On / off problem, upper limit evaluation, CLb depends on POI

[andrea.celentano]

Dear all,
I developed a model for an on/off problem, where my likelihood is the product of two Poisson functions, the first depends on the measured number of events “n” in the signal region, with mean value S+B+B’, and the second is a Poisson function that depends on the measured number of events “m” in the control region, with mean value “tau * B”. “tau” and “B’” are two constant parameters, with no uncertainty. B is a nuisance parameter.
If I understood correctly, the CLb value should not depend on the POI (here, S). However, If I try to calculate an upper limit, both with the AsympoticCalculator and with the FrequentistCalculator, I get a dependence on “S” for small value of this. I attach two plots to show this, obtained, respectively, from the AsymptoticCalculator and from the FrequentistCalculator.

I also attach the workspace, and the code I use for hypo inversion.
I am using ROOT version 6.20/04 on Centos7.

poissonRuns.out_tot.root (12.8 KB)
poissonRuns_HipoInverter_minimal.C (4.5 KB)

Thanks in advance,
Andrea

[couet]

I guess @moneta can help you.

[moneta]

Hi,
I would not worry about this. It is an artifact of the definition of the one side test statistics, see eq. 53 of https://link.springer.com/content/pdf/10.1140/epjc/s10052-011-1554-0.pdf.
The test statistics is defined as zero for tested values less than the fitted signal value, so you see a flat blue line and this dependency, since it does not make sense to look in that region of parameter space.

Lorenzo

[andrea.celentano]

Dear Lorenzo,
thanks for your clear explanation!

Bests,
Andrea