How to treat limited background statistics

[maxnoe]

The the current implementations of calculating sensitivities use different approaches of handling the limited background statistics, especially when rather hard cuts are applied.

Possible solutions:

• Increased background region size by using an alpha << 1 and then just do the normal calculations with that alpha

• Using all background events without a directional cut and then scale the number to the size of the off region, so basically the off region is the whole fov and alpha calculated according to the on region size.

Other approaches?

What are advantages and disadvantages?

What is used in EventDisplay (@GernotMaier) and what is used in MARS-CTA (@moralejo)?

[GernotMaier]

Eventdisplay uses all gamma_diffuse, electrons, and protons in the following off-axis angle bins:

THETAMIN=( 0.0 1.0 2.0 3.0 4.0 5.0 )
THETAMAX=( 1.0 2.0 3.0 4.0 5.0 6.0 )

Direction cut is only applied to the gamma_diffuse events (relative to the true direction). This approach assumes that the change of acceptance in this offset interval is such, that it does not affect the sensitivity calculation.

[maxnoe]

So that means that for the alpha that enters Li & Ma you divide the size of the circle with the radius of the theta cut by the size of the ring?

And you evaluate the offset using the reconstructed or the true origin? I think for the background estimation, reconstructed would make more sense.

To simply check with the existing script now: for the on-axis performance, that would be identical to using a global theta cut of 1 degree for the background and calculating alpha as (theta_cut / 1°)²

[GernotMaier]

That does not enter Li & Ma, this is before: this allows us to calculate signal/background rate curves vs energy from which we then can calculation the number of Non/Noff events.

I didn't see any difference between using reconstructed or true directions.

[maxnoe]

So you don't actually calculate the sensitivity based on the DL2 event lists but estimate the numbers from the Background rate / effective area?

Wouldn't this hide the statistical uncertainties arising from the limited simulation statistics from the sensitivity calculation?

[GernotMaier]

This is where toy experiments come into play: I am running 100 of them with non/off determined from expected rates + errors.

[moralejo]

Eventdisplay uses all gamma_diffuse, electrons, and protons in the following off-axis angle bins:

THETAMIN=( 0.0 1.0 2.0 3.0 4.0 5.0 )
THETAMAX=( 1.0 2.0 3.0 4.0 5.0 6.0 )

Direction cut is only applied to the gamma_diffuse events (relative to the true direction). This approach assumes that the change of acceptance in this offset interval is such, that it does not affect the sensitivity calculation.

It is done in exactly the same way in Mars.
If the proton statistics is too low for some Eest bin (<4 events, happens rarely in full productions) we take the hadronness distribution of protons in the given Eest bin, and extrapolate to low hadronness (g-like region) with both a power-law and an exponential, then we obtain the proton rate for the actual hadronness cut by integrating the fitted functions and averaging the two values. We take the full range between the two extrapolations as uncertainty.