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

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,
MC_Sig_500GeV_Bck.root (5.17 KB)
BinnedLikelihood.C (4.67 KB)


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 [] to see how they perform the statistical inference.


– Gregory