Difference in upper limits for profile likelihood and frequentist approach

[CS_p]

Dear Experts,

I want to set 90% CL upper limits on the signal yield (Nsig). I have done this using two methods, the profile likelihood projection and the frequentist approach. The plots for them are attached herewith;

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I would expect similar Nsig(UL) since the same PDF is used for both methods. But from the likelihood method, the Nsig(UL) is ~5, while from the frequentist approach, it’s ~3.8. What could be the reason for this difference?

Thanks,

[vpadulan]

Dear @CS_p ,

Thanks for your question. Maybe @jonas or @moneta can help you.

Cheers,
Vincenzo

[Dilicus]

Probably the difference in the two method is that your N_{sig} for profile likelihood is allowed to have negative value. If you force N_{sig} to be larger or equal to zero, the profile likelihood distribution will change shape.

[CS_p]

Hello @Dilicus,

Thank you for your response. Herewith I have attached the profile likelihood plot confining Nsig to be positive, but still, the Nsig(UL) is quite different from the frequentist approach.

Any other views on this issue?

Thanks,