Dear all
I have a few questions concerning the following problem:
I have a numbercounting experiment with uncertainty in both, signal and background efficiency (sigEff and bkgEff) and the two are correlated.
I want to calculate a Confidence Interval on s using the profile likelihood method.
As a reference, I use the tutorial code rs101limitexample, which does the job, except for the correlations.
One first question concerning the tut code:
The signal expectation s is taken as an input along with b and obs. But later, before the Interval calculation begins, a fit of the model to the data is performed, resulting in a modification of s to obs-b.
This means, that the input parameter s is unnecessary, you could set it to obs-b just from the beginning and skip the fit. Is this correct?
Now to my modification:
Instead of the two independent gaussians for sigEff and bkgEff, I multiply a two dimensional gaussian of the two quantities and proceed as in the tut.
Is this the correct way to do it?
And one further question:
How do I build this gaussian?
What I did, is to use a 1D gaussian with mean 0 and sigma=1 and use a RooFormulaVar to construct an x, which mimics the 2D case.
Is there any objection to this approach?
One last question to the outcome of all this: Do you have any idea, what influence correlation should have?
In my case, positive correlation worsens the result, negative makes it better and I have no idea, if this is reasonable.
I hope, I could specify the problem well enough.
Thank you in advance
best regards Markus