Binned fit using ROOT::Fit::PoissonLLFunction

ROOT
1

Hello,

I am trying to use ROOT::Fit::PoissonLLFunction to fit some low statistics histograms. Using directly TH1::Fit is not an options since I need to do a combined (simultaneous) fit of many of such histograms. However, I must be attempting to use ROOT::Fit::PoissonLLFunction not correctly, since I get too large errors (by a factor of ~1.5); while if I use TH1::Fit (on a single histogram), the results look reasonable.

Here is a simplified example of how I use ROOT::Fit::PoissonLLFunction (a full macro is attached as well):

 // h1 is a histogram with 100 events with Gaus(2,20) distribution
 // f1 is a Gaus function
 // xMin = -100.0, xMax = +100.0
 ROOT::Fit::Fitter fitter;
 const int nPar = f1->GetNpar();
 fitter.Config().SetParamsSettings(nPar, f1->GetParameters());
 fitter.Config().ParSettings(0).SetLimits(0.0, 20.0*nEvents);
 fitter.Config().ParSettings(1).SetLimits(xMin, xMax);
 fitter.Config().ParSettings(2).SetLimits(xMin, xMax);
 fitter.Config().MinimizerOptions().SetPrintLevel(2);
 fitter.Config().SetMinimizer("Minuit2", "Migrad");

 TF1 * fitFun = new TF1("fitFun", Gaus, xMin, xMax, nFitFunPar);
 ROOT::Math::WrappedMultiTF1 * wf = new ROOT::Math::WrappedMultiTF1(*fitFun, 1);
 ROOT::Fit::DataOptions opt;
 opt.fUseEmpty = true;
 ROOT::Fit::DataRange range;
 range.SetRange(xMin, xMax);
 ROOT::Fit::BinData * data = new ROOT::Fit::BinData(opt, range);
 ROOT::Fit::FillData(*data, h1);

 const bool chi2Fit = false;
 ROOT::Math::FitMethodFunction * localFitFun = new ROOT::Fit::PoissonLLFunction(*data, *wf);
 // also tried to set explicitly weight=0/1 and extended=true/false

 fitter.FitFCN(fitter.Config().NPar(), *localFitFun, 0, data->Size(), chi2Fit);
 const ROOT::Fit::FitResult result = fitter.Result();
 result.Print(cout);

I would really appreciate if somebody could help me to understand how to use PoissonLLFunction correctly.

Thank you,
Siarhei.

TestPLLFit.C (4.06 KB)

2

Hi,

Since this is a likelihood fit, you should define the correct level for the error (it is 0.5 instead of 1 as in a least square fit).

fitter.Config().MinimizerOptions().SetErrorDef(0.5);

Best Regards

Lorenzo

3

Dear Lorenzo (or anybody who knows the answer),

Could you please help me to figure out what I should do to be able to use ROOT::Fit::PoissonLLFunction on weighted histograms (i.e. to make the fit to be equivalent to the fit option “WL” of a direct fit with a TF1)?

Thank you very much for your help!!!
Siarhei.

4

Hi,

You need to create the ROOT::Fit::PoissonLLFunction class passing in the constructor the option that is a weighted fit,

ROOT::Math::FitMethodFunction * localFitFun = new ROOT::Fit::PoissonLLFunction(*data, *wf, true);

Then after having minimiser the function you need to apply a correction for the error using the square of the weights when building the likelihood.

// minimise first the likelihood
fitter.FitFCN(fitter.Config().NPar(), *localFitFun, 0, data->Size(), chi2Fit);
// apply the correction
localFitFun->UseSumOfWeightSquare();
fitter.ApplyWeightCorrection(*localFitFun);

This should work. You can look also at the relevant code in the implementation of the Fitter class

Best Regards

Lorenzo

5

Dear Lorenzo,

Could you please let me know if the code of ROOT::Fit::PoissonLLFunction multithread safe?

Thank you very much for your help!!!
Siarhei.