# Correlated event-by-event uncertainties?

Hi,

I’m doing an angular fit in which there are per-event uncertainties for each of the angles, but: they are correlated with one another. Is there any way to input per-event uncertainties as a covariance matrix, rather than just the per-event uncertainties on each variable individually?

thanks!
justin

Hi,

the standard least square (chi2) function used for fitting in ROOT the uncertainties are considered uncorrelated. If you have correlated uncertainty you have to write yourself the chi2 function using the covariance matrix and then minimize directly using Minuit or any other minimizer provided by ROOT. See root.cern.ch/drupal/content/nume … idim_minim

Best Regards

Lorenzo

Hi,

I should have mentioned that this is RooFit-based fitting code. So integrating it with the standard ROOT fitting would not be entirely trivial. But probably I have to do some poking around with things.

thanks,
justin

Hi Justin,

I’m not sure I understand what you are trying to do. Can you go into a little more detail? To me it sounds as if you are talking about both a statistical uncertainty (which is uncorrelated between events) and a systematic uncertainty (which is correlated between events). You may be able to construct your fit this way…

Cheers,
Charles

Hi Charles,

Sure! Indeed you are right that the correlations themselves should not vary event-to-event, just the statistical uncertainties that they modulate. We have a particle A that undergoes a two-body decay to B and C. B and C then both undergo two-body decays to D & E, and F & G respectively. I am trying to fit for the spin of A (B and C are both vector particles).

There are 5 independent angles (and two invariant masses) describing this decay chain, but their measurements have correlations.

cheers,
justin