Finding weights with TFractionFitter

ROOT
1

Hi,

I’m running ROOT 4.00/08 under a Linux RH9 and gcc 3.4.2.
I’m using TFractionFitter to fit a TH1 experimental data histogram as the sum of three Monte Carlo sources. I’m using the follow example, that works very well. But I know that the histogram corresponding to the total Monte Carlo prediction is not the same as a simple weighted sum of the input Monte Carlo distributions. My problem is how to find the weights, in such way I can multiply each MC histogram and than, sum all three in order obtain the exp. data histogram?

{
TH1F *data;
TH1F *mc0;
TH1F *mc1;
TH1F *mc2;

TObjArray mc = new TObjArray(3);
mc->Add(mc0);
mc->Add(mc1);
mc->Add(mc2);
TFractionFitter fit = new TFractionFitter(data, mc);
fit->Constrain(1,0.0,0.0);
fit->SetRangeX(1,34);
Int_t status = fit->Fit();
cout << "fit status: " << status << endl;
if (status == 0) {
TH1F* prediction = (TH1F*) fit->GetPlot();
data->Draw(“Ep”);
prediction->Draw(“same”);
}
}

Thanks for any help,

Sergio

2

Dear Sergio,

strictly speaking, it’s incorrect to speak about weights per MC source: it is the individual bins in the MC templates that are fluctuated according to (Poisson) statistics.

You can use the

method to obtain the “fluctuated” histograms.

                                         Regards
                                           Frank
3

Dear Frank,

Thanks for your answer. Yes, you are right. But what was trying to say is that what I need are some parameters (w) in order to have “data = w1MC1 + w2MC2 + w3*MC3”, like the Minuit. I don’t know if I’m using the best option (TFractionFitter). Besides I’ve tried what you told me, but I can’t access the value, only something like 0x9049158.

Thanks,

Sergio

4

Dear Sergio,

the method that I pointed you to does not return a weight, but rather the fluctuated histogram.

Now, the weights you’re after can be obtained from these fluctuated histograms combined with the fit results (the template fractions), as

[i]weight[i] = fraction[i] * integral[data] / integral

where the integral[] terms are simply the integrated bin contents for either your (fluctuated) template histogram or the data histogram. Note that this assumes you’re
not using a priori weights; otherwise, you have to account for these explicitly.

Regards,
Frank