Calculation of lower limit of expected 2 sigma band in StandardHypoTestInvDemo.C

I have a question regarding the output of the ROOT macro StandardHypoTestInvDemo.C, which I am using to carry out an inverted hypothesis test.

As you might know, the value of the expected upper limit using the median of the alternate model (for sensitivity studies) is given by the crossing point between the (1-CL) horizontal line and the median line in the p-value plot (see figure attached). The 1sigma and 2sigma expected limits are also calculated from this plot, and although I can see clearly where the values for the (-1 sig), (+1 sig) and (+2sig) expected limits come from, I am finding difficult to understand how the (-2sig) point is actually calculated.

As you can see in the example attached, the red horizontal line is crossing the 1sigma green band and the upper part of the 2sigma band. However, what is happening for the lower part of the 2 sigma band? For this particular example I am getting the following results:
expected limit (median) 6.618925
expected limit (-1 sig) 3.913686
expected limit (+1 sig) 12.378785
expected limit (-2 sig) 2.281817
expected limit (+2 sig) 18.912360

What is the program doing to get a value which is different from 0 for the expected limit (-2 sig)?
Also, if the right answer is actually 0, do you have any recommendation on how to calculate this lower 2 sigma limit properly to avoid the 0 (which will result in a limit with an error bar that goes all the way to 0)?

Thanks and kind regards,

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I agree it looks to me a problem in the calculation of the -2 sigma. Probably because the band changed the slope. If you can send me the result file produced by the macro, I can check this.

In general I would recommend to have more scan points in this case.

Best Regards


Hi Lorenzo,
Thank you for your answer and sorry for my late reply. Please find attached some data in which there are some plots and a couple of HypoTesInverterResult files that you can look at.

I am sending you one version using the two-sided test statistic (Eq. 8 from Cowan et al.) and another one with the one-sided type (Eq. 14). I started playing with these settings to see if that changes anything regarding this issue, but it seems that for the one-sided version the value at -2sigma is also not properly calculated.

Let me know if you require any more information from my side.
Kind regards,
Ibles (1.5 MB)

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