# Strange (?) behaviour with RooStats::AsymptoticCalculator

Hi,

I am combining several channels via HistFactory to set a limit on a BR with the CLs method.
Here is an example of how I define some of the channels in the combination:

```<Function Name="ch1" Expression="(BR)*276." Dependents="BR[-20,20]" /> <Function Name="ch2" Expression="(BR)*622." Dependents="BR[-20,20]" /> <Function Name="ch3" Expression="(BR)*226." Dependents="BR[-20,20]" />```

where the numbers in the Expression are conversion factors between the BR (times 10^-5) and the observed number of signal candidates. Given existing limits and the size of my data I expect the limit at 90% CL on BR to be within the range [1.0,5.0] x 10^-5.
This is indeed confirmed by the expected limit, as you can see in the attached plot, calculated from toy data generated from the background distribution.
When running the algorithm on data, instead, the CLs distribution has a strange shape.
It goes asymptotically to 0.5 and, after a certain point, starts to go to zero. This point is exactly the minimum of the combined profile likelihood ratio.
Before this point, CLs+b is always exactly 0.5. After this point it starts going to zero.

In parallel I perform a simple fit to the data on every single channel, with the same background and signal models I am using for the CLs. When plotting the CLs distribution for the single channels I noticed that this behaviour is present on some of them, and specifically only on those channels where the signal yield is positive and more than one sigma away from zero.

The AsymptoticCalculator is set up as follows:

[code]AsymptoticCalculator * ac = new AsymptoticCalculator(*data, *bModel, *sbModel);

ac->SetOneSided(true);
ac->SetOneSidedDiscovery(false);
ac->SetQTilde(true); [/code]

My question is: is this behaviour expected? Or is there something wrong with the calculation?

I attach the CLs distribution and the combined profile likelihood ratio plots.

Cheers,
Lorenzo
CLs_plot.pdf (29.6 KB)

Hi,

It seems to me that you have a clear excess, your BR is significant greater than zero. The plot you are observing could be correct, since on the left side of your likelihood minimum the CL procedure does not make sense.

You can try in this case to use the FC procedures and use CLs+b and set the test statistics to be two-sided.

Best Regards

Lorenzo