The FCN of simultaneous fit of two data samples

Roofit and RooStats
1

Dear All,
I have two data samples: data and data_ctl, I perform individual fits on data and data_ctl, I also perform a simutaneous fit on data and data_ctl;

My first problem is:

  1. I use Likelihood method to fit data with model, fit data_ctl with model_ctl, and obtain the minimum FCN_1min and FCN_2min, respectively;
  2. I use Likelihood method to simultaneously fit data with model and data_ctl with model_ctl, and obtain the FCN_min of the simultaneous fit; (in the simultaneous fit, the parameters of model and model_ctl are free);
  3. I find FCN_min != FCN_1min + FCN_2min;
  4. But, in mathematics, a simultaneously fit means to search the minmum value of FCN = FCN_1 + FCN_2; it should be FCN_min = FCN_1min + FCN_2min; because FCN_1min and FCN_2min are the minimum value of each part; the minimum value of FCN shoule be FCN_1min + FCN_2min, right?
    the script is attached as: rf501_simultaneouspdf_likelihood.C

My second problem is:

  1. I use Least-Chi2 method to fit data with model, fit data_ctl with model_ctl, and obtain the minimum FCN_1min and FCN_2min, respectively;
  2. I use Least-Chi2 method to simultaneously fit data with model and data_ctl with model_ctl, and obtain the FCN_min of the simultaneous fit; (in the simultaneous fit, the parameters of model and model_ctl are free);
  3. I find FCN_min = FCN_1min + FCN_2min, which is as the mathematical prediction;
  4. However, when I use my real data, for Least-Chi2 method I find FCN_min != FCN_1min + FCN_2min,
    so I am very confused now, please help me !
    the chi2 fit script is attached as: rf501_simultaneouspdf_chi2.C
    rf501_simultaneouspdf_likelihood.C (6.33 KB)
    rf501_simultaneouspdf_chi2.C (6.9 KB)
2

Hi,

It is not correct to say that you have always FCN_min = FCN_1min + FCN_2min. This statement is correct only if the FCN_1 and FCN_2 have independent parameters. As far you have common parameters between the two FCN, then it is trivial to show that FCN_min != FCN_1min + FCN_2min. It can only be true when FCN_1 and FCN_2 have the minimum at the same parameter values, since only there their derivatives are zero and therefore the sum of the derivative is also zero.

Best Regards

Lorenzo