# How you go about finding correlations?

• A
• ChrisVer
In summary, correlation between systematics is studied by varying them independently and studying the resulting correlation.

#### ChrisVer

Gold Member
Suppose you have several systematics [as happens in any analysis].
How can you go and determine the correlation matrix between each of their NPs?
so for example if you have (let's say roughly) 3 systematics: TES, JES , JER (tau/jet energy scale and jet energy resolution), how could you make a table that hase:

\begin{tabular}{c|c|c|c}
TES JES JER
TES
JES
JER
\end{tabular}

and entries the correlation coefficients $\rho \in [-1, 1]$?
Of course the diagonal will have +1 ...

A correlation matrix between the actual NP? Ask the experts who made them.
A correlation between their effect on the final numbers? Ideally there is no such correlation (otherwise the NP are not well chosen), but you can vary more than one at the same time to study correlations. Keep in mind that statistics will can fake nonexistent correlations.

mfb said:
A correlation matrix between the actual NP? Ask the experts who made them.
I think that's the case... huh...

mfb said:
A correlation between their effect on the final numbers? Ideally there is no such correlation (otherwise the NP are not well chosen), but you can vary more than one at the same time to study correlations. Keep in mind that statistics will can fake nonexistent correlations.
Well that would be a way to go if I actually had the ability to produce events with more than just 1 NP altered per time.

In fact what I don't understand is that [as far as I know] correlation is between two variables which might be random distributed... I don't understand how it can be applied to the case of a whole bunch of "events". In fact they change the experiment [eg 1 TES has the ability to change the amount of the detector matterial I think].

The random distribution is in the value of the NP. You hope that the nominal value is correct, but it could also be a bit higher or lower.

As an example, let's say two NP correspond to the amount of material in your detector, relevant for scattering or showering. Maybe one NP for the barrel, one for the endcaps, or something like that. You can now study two things:

- if we overestimate the amount of material in the barrel, do we also overestimate it in the endcap? This could happen if the same components are used in both detector parts. It would correlate the NP itself.
- how does our measured value change if we (a) vary the barrel NP up and down within its uncertainties, (b) vary the endcap NP up/down, (c) vary both at the same time? Ideally this is linear, if it is not things can get interesting.