Change binomial error calculation for efficiencies
Errors of efficiencies are calculated in umami with binomial errors as described in section 2.2 here.
In my opinion, we have to correct the code in view of what number of total jets we use.
Say we want to calculate the c-jets efficiency at a b-tagging WP of 70%. Then we assume that our "c-jets cut" is a binomial process with probability c_jets_efficiency
.
Our estimator is c_jets_efficiency = k_c / N_c
where k_c
is the number of c-jets below the cut and N_c
the total number of c-jets.
In my opinion, these are the values we have to take for N
and k
when we calculate the error with the following formula from the paper
I think this is not done correctly atm.