RooHistPdf plot depends on plot order

[lepton]

Hello experts,

I am trying to create a 2d pdf from a 2d weighted histogram, then use the 2d pdf to fit some data. The fit worked but there was something strange for the plotting.

1. If I plot dataHistT1 only, I can get projection of the original histogram as expected.

2. If I plot model only, the plot seems to be normalized to 1 instead of the number of events. And the shape does not look right.
   

3. If I plot model first, then dataHistT1. model seems to be normalized to 1.
   

4. If I plot dataHistT1 first, then model. I see a good agreement between the fitted model and the data.
   

I am glad I found a way myself but I have no idea why 2) and 3) did not work. Can someone tell me what I did wrong?

Thanks

The code:

#include <iostream>
#include <vector>
#include <string>
#include <memory>

#include "TCanvas.h"
#include "TFile.h"
#include "TH2D.h"
#include "TFractionFitter.h"
#include "TObjArray.h"

#include "RooRealVar.h"
#include "RooDataHist.h"
#include "RooDataSet.h"
#include "RooHistPdf.h"
#include "RooHistFunc.h"
#include "RooAddPdf.h"
#include "RooRealSumPdf.h"
#include "RooPlot.h"
#include "RooGaussian.h"

using namespace RooFit;
using std::cout;
using std::endl;

void create_and_plot_pdf()
{
    TH1::AddDirectory(kFALSE);

    RooRealVar s12("s12", "s12", 0.075, 0.12);
    RooRealVar s13("s13", "s13", 5.85, 6.2);   

    RooRealVar a1("a1", "T1 counts", 1e6, 0, 1e9);
    auto fTemps = new TFile("amps.root");
    auto histT1 = (TH2D*)fTemps->Get("hist_dalitz_T1");
    auto dataHistT1 = new RooDataHist("dataHistT1", "dataHistT1", 
        RooArgSet(s12, s13), histT1);
    // Create PDF from histograms with 1st order interpolation
    RooHistPdf pdfT1("pdfT1", "pdfT1", RooArgSet(s12, s13), *dataHistT1, 1);

    RooAddPdf model("model", "model", RooArgList(pdfT1), RooArgList(a1));

    model.fitTo(*dataHistT1, Extended(kTRUE), Save());

    RooPlot * s12Frame = s12.frame(Title("s12 projection"));
    
    // pdfT1.plotOn(s12Frame);
    dataHistT1->plotOn(s12Frame);
    // Model has to be plotted at last to ensure correct normalization
    model.plotOn(s12Frame);
    s12Frame->Draw();
}

[StephanH]

This is expected, see here:
https://root.cern.ch/doc/master/classRooAbsPdf.html#a7f01ccfb4f3bc3ad3b2bc1e3f30af535

The short version of all this is:
Plot data first, because otherwise it’s not clear what the PDF should be normalised to. (In absence of any normalisation information, it’s normalised to unity).

[lepton]

Thanks for pointing that out! But one thing I do not understand is how can the normalization possibly change the shape of the PDF? The first plot looks drastically different from the shape of the data.

[StephanH]

That could be the interpolation that’s applied. Did you try to compare with and without interpolation?

[lepton]

I tried to remove the interpolation but the shape stayed basically the same.

[StephanH]

Could you check the coefficient of the AddPdf? Does the value of this coefficient change the shape?

[lepton]

Not sure if I understand what you mean but if I change the value of a1, the plot still looks like the first plot if I do not plot the data set first.

[StephanH]

Ok, I don’t know why the shape changes, then.

If you want to investigate further, I guess we need an example to run.