| The data have been binned in such a way that every bin contains more than 10 events. For every bin the integral of the S+B postfit pdf has been computed ($E_i$). | |
| In the table the value of the Pearson-$\chi^2 = \sum_i (E_i - O_i)^2 / E_i$ is reported with the number of bins of $m_{\gamma\gamma}$. | |
| Note that the $\chi^2$ is taking into account only the physical pdf, and not the product of constraints. In fact it is difficult to compute the number of degrees of freedom. We have 5 NPs for the background (4 "$\alpha$" + normalization) plus all the NPs for the statistical fluctuations (100+). Since these parameters are constrained they don't count -1 in the sum of the degree of freedom (something between 0 and -1). To try to evaluate their contribution we can imagine to add the constraint pdf to the computation of the $\chi^2$. This means to add 1 "bin", to subtract 1 dof, and to add a contribution to the $\chi^2$. This can (?) be evaluated as | |
| $$-2\log (pdf(x | x_{true})) + 2\log(pdf(x_{true}|x_{true}))$$ | |
| for e |
| The data have been binned in such a way that every bin contains more than 10 events. For every bin the integral of the S+B postfit pdf has been computed ($E_i$). | |
| In the table the value of the Pearson-$\chi^2 = \sum_i (E_i - O_i)^2 / E_i$ is reported with the number of bins of $m_{\gamma\gamma}$. | |
| Note that the $\chi^2$ is taking into account only the physical pdf, and not the product of constraints. In fact it is difficult to compute the number of degrees of freedom. We have 5 NPs for the background (4 "$\alpha$" + normalization) plus all the NPs for the statistical fluctuations (100+). Since these parameters are constrained they don't count -1 in the sum of the degree of freedom (something between 0 and -1). To try to evaluate their contribution we can imagine to add the constraint pdf to the computation of the $\chi^2$. This means to add 1 "bin", to subtract 1 dof, and to add a contribution to the $\chi^2$. This can (?) be evaluated as | |
| $$-2\log (pdf(x | x_{true})) + 2\log(pdf(x_{true}|x_{true}))$$ | |
| for e |
Very quick implementation of spline in RooFit, using ROOT TSpline. It supports splines of order 3 or 5. It also support interpolation in the log-space (x or y), for example exp(spline({x0}, {log y0})), useful when you have something (as xsections) that is more similar to exponentials than polynomials.
import ROOT
ROOT.gROOT.ProcessLine('.L RooSpline.cxx+')