Compute +/-1 and +/-2 sigma bands around the expected limit

Roofit and RooStats
1

I hope this is the right forum for my question:
I am using a binned LikelihoodMethod to compute an (“observed”) upper limit on the Zprime (to ttbar) prduction cross section, as function of a physical parameter ( Zprime mass).
Using the sum of (Standard Model) background processes, I also compute an expected upper limit as function of the physical parameter.

I would like to compute +/-1 and +/-2 sigma bands around the expected limit, in order to provide an estimate of how compatible a certain observed upper limit with the expected value of the limit.

I am wondering if there is a recommended way to compute the +/-1 and +/-2 sigma bands ?

so the code is attached

Thank you very much,
Wael
MC_Sig_500GeV_Bck.root (5.17 KB)
BinnedLikelihood.C (4.67 KB)

2

Hello,

It would not be the ROOT developpers but the statistical committee of you experiment to consult as of statistical recommandations.

However, what is usually do is to toss toy-MC experiments accourding to your model, compute for each the upper limit as you would do for your data, and take the 50% quantile (median) as expected limit and the 16%, 84% quantiles for the 1 sigma bound.

I would add that ProfileLikelihood is not always an accurate approach for limit calculation (in low statistics tails of distributions).

You could have a look at [cdsweb.cern.ch/record/1375842] to see how they perform the statistical inference.

Regards,

– Gregory