Treatment of errors for fits to unbinned/.binned/weighted datasets

tst_1.py

import ROOT, random

## 1) create Gaussian fit models
xvar  = ROOT.RooRealVar( 'x'     , 'x-observable'             , 0 ,    10 )
mean  = ROOT.RooRealVar( 'mean'  , 'mean-value for Gaussian'  , 5 , 2 , 8 )
sigma = ROOT.RooRealVar( 'sigma' , 'sigma-value for Gaussian' , 1 , 0.5 , 2.0 )

gauss = ROOT.RooGaussian( 'G' , 'Gaussian model' , xvar , mean , sigma ) 

## 2) create and fill dataste & histogram
varset  = ROOT.RooArgSet( xvar )
dataset = ROOT.RooDataSet ( 'data' , 'unbineed dataset' , varset ) 
histo = ROOT.TH1D( 'h1000' , 'Test histogram' , 200 , 0 , 10 )
for i in range ( 1000 ) :
    value = random.gauss ( 5 , 1 )
    xvar.setVal ( value )
    dataset.add ( varset )
    histo.Fill  ( value ) 

## 4) convert histogram into RooDataHist 
vlst = ROOT.RooArgList ( xvar )
hdset = ROOT.RooDataHist ( 'bdset' , '(binned) data as RooFataHist' , vlst , ROOT.RooFit.Import ( histo ) )

## 4) convert historgam into weighted dataset 
wvar  = ROOT.RooRealVar ('weight' , 'weight-variable' , 1 , -100 , +1e+6 )
wset  = ROOT.RooArgSet  ( wvar )
vset  = ROOT.RooArgSet  ( xvar , wvar ) 
wargs = ROOT.RooFit.WeightVar ( wvar ) ,  ROOT.RooFit.StoreError ( wset )    
wdset = ROOT.RooDataSet ( 'wdset' , '(binned) data as Weighted RooDataSet' , vset , *wargs ) 
for ibin in range ( 1 , histo.GetNbinsX()+1 ) :
    value  = histo.GetBinContent ( ibin )
    error  = histo.GetBinError   ( ibin )
    xvalue = histo.GetBinCenter  ( ibin )
    xvar.setVal ( xvalue ) 
    wdset.add ( vset , value , error ) 


# 5) make reference fit to unbinned RooDataHist
r0 = gauss.fitTo ( dataset  , ROOT.RooFit.Save() )
r0.Print ()

# 6) make fit to the binned dataset (as RooDataHist)
rh = gauss.fitTo ( hdset , ROOT.RooFit.Save() )
rh.Print ()

# 7) make fit to the binned datatset (as weighted RooDataSet with no special treatment of errors) 
rw1 = gauss.fitTo ( wdset , ROOT.RooFit.Save() )
rw1.Print ()

# 8) make fit to the binned datatset (as weighted RooDataSet with SumW2 options) 
rw2 = gauss.fitTo ( wdset , ROOT.RooFit.Save() , ROOT.RooFit.SumW2Error ( True ) )
rw2.Print ()

# 9) make fit to the binned datatset (as weighted RooDataSet with "correct" treatment of weights&errors) 
rw3 = gauss.fitTo ( wdset , ROOT.RooFit.Save() , ROOT.RooFit.AsymptoticError ( True ) )
rw3.Print ()