Asymptotic validity

Dear experts,

I would like to compare the test statistic distribution with the pdf expected in the context on the asymptotic approximation in order to test de validity of the asymptotic approximation (for both limit setting tests and discovery test).

  1. Are there macros proposing such comparisons (for instance to get the plots of Figures 3 and 5 of arxiv.org/pdf/1007.1727v3.pdf) ?

  2. If not, to obtain the asymptotic predictions, is there any other ways that the use of q_muA, … printed in the asymptotic calculator outputs ?

Thanks in advance,
Best,
Loïc

Hi,

A macro who can make similar plot is the roostats/StandardHypoTestDemo.C macro. You can run this macro with a number counting mod which is quite easy to create in RooFit, one examples is here

twiki.cern.ch/twiki/bin/view/Ro … isson_Coun

Running the StandardHypoTestDemo.C for the FrequentistCalculator you should get the test statistics distribution for the Null (mu = 0) and the Alternate (mu = 1) hypothesis.
With the asymptotic Calculator you get directly the p-values, but by reversing the formulae you should be able to get the functional forms for the null and alternate test statistic distribution. Otherwise you can always use the printed value of observed qmu and Asimov qmu.

Cheers

Lorenzo

Hi Lorenzo,

Thanks for your answer :slight_smile:
I was actually wondering if anyone implemented the functional forms for more general cases f(qmu | mu’), just to avoid reinventing the wheel (and potentially introduce bugs).

Thanks,
Cheers,
Loïc

HI,

For the general case the functional form is the non-central chi-square distribution for one-degree of freedom. This is implemented in ROOT as a function in the MathMore library, ROOT::Math::noncentral_chisquared_pdf

Cheers

Lorenzo