This is a follow-up on the following thread which is now closed: Significance bin by bin so I am creating a new thread.
I have a similar construct with a background and a signal histogram, and I want to manually calculate an estimate of the Asimov significance. I am calculating the significance in the i-th bin using:
Si = si/sqrt(bi+uncbi^2),
where si, bi and uncbi, are the signal, background and uncertainty in the background yield, respectively.
Now I wish to quantify the significance from all the bins, with a goal to maximize this sum. From @moneta 's answer in the above thread, I see that it is not simply the sum in quadrature of Si’s, but instead should be distributed like a Chi^2 distribution. Given this, does it make sense, for example, to maximize the reduced Chi^2? I would then evaluate:
Sum(Si^2)/N, with N as the total number of bins, and then maximize this for different binning choices. Is this valid? Does this still work if I choose varying bin widths?
I shall appreciate any help in this regard!