MadGraph5_aMC@NLO

Combining runs to reduce statistical error

Asked by jannisgebbo

Dear Madgraph experts,

I am generating
p p > j j [QCD]
and shower the events with PYTHIA8.

At the moment, I am struggling with reaching numerical accuracy for some observables I want to compute. This is because I need to cover quite a wide range of transverse momenta. For this, I added a bias to cuts.f by taking the max parton p_T of an event and exponentiating it with a constant predefined power. If I choose this power a bit lower, I get good statistics for lower momenta but bad statistics for higher momenta. If I choose it a bit higher, the statistics are simply inverted.
So the idea was to combine these two runs to get good statistics on the whole momentum range. For my analysis, I am using the HwU output. I want to combine each histogram for the two runs. To weight the cross section in each bin of each histogram correctly, it would be helpful to know the number of events N_bin that contributed to this precise bin. This is not stored in the HwU format (as far as I know) but maybe one can find out through the statistical uncertainty corresponding to the cross section of each bin. If the relative error equals the inverse square root of the number of events in that bin (deltaSigma/Sigma = 1/sqrt(N_bin)), it would be possible to calculate N_bin.

So my question is if the statistical error is calculated this way and if one can do what I described above to get better statistics.

Thank you in advance!
Best,
Jannis

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Olivier Mattelaer (olivier-mattelaer) said : 		#1

Hi,

The weight of each event is not identical so not the error does not scale like deltaSigma/Sigma = 1/sqrt(N_bin))
So you can not use variable/information to combine two HwU file, but they are statistical formula that you should be able to do it without N_bin since you know the value in each plot and the variance of each plot.

Cheers,

Olivier

> On 29 Jan 2024, at 17:55, jannisgebbo <email address hidden> wrote:
>
> New question #709147 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/709147
>
> Dear Madgraph experts,
>
> I am generating
> p p > j j [QCD]
> and shower the events with PYTHIA8.
>
> At the moment, I am struggling with reaching numerical accuracy for some observables I want to compute. This is because I need to cover quite a wide range of transverse momenta. For this, I added a bias to cuts.f by taking the max parton p_T of an event and exponentiating it with a constant predefined power. If I choose this power a bit lower, I get good statistics for lower momenta but bad statistics for higher momenta. If I choose it a bit higher, the statistics are simply inverted.
> So the idea was to combine these two runs to get good statistics on the whole momentum range. For my analysis, I am using the HwU output. I want to combine each histogram for the two runs. To weight the cross section in each bin of each histogram correctly, it would be helpful to know the number of events N_bin that contributed to this precise bin. This is not stored in the HwU format (as far as I know) but maybe one can find out through the statistical uncertainty corresponding to the cross section of each bin. If the relative error equals the inverse square root of the number of events in that bin (deltaSigma/Sigma = 1/sqrt(N_bin)), it would be possible to calculate N_bin.
>
> So my question is if the statistical error is calculated this way and if one can do what I described above to get better statistics.
>
> Thank you in advance!
> Best,
> Jannis
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

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