FeldmanCousins includes an uncertainty of background?

Roofit and RooStats
1

Hi everyone,

I am using TFeldmanCousins ( root.cern.ch/root/html/TFeldmanCousins.html ) to compute the upper limit.
But this class does not include the uncertainty of background.
Is there another class which uses the FeldmanCousins method and includes this uncertainty?

Thank you very much.
Cheers,
Viet Nga

2

Hi,
It is correct, TFeldmanCousins does not include systematics. You would need to use RooStats for dealing with systematics. You would need to provide a full model in term of a Roofit workspace (Rooworkspace) and your
uncertainty in the background will be taken into account by profiling the nuisance parameter representing the background level.
See for example twiki.cern.ch/twiki/bin/view/Ro … ting_model

how to create a Poisson counting model and then you can run the macro StandardHypoTestInvDemo
(see twiki.cern.ch/twiki/bin/view/Ro … tInvDemo_C )
to compute a FeldmanCousins interval

Best Regards

Lorenzo

3

Hi Lorenzo,

I can now run the script and obtain the result I want.

I have another questions :
1: If I want to include the uncertainty of data (observed), how can I do?
2: Can we include both uncertainties of background and of data at the same time ?

Thank you so much.
Cheers,
Viet Nga

4

Hi,

What do you mean with the uncertainty in the data ? The statistical fluctuations of your observed data are automatically taking into account (also in TFeldmanCousins) by using for example a Poisson model for the observed data, e.g Poisson ( n_observed | n_expected (signal,background) )

Lorenzo

5

Dear Lorenzo,

I mean the systematic uncertainty on data. What do you think about this?
Thank you for your comments.

Cheers,
Viet Nga

6

Hi,

I guess you mean other systematic uncertainties affecting for example signal and/or background, for example theoretical uncertainties in cross section, luminosity, efficiencies, etc…
You can include all of these in your RooStats model, you just need to express them in term of some parameters and a constraint expressing the uncertainty. Again see the example I have sent you, twiki.cern.ch/twiki/bin/view/Ro … ting_model
and see how the uncertainty in the efficiency is introduced

Best Regards

Lorenzo

7

Hi Lorenzo,

I understand I need to create a Model = Poisson(nobs| s+b) * Gauss(b|b0,sigma_b) * Gauss(s|s0,sigma_s)
to include the systematic uncertainties on both signal and background. Is this right?

Thank you very much.
Best regards,
Viet Nga

[quote=“moneta”]Hi,

I guess you mean other systematic uncertainties affecting for example signal and/or background, for example theoretical uncertainties in cross section, luminosity, efficiencies, etc…
You can include all of these in your RooStats model, you just need to express them in term of some parameters and a constraint expressing the uncertainty. Again see the example I have sent you, twiki.cern.ch/twiki/bin/view/Ro … ting_model
and see how the uncertainty in the efficiency is introduced

Best Regards

Lorenzo[/quote]

8

Yes, you could do like this if you have a prior knowledge of s (e.g. from an external measurement) as
s0 +/- sigma
What is often done is to express s = mu * eff * xsec and you leave mu without any constraint and you add constraints on the efficiency eff and the cross -section estimate xsec

Best Regards

Lorenzo

9

Thank you so much, Lorenzo !
I got it. :slight_smile:
Cheers,
Viet Nga