Studies on the CombinatorialConstraint (constraining bkg slope) were performed after observing positive values in BDT bin 4 and η bin 2. Two forms of the constraints were tested:
  1. Hard upper limit at zero on the slope parameter
  2. Using -Abs(slope) in the model

Intermediate steps in unconstrained case:

η evolution:

binnedSBFits BDT1ETA1etaEv.png
eta bin 1
binnedSBFits BDT1ETA2.png
eta bin 2
binnedSBFits BDT1ETA3.png
eta bin 3
unbinnedSBFits BDT1ETA1etaEv.png
eta bin 1
unbinnedSBFits BDT1ETA2.png
eta bin 2
unbinnedSBFits BDT1ETA3.png
eta bin 3
finalFits BDT1ETA1etaEv.png
eta bin 1
finalFits BDT1ETA2.png
eta bin 2
finalFits BDT1ETA3.png
eta bin 3
"Check sums" (Do the components sum up to the final model?) for the final fit: checkModel_BDTBin1ETAbin1etaEv, checkModel_BDTBin1ETAbin2, checkModel_BDTBin1ETAbin3

BDT evolution:

binnedSBFits BDT1ETA1.png
BDT bin 1
binnedSBFits BDT2ETA1.png
BDT bin 2
binnedSBFits BDT3ETA1.png
BDT bin 3
binnedSBFits BDT4ETA1.png
BDT bin 4
unbinnedSBFits BDT1ETA1.png
BDT bin 1
unbinnedSBFits BDT2ETA1.png
BDT bin 2
unbinnedSBFits BDT3ETA1.png
BDT bin 3
unbinnedSBFits BDT4ETA1.png
BDT bin 4
finalFits BDT1ETA1.png
BDT bin 1
finalFits BDT2ETA1.png
BDT bin 2
finalFits BDT3ETA1.png
BDT bin 3
finalFits BDT4ETA1.png
BDT bin 4
"Check sums" checkModel_BDTBin1ETAbin1, checkModel_BDTBin2ETAbin1, checkModel_BDTBin3ETAbin1, checkModel_BDTBin4ETAbin1

Hard upper limit

Constraining only the first step of the fitting procedure (polynomial binned fit on the upper sideband) does not help. Neither does adding the constraint also to the second step - unbinned fit on the upper sideband. Only after constraining also the final step (combined unbinned fit on both sidebands) the final slope is negative. Varying the lower limit (for instance -10000 instead of -10) results in negligible (O(1E-3)) variation of the slope and its error. These are the results for η and BDT bins respectively, with lower limit -10000:

Bkg etaBin1 hardConstraint.png
eta bin 1
Bkg etaBin2 hardConstraint.png
eta bin 2
Bkg etaBin3 hardConstraint.png
eta bin 3
Bkg BDTBin1 hardConstraint.png
BDT bin 1
Bkg BDTBin2 hardConstraint.png
BDT bin 2
Bkg BDTBin3 hardConstraint.png
BDT bin 3
Bkg BDTBin4 hardConstraint.png
BDT bin 4

-abs(slope) constraint

The values of the slope are presented with minus sign, although it's redundant - it only enters the model as -Abs(slope).

Bkg etaBin1 minAbs.png
eta bin 1
Bkg etaBin2 minAbs.png
eta bin 2
Bkg etaBin3 minAbs.png
eta bin 3
Bkg BDTBin1 minAbs.png
BDT bin 1
Bkg BDTBin2 minAbs.png
BDT bin 2
Bkg BDTBin3 minAbs.png
BDT bin 3
Bkg BDTBin4 minAbs.png
BDT bin 4
slope vsEta minAbs.png
slope vs. Eta
slope vsBDT minAbs.png
slope vs. BDT
 

Intermediate steps for constrained cases in problematic bins

The η bin 2 hard zero:

binnedSBFits BDT1ETA2 hardZero.png
Fit step 1
unbinnedSBFits BDT1ETA2 hardZero.png
Fit step 2
finalFits BDT1ETA2 hardZero.png
Fit step 3

The η bin 2 -abs():

binnedSBFits BDT1ETA2 minAbs.png
Fit Step 1
unbinnedSBFits BDT1ETA2 minAbs.png
Fit step 2
finalFits BDT1ETA2 minAbs.png
Fit step 3

The BDT bin 4 hard zero:

binnedSBFits BDT4ETA1 hardZero.png
Fit step 1
unbinnedSBFits BDT4ETA1 hardZero.png
Fit step 2
finalFits BDT4ETA1 hardZero.png
Fit step 3

The BDT bin 4 -abs():

binnedSBFits BDT4ETA1 minAbs.png
Fit step 1
unbinnedSBFits BDT4ETA1 minAbs.png
Fit step 2
finalFits BDT4ETA1 minAbs.png
Fit step 3

RooFit vs. ROOT initial values

This is the result of the Fabio's RooFit fitter:

Fabios BDT4.png
Fit result by the RooFit fitter fitResult_Fabios_BDT4

If the values resulting from Fabio's RooFit fitter are used as initial values for the ROOT fit, the slope is still wrong. Since Fabio's fitter uses different parametrization (nComb, nSSSV instead of nComb, nTot) and interprets the event numbers on the whole range, the initial values for the event numbers were calculated from ratio of Fabio's nComb/(nSSSV+nComb) times the number of events in sidebands, and nTot was initialized as the number of sideband events itself (this is the log file: log_BDT4_FabioInit.txt):

finalFits BDT4ETA1 FabioInit.png
Fit step 3, overriden initial values to those fitted by RooFit checkModel_BDTBin4ETAbin1_FabioInit

Attempts to double up the number of combinatorial bkg events were carried out with both 'native' (those the ROOT fitter uses normally) and overriden initial values of fit parameters. The values from both internal note (expConst = -0.0064, slope = 1.0022) and Fabio's fitter (expConst = -0.0063608, slope = 1.0077) were used for overriding the native parameters. These are reffered to as 'intNoteInit' and 'FabioInit' respectively.

finalFits BDT4ETA1 doubleNComb nativeInit.png
Native initial values, double init nComb checkModel_BDTBin4ETAbin1_doubleNComb_nativeInit

Attempts to fit the combinatorial component with a constant were carried out. The constant trend was achieved by fixing the value of slope in the polynomial parametrization to zero.

New vs. Old RooFit fitter cross-check

This is the fit log for BDT bin 4 as fitted by Fabio's old fitter: oldRooFitLog_BDT4.txt

And This is the log for BDT bin 4 by my RooFit fitter: newRooFitLog_BDT4.txt

The difference is not caused by different libraries - the 'old' fitter was compiled as a standalone program linked to the same libraries as the 'new' version. Results were unchanged.

It's also not caused by different parametrization - the same parametrization (and of course initialization) as used in the 'old' version was implemented to the 'new' one. Some minor differences were still present, plus the error matrix was not pos def.

Neither it's caused by fitting different data points - data from both fitters were written out and compared.

A test was performed to check whether this could be caused by supplying initial values with different decimal precision. Only values printed out to the terminal were supplied to the new fitter as the starting values - those might have been rounded before printed out. Therefore, both fitters were overriden with same starting values as those printed out to the screen by the old fitter. Now, both converged to the same parameter values, yet the old fitter produced sensible covariance matrix, while the new one failed at that. Later, the source of all evil has been found - RooFit sorts parameters (almost?) alphabetically. The order of the parameters in the new fitter was different than in the old one, and the covariance matrix wasn't positive definite due to this. When the parameter names in the old fitter were sorted in the same order as in the old one, both converge from same initial values to same final ones and same errors. Heureka!

Adding Roo fit step to the ROOT fitter

It's there for the background. The nComb and nTot are re-calculated using full-range implementations of the bkg model - normalized in sidebands but also returning values in the blinded region. They are calculated as integrals over whole mass range (4766 MeV - 5966 MeV) of the chebychev and combined model in the last step (the extended fit returns number of events in side bands only, by this integration, this is interpolated into the blinded region). The RooFit fit step is then performed. The numbers of events in sidebands (to be compared to the previous step) are obtained as integrals of the resulting RooFit pdfs (total, resp. chebychev) over the side bands, multiplied by the full-range nubers of events.

In the BDT bin 4, the RooFit step, starting from the values of the previous step, resulted in the same (nonsensical) values, plus failed error calculation. Therefore, a condition was implemented, forcing the initial value of the slope to zero whenever the preceeding step fits value greater than zero. This resulted in sensible behavior in BDT bin 4, while leaving other bins unaffected.

Next step is to test the robustness with respect to sample fluctuations, i.e. change the binning so that the event number changes significantly, and see the fit result (last bin only, since it's the problematic one).

  BDT 0.420 - 1.000 (41 SB events) BDT 0.418 - 1.000 (45 SB events) BDT 0.415 - 1.000 (53 SB events) BDT 0.413 - 1.000 (55 SB events) BDT 0.410 - 1.000 (63 SB events) BDT 0.400 - 1.000 (72 SB events)
ROOT
RooFit
-- OndrejKovanda - 2020-04-08
Topic attachments
I Attachment History Action Size Date Who Comment
PNGpng Bkg_BDTBin1_hardConstraint.png r1 manage 40.0 K 2020-04-09 - 17:46 OndrejKovanda  
PNGpng Bkg_BDTBin1_minAbs.png r1 manage 60.5 K 2020-04-21 - 14:45 OndrejKovanda  
PNGpng Bkg_BDTBin2_hardConstraint.png r1 manage 39.3 K 2020-04-09 - 17:46 OndrejKovanda  
PNGpng Bkg_BDTBin2_minAbs.png r1 manage 59.2 K 2020-04-21 - 14:45 OndrejKovanda  
PNGpng Bkg_BDTBin3_hardConstraint.png r1 manage 38.2 K 2020-04-09 - 17:46 OndrejKovanda  
PNGpng Bkg_BDTBin3_minAbs.png r1 manage 57.9 K 2020-04-21 - 14:45 OndrejKovanda  
PNGpng Bkg_BDTBin4_hardConstraint.png r1 manage 34.3 K 2020-04-09 - 17:46 OndrejKovanda  
PNGpng Bkg_BDTBin4_minAbs.png r1 manage 53.5 K 2020-04-21 - 14:45 OndrejKovanda  
PNGpng Bkg_etaBin1_hardConstraint.png r1 manage 39.5 K 2020-04-09 - 17:47 OndrejKovanda  
PNGpng Bkg_etaBin1_minAbs.png r1 manage 60.1 K 2020-04-21 - 14:45 OndrejKovanda  
PNGpng Bkg_etaBin2_hardConstraint.png r1 manage 39.6 K 2020-04-09 - 17:47 OndrejKovanda  
PNGpng Bkg_etaBin2_minAbs.png r1 manage 60.2 K 2020-04-21 - 14:45 OndrejKovanda  
PNGpng Bkg_etaBin3_hardConstraint.png r1 manage 40.0 K 2020-04-09 - 17:47 OndrejKovanda  
PNGpng Bkg_etaBin3_minAbs.png r1 manage 60.3 K 2020-04-21 - 14:45 OndrejKovanda  
PNGpng Fabios_BDT4.png r1 manage 13.2 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng RooFit_BDT1ETA1.png r1 manage 22.9 K 2020-05-05 - 16:25 OndrejKovanda  
PNGpng RooFit_BDT2ETA1.png r1 manage 23.0 K 2020-05-05 - 16:25 OndrejKovanda  
PNGpng RooFit_BDT3ETA1.png r1 manage 22.7 K 2020-05-05 - 16:25 OndrejKovanda  
PNGpng RooFit_BDT4ETA1.png r1 manage 21.0 K 2020-05-05 - 16:44 OndrejKovanda  
PNGpng RooFit_BDT4ETA1_0-413--1.png r1 manage 20.4 K 2020-05-05 - 18:13 OndrejKovanda  
PNGpng RooFit_BDT4ETA1_0-418--1.png r1 manage 20.6 K 2020-05-05 - 18:14 OndrejKovanda  
PNGpng RooFit_BDT4ETA1_0-420--1.png r1 manage 20.0 K 2020-05-05 - 17:49 OndrejKovanda  
PNGpng binnedSBFits_BDT1ETA1.png r2 r1 manage 19.6 K 2020-04-23 - 16:42 OndrejKovanda  
PNGpng binnedSBFits_BDT1ETA1etaEv.png r2 r1 manage 19.9 K 2020-04-29 - 13:00 OndrejKovanda  
PNGpng binnedSBFits_BDT1ETA2.png r1 manage 19.3 K 2020-04-29 - 13:07 OndrejKovanda  
PNGpng binnedSBFits_BDT1ETA2_hardZero.png r1 manage 19.1 K 2020-04-29 - 13:36 OndrejKovanda  
PNGpng binnedSBFits_BDT1ETA2_minAbs.png r1 manage 19.3 K 2020-04-29 - 13:21 OndrejKovanda  
PNGpng binnedSBFits_BDT1ETA3.png r2 r1 manage 19.8 K 2020-04-29 - 13:01 OndrejKovanda  
PNGpng binnedSBFits_BDT2ETA1.png r1 manage 20.2 K 2020-04-23 - 16:42 OndrejKovanda  
PNGpng binnedSBFits_BDT3ETA1.png r1 manage 19.5 K 2020-04-23 - 16:42 OndrejKovanda  
PNGpng binnedSBFits_BDT4ETA1.png r1 manage 18.4 K 2020-04-23 - 16:42 OndrejKovanda  
PNGpng binnedSBFits_BDT4ETA1_hardZero.png r1 manage 18.2 K 2020-04-29 - 13:30 OndrejKovanda  
PNGpng binnedSBFits_BDT4ETA1_minAbs.png r1 manage 18.3 K 2020-04-29 - 13:37 OndrejKovanda  
Unknown file formatext checkModel_BDTBin1ETAbin1 r2 r1 manage 0.3 K 2020-04-23 - 16:42 OndrejKovanda  
Unknown file formatext checkModel_BDTBin1ETAbin1_withRooFit r1 manage 2.6 K 2020-05-05 - 16:29 OndrejKovanda  
Unknown file formatext checkModel_BDTBin1ETAbin1etaEv r1 manage 0.3 K 2020-04-23 - 16:57 OndrejKovanda  
Unknown file formatext checkModel_BDTBin1ETAbin2 r1 manage 0.3 K 2020-04-23 - 16:39 OndrejKovanda  
Unknown file formatext checkModel_BDTBin1ETAbin3 r1 manage 0.3 K 2020-04-23 - 16:39 OndrejKovanda  
Unknown file formatext checkModel_BDTBin2ETAbin1 r1 manage 0.3 K 2020-04-23 - 16:42 OndrejKovanda  
Unknown file formatext checkModel_BDTBin2ETAbin1_withRooFit r1 manage 2.5 K 2020-05-05 - 16:29 OndrejKovanda  
Unknown file formatext checkModel_BDTBin3ETAbin1 r1 manage 0.3 K 2020-04-23 - 16:42 OndrejKovanda  
Unknown file formatext checkModel_BDTBin3ETAbin1_withRooFit r1 manage 2.5 K 2020-05-05 - 16:29 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1 r1 manage 0.3 K 2020-04-23 - 16:42 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_0-400--1 r1 manage 2.5 K 2020-05-05 - 17:47 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_0-410--1 r1 manage 2.5 K 2020-05-05 - 17:47 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_0-413--1 r1 manage 2.5 K 2020-05-05 - 17:47 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_0-415--1 r1 manage 2.5 K 2020-05-05 - 17:47 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_0-418--1 r1 manage 2.5 K 2020-05-05 - 17:47 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_0-420--1 r1 manage 2.5 K 2020-05-05 - 17:48 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_FabioInit r1 manage 1.5 K 2020-05-01 - 11:38 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_constComb_FabioInit r1 manage 1.3 K 2020-05-01 - 11:37 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_constComb_FabioInit_fixed r1 manage 1.3 K 2020-05-01 - 12:46 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_constComb_intNoteInit r1 manage 1.3 K 2020-05-01 - 11:37 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_constComb_nativeInit r1 manage 1.3 K 2020-05-01 - 11:38 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_doubleNComb_FabioInit r1 manage 1.5 K 2020-05-01 - 11:38 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_doubleNComb_FabioInit_fixed r1 manage 1.5 K 2020-05-01 - 12:46 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_doubleNComb_intNoteInit r1 manage 1.5 K 2020-05-01 - 11:38 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_doubleNComb_nativeInit r1 manage 1.5 K 2020-05-01 - 11:38 OndrejKovanda  
Unknown file formatext checkModel_BDTBin4ETAbin1_withRooFit r1 manage 2.5 K 2020-05-05 - 16:44 OndrejKovanda  
PNGpng finalFits_BDT1ETA1.png r2 r1 manage 18.7 K 2020-04-23 - 16:42 OndrejKovanda  
PNGpng finalFits_BDT1ETA1etaEv.png r1 manage 18.7 K 2020-04-23 - 16:57 OndrejKovanda  
PNGpng finalFits_BDT1ETA2.png r1 manage 18.3 K 2020-04-23 - 16:14 OndrejKovanda  
PNGpng finalFits_BDT1ETA2_hardZero.png r1 manage 21.6 K 2020-04-29 - 13:36 OndrejKovanda  
PNGpng finalFits_BDT1ETA2_minAbs.png r1 manage 21.1 K 2020-04-29 - 13:21 OndrejKovanda  
PNGpng finalFits_BDT1ETA3.png r1 manage 17.9 K 2020-04-23 - 16:14 OndrejKovanda  
PNGpng finalFits_BDT2ETA1.png r1 manage 19.3 K 2020-04-23 - 16:43 OndrejKovanda  
PNGpng finalFits_BDT3ETA1.png r1 manage 19.0 K 2020-04-23 - 16:43 OndrejKovanda  
PNGpng finalFits_BDT4ETA1.png r1 manage 18.0 K 2020-04-23 - 16:43 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_0-400--1.png r1 manage 21.9 K 2020-05-05 - 17:48 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_0-410--1.png r1 manage 21.9 K 2020-05-05 - 17:48 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_0-413--1.png r1 manage 21.7 K 2020-05-05 - 17:48 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_0-418--1.png r1 manage 21.2 K 2020-05-05 - 18:02 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_0-420--1.png r1 manage 21.0 K 2020-05-05 - 17:48 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_FabioInit.png r1 manage 20.9 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_constComb_FabioInit.png r1 manage 20.4 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_constComb_FabioInit_fixed.png r1 manage 20.7 K 2020-05-01 - 12:46 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_constComb_intNoteInit.png r1 manage 20.4 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_constComb_nativeInit.png r1 manage 20.4 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_doubleNComb_FabioInit.png r1 manage 21.1 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_doubleNComb_FabioInit_fixed.png r1 manage 21.3 K 2020-05-01 - 12:46 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_doubleNComb_intNoteInit.png r1 manage 21.0 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_doubleNComb_nativeInit.png r1 manage 21.0 K 2020-05-01 - 11:38 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_hardZero.png r1 manage 20.0 K 2020-04-29 - 13:30 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_initOverride.png r1 manage 20.1 K 2020-04-30 - 14:31 OndrejKovanda  
PNGpng finalFits_BDT4ETA1_minAbs.png r1 manage 19.5 K 2020-04-29 - 13:37 OndrejKovanda  
Unknown file formatext fitResult_Fabios_BDT4 r1 manage 1.0 K 2020-05-01 - 11:38 OndrejKovanda  
Texttxt log_BDT4_FabioInit.txt r1 manage 66.1 K 2020-05-01 - 12:26 OndrejKovanda  
Texttxt newRooFitLog_BDT4.txt r1 manage 52.0 K 2020-05-01 - 18:46 OndrejKovanda  
Texttxt oldRooFitLog_2.txt r1 manage 41.5 K 2020-05-01 - 19:19 OndrejKovanda  
Texttxt oldRooFitLog_BDT4.txt r1 manage 41.5 K 2020-05-01 - 18:46 OndrejKovanda  
PNGpng slope_vsBDT_minAbs.png r1 manage 21.8 K 2020-04-21 - 16:26 OndrejKovanda  
PNGpng slope_vsEta_minAbs.png r1 manage 22.1 K 2020-04-21 - 16:26 OndrejKovanda  
PNGpng unbinnedSBFits_BDT1ETA1.png r2 r1 manage 20.3 K 2020-04-23 - 16:43 OndrejKovanda  
PNGpng unbinnedSBFits_BDT1ETA1etaEv.png r1 manage 20.0 K 2020-04-23 - 16:57 OndrejKovanda  
PNGpng unbinnedSBFits_BDT1ETA2.png r1 manage 18.9 K 2020-04-23 - 16:14 OndrejKovanda  
PNGpng unbinnedSBFits_BDT1ETA2_hardZero.png r1 manage 19.5 K 2020-04-29 - 13:36 OndrejKovanda  
PNGpng unbinnedSBFits_BDT1ETA2_minAbs.png r1 manage 19.7 K 2020-04-29 - 13:21 OndrejKovanda  
PNGpng unbinnedSBFits_BDT1ETA3.png r1 manage 19.8 K 2020-04-23 - 16:14 OndrejKovanda  
PNGpng unbinnedSBFits_BDT2ETA1.png r1 manage 20.7 K 2020-04-23 - 16:43 OndrejKovanda  
PNGpng unbinnedSBFits_BDT3ETA1.png r1 manage 19.8 K 2020-04-23 - 16:43 OndrejKovanda  
PNGpng unbinnedSBFits_BDT4ETA1.png r1 manage 18.9 K 2020-04-23 - 16:43 OndrejKovanda  
PNGpng unbinnedSBFits_BDT4ETA1_hardZero.png r1 manage 18.5 K 2020-04-29 - 13:30 OndrejKovanda  
PNGpng unbinnedSBFits_BDT4ETA1_minAbs.png r1 manage 18.5 K 2020-04-29 - 13:37 OndrejKovanda  
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