Chi^2 of 3D RooFit PDF fit to TH3D


I want to get the chi^2 of a 3D fit. I have done this with a 1D fit:

        RooRealVar n("n","n",histmin,histmax);
        RooDataHist ndata("ndata","ndata",n,test_hist);
        RooRealVar fake("fake","fake",fakefraction,0,1);
        RooDataHist real_temp("real_temp","real_temp",n,real_hist);
        RooHistPdf pdf_real("pdf_real","pdf_real",n,real_temp,0);

        RooDataHist fake_temp("fake_temp","fake_temp",n,fake_hist);
        RooHistPdf pdf_fake("pdf_fake","pdf_fake",n,fake_temp,0);
        RooAddPdf pdf("pdf","pdf",RooArgList(pdf_fake,pdf_real),fake);
        RooFitResult *result = pdf.fitTo(ndata,Range(fitmin,fitmax),Save(kTRUE),PrintLevel(1),SumW2Error(kFALSE));
        RooPlot *nframe = n.frame();
        int n_param = result->floatParsFinal().getSize();

but this uses a RooPlot frame which is only 1D (as far as I know).
I want to do a 3D fit:

        double_t nevents = test_hist->Integral(binx1,binx2,biny1,biny2,binz1,binz2);

        RooRealVar nx("nx","nx",histmin[0],histmax[0]);
        RooRealVar ny("ny","ny",histmin[1],histmax[1]);
        RooRealVar nz("nz","nz",histmin[2],histmax[2]);
        RooDataHist ndata("ndata","ndata",RooArgList(nx,ny,nz),test_hist);

        RooRealVar fake("fake","fake",fakefraction,0,1);

        RooDataHist real_temp("real_temp","real_temp",RooArgList(nx,ny,nz),real_hist);
        RooHistPdf pdf_real("pdf_real","pdf_real",RooArgList(nx,ny,nz),RooArgList(nx,ny,nz),real_temp,0);

        RooDataHist fake_temp("fake_temp","fake_temp",RooArgList(nx,ny,nz),fake_hist);
        RooHistPdf pdf_fake("pdf_fake","pdf_fake",RooArgList(nx,ny,nz),RooArgList(nx,ny,nz),fake_temp,0);
        RooAddPdf pdf3D("pdf3D","pdf3D",RooArgList(pdf_fake,pdf_real),fake);


        RooFitResult *result = pdf3D.fitTo(ndata,Range("fitRange"),Save(kTRUE),PrintLevel(1),SumW2Error(kFALSE));

And then calculate the chi^2/ndof for the fit. Both the 1D and 3D fits are PDFs from histogram templates.

If there is a roofit function that will do a chi^2 for a 3D fit, that is what I would want. But there doesn’t seem to be one so I am trying to code my own chi^2 and get the same answer for the 1D fit as the nframe->chiSquare(n_param); gives (as a sanity check, then apply the same method to the 3D fit).

This has led me to this bit of code: and I am trying to recreate it:

        TH1D *fit_hist = new TH1D("fit_hist","fit_hist",test_hist->GetNbinsX(),histmin,histmax);
        RooDataHist *fit_data = pdf.generateBinned( n, Name("fit_data"), Verbose(0), NumEvents(nevents), ExpectedData() );
        chi2ndof_out =0;
        int nbins = 0;
        double_t x,y,eyl,eyh,avg;
            for (int i = test_hist->FindBin(fitmin); i <= (test_hist->FindBin(fitmax)); i++) {
                x = test_hist->GetXaxis()->GetBinCenter(i);
                y = test_hist->GetBinContent(i);
                eyl = test_hist->GetBinErrorLow(i);
                eyh = test_hist->GetBinErrorUp(i);
                avg = fit_hist->GetBinContent(i);
                        Double_t pull = (y>avg) ? ((y-avg)/eyl) : ((y-avg)/eyh) ;
                        chi2ndof_out  += pull*pull;
        int ndof = nbins - n_param;
        chi2ndof_out = chi2ndof_out/ndof;

But there must be something that I am doing wrong. I get a chi^/ndof of 61.9025 compared to the nframe->chiSquare(n_param); gives 3.6192e-13.

I am wondering if it has something to do with the errors of the pdf vs the errors of the generated histogram.
I hope someone can help me see what I am missing.


Hi Sarah,

for plots, you can indeed only compare the Chi^2 of the stuff that’s in the plot. That will give very different Chi^2 values because the PDF is projected onto the plot variable.
You could try to construct a RooChi2Var:

That’s what the Chi^2 fit uses.

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