break;
            // use the center of the region as default
            default:
               fMCMCx.push_back(fMCMCBoundaryMin[i] + 0.5 * (fMCMCBoundaryMax[i] - fMCMCBoundaryMin[i]));
               break;
         }

   // copy the point of the first chain
   fMCMCxLocal.clear();
   for (int i = 0; i < fMCMCNParameters; ++i)
      fMCMCxLocal.push_back(fMCMCx[i]);

   // define 1-dimensional histograms for marginalization
   for(int i = 0; i < fMCMCNParameters; ++i)
   {
      double hmin1 = fMCMCBoundaryMin.at(i);
      double hmax1 = fMCMCBoundaryMax.at(i);

      TH1D * h1 = new TH1D(TString::Format("h1_%d_parameter_%i", BCLog::GetHIndex() ,i), "", fMCMCH1NBins[i], hmin1, hmax1);
      fMCMCH1Marginalized.push_back(h1);
   }

   for(int i = 0; i < fMCMCNParameters; ++i)
      for (int k = 0; k < i; ++k)
      {
         double hmin1 = fMCMCBoundaryMin.at(k);
         double hmax1 = fMCMCBoundaryMax.at(k);
         double hmin2 = fMCMCBoundaryMin.at(i);
         double hmax2 = fMCMCBoundaryMax.at(i);

         TH2D * h2 = new TH2D(Form("h2_%d_parameters_%i_vs_%i", BCLog::GetHIndex(), i, k), "",
               fMCMCH1NBins[i], hmin1, hmax1,
               fMCMCH1NBins[k], hmin2, hmax2);
         fMCMCH2Marginalized.push_back(h2);
      }

   // define plot for R-value
// if (fMCMCNChains > 1)
// {
//    fMCMCH1RValue = new TH1D("h1_rvalue", ";Iteration;R-value",
//           100, 0, double(fMCMCNIterationsMax));
//    fMCMCH1RValue -> SetStats(false);
// }

// fMCMCH1Efficiency = new TH1D("h1_efficiency", ";Chain;Efficiency",
//       fMCMCNParameters, -0.5, fMCMCNParameters - 0.5);
// fMCMCH1Efficiency -> SetStats(false);

   return 1;
}

// ---------------------------------------------------------

int BCEngineMCMC::SetMarginalized(int index, TH1D * h)
{
   if((int)fMCMCH1Marginalized.size()<=index)
      return 0;

   if(h==0)
      return 0;

   if((int)fMCMCH1Marginalized.size()==index)
      fMCMCH1Marginalized.push_back(h);
   else
      fMCMCH1Marginalized[index]=h;

   return index;
}

// ---------------------------------------------------------

int BCEngineMCMC::SetMarginalized(int index1, int index2, TH2D * h)
{
   int counter = 0;
   int index = 0;

   // search for correct combination
   for(int i = 0; i < fMCMCNParameters; i++)
      for (int j = 0; j < i; ++j)
      {
         if(j == index1 && i == index2)
            index = counter;
         counter++;
      }

   if((int)fMCMCH2Marginalized.size()<=index)
      return 0;

   if(h==0)
      return 0;

   if((int)fMCMCH2Marginalized.size()==index)
      fMCMCH2Marginalized.push_back(h);
   else
      fMCMCH2Marginalized[index]=h;

   return index;
}

// ---------------------------------------------------------

void BCEngineMCMC::MCMCSetValuesDefault()
{
   this -> MCMCSetValuesDetail();
}

// ---------------------------------------------------------

void BCEngineMCMC::MCMCSetValuesQuick()
{
   fMCMCNChains              = 1;
   fMCMCNIterationsMax       = 1000;
   fMCMCNIterationsRun       = 10000;
   fMCMCNIterationsBurnIn    = 0;
   fMCMCNIterationsPCA       = 0;
   fMCMCNIterationsPreRunMin = 0;
   fMCMCFlagIterationsAuto   = false;
   fMCMCTrialFunctionScale   = 1.0;
   fMCMCFlagInitialPosition  = 1;
   fMCMCRValueCriterion      = 0.1;
   fMCMCRValueParametersCriterion = 0.1;
   fMCMCNIterationsConvergenceGlobal = -1;
   fMCMCFlagConvergenceGlobal = false;
   fMCMCRValue               = 100;
   fMCMCFlagPCA              = false;
   fMCMCFlagPCATruncate      = false;
   fMCMCPCA                  = 0;
   fMCMCPCAMinimumRatio      = 1e-7;
   fMCMCNIterationsUpdate    = 1000;
   fMCMCFlagOrderParameters  = true;
}

// ---------------------------------------------------------

void BCEngineMCMC::MCMCSetValuesDetail()
{
   fMCMCNChains              = 5;
   fMCMCNIterationsMax       = 1000000;
   fMCMCNIterationsRun       = 100000;
   fMCMCNIterationsBurnIn    = 0;
   fMCMCNIterationsPCA       = 10000;
   fMCMCNIterationsPreRunMin = 500;
   fMCMCFlagIterationsAuto   = false;
   fMCMCTrialFunctionScale   = 1.0;
   fMCMCFlagInitialPosition  = 1;
   fMCMCRValueCriterion      = 0.1;
   fMCMCRValueParametersCriterion = 0.1;
   fMCMCNIterationsConvergenceGlobal = -1;
   fMCMCFlagConvergenceGlobal = false;
   fMCMCRValue               = 100;
   fMCMCFlagPCA              = false;
   fMCMCFlagPCATruncate      = false;
   fMCMCPCA                  = 0;
   fMCMCPCAMinimumRatio      = 1e-7;
   fMCMCNIterationsUpdate    = 1000;
   fMCMCFlagOrderParameters  = true;
}

// ---------------------------------------------------------

---