[RF] Use integral of PDF curves for pull plots and residuals

[hageboeck]

Explain what you would like to see improved

When using pullHist, don't take curve at bin centre, but integrate curve over the bin. That should fix the following pull plot:

Wrong	Correct

Optional: share how it could be improved

• Alter this part of the function:
  

  root/roofit/roofitcore/src/RooHist.cxx

  Lines 777 to 787 in 478d84e

  	if (useAverage) {
  	Double_t exl = GetErrorXlow(i);
  	Double_t exh = GetErrorXhigh(i) ;
  	if (exl<=0 ) exl = GetErrorX(i);
  	if (exh<=0 ) exh = GetErrorX(i);
  	if (exl<=0 ) exl = 0.5*getNominalBinWidth();
  	if (exh<=0 ) exh = 0.5*getNominalBinWidth();
  	yy = point - curve.average(x-exl,x+exh) ;
  	} else {
  	yy = point - curve.interpolate(x) ;
  	}

• Instead of interpolating the curve to the middle of the bin, find the bin edges from RooHist using the x errors. (Note that RooHist inherits from TGraphAsymErrors).
• Then, find the corresponding points on the PDF curve.
• Then, integrate the PDF curve from the first to the last point from above step.

Code to produce such a plot

From here

RooRealVar x("x", "x", -10, 10);
x.setBins(20);
RooRealVar m("m", "mean",  1.5, -10, 10);
RooRealVar s("s", "sigma", 0.5, -10, 10);
RooGaussian gaus("gaus", "Gaussian distribution", x, m, s);

RooDataSet* dataset = gaus.generate(x, 10000);
RooDataHist binnedDataset("binnedData", "BinnedData", x, *dataset);

TCanvas c("c", "Pull demo", 1200, 800);
c.Divide(2,2);

c.cd(1);
auto frame = x.frame();
dataset->plotOn(frame);
gaus.plotOn(frame);
frame->Draw();

c.cd(3);
auto pulls = frame->pullHist();
pulls->Draw("P");
c.Draw();

[olantwin]

Thanks @hageboeck ! I will give this a go, when I find some time.

[etejedor]

@olantwin do you want this to be assigned to you then?

[olantwin]

I can't promise being able to look at this soon, but as long as that is understood, feel free to do so.

[hageboeck]

Stop, stop, stop!

It's much easier, all the code is already there! See this:

auto pulls = frame->pullHist();	auto pulls = frame->pullHist(nullptr, nullptr, true);

So,

Revised version of what has to happen

• Change the default arguments of pullHist and residHist to average = true.
• Update documentation to clarify that by default, the curve will be integrated over all bins.
• Mention the change in the Release notes

[guitargeek]

Thanks @hageboeck! I'll take care of it.

[olantwin]

Thanks Jonas, Stephan!