Upper limit calculation with uncertainty using Asymptotic Calculator (with CLs)

[Konwel]

Hi @StephanH,

thanks for the quick answer!

• I set alpha_lumi as global observable and glob_lumi as nuisance, and set the Gaussian as
  Gaussian::constr_lumi(alpha_lumi, glob_lumi, 0.1)
  trying to mimic what you recommended here (but the naming scheme there was highly non-trivial):
  Upper Limit calculation - #6 by StephanH
  and what is in this example:
  ROOT: ROOT Reference Documentation
  but I may have got things mixed up. But in the end it may be just a naming scheme, I’ll make it more conventional for the sake of readability.

@StephanH

Next, you don’t need to limit the range of the global observable.

• I saw other examples where it is limited, but I see your point. In my case, I wanted to set at least a lower limit cause negative values are non-physical.

• If alpha_lumi acts, in my script, as global observable, shouldn’t it be set as a constant? I think I saw that in the two examples I linked above, in particular:

  gEff is global observable that should be constant, and is has the value of the monte carlo efficiency.

  What am I missing?

• sigeff is just a constant, too, like lumi_nom?

• Thanks for the likelihood example, is very useful!

@StephanH

The nuisance parameters are parameters of the likelihood, so all the alpha_i that are getting constrained and also all other parameters without constraints should be added to this set. Parameters are the things that should be optimised by the fitter. You definitely should not add glob_lumi to this set!

• Just to be rock sure: when you say should be added to this set, you are referring to the nuisance parameters set, right? And the same when alphas are parameters: for parameters here we mean nuisance parameters, correct?
  (But with my reversed naming scheme, glob_lumi (the mean of the Gaussian) is a nuisance parameter, isn’t it?)
  On the same line, just for confirmation: bkg_yield_nom, a0, and a1 all belong to the unconstrained parameters, i.e. they are to be set in the nuisance parameters set, right?

@StephanH

When setting up the model as I outlined above, switching on a systematic is just to set the parameter to “not const”.

• In practical terms, this means that I can turn off a systematic simply setting its corresponding “alpha_i” value to constant, while keeping it amongst the nuisance parameters?

Thanks really a ton for the thorough answer! I’ll adjust the naming scheme for clarity, apply your suggestions, and let you know if it works.
(It may be that in the end the this particular systematic will have very little or no effect, because it affects signal and background in the same way, so it’s basically an overall scale, to which a fit is very little sensitive.)