ConfInterval with correlations

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

Hi Markus,

I can answer the technical question of your mail right away:

As of ROOT version 5.24 there is a special class to construct multi-variate
Gaussian with correlations: it is class RooMultiVarGaussian, it takes as
input the variables, a mean vector mu (RooArgList or TVectorD) and the
covariance matrix (a TMatrixSymD).

I will bring your post to the attention of the RooStats experts to answer your
other questions.

Wouter

Thank you very much for your quick reply

kind regards

Markus