Each event has a weight. What is its error?

Hi,

You can not assign an statistical error to a single event, the weight of the event already include the Jacobian and therefore the fact that we have under/over probed part of the phase-space.
You can assign other type of error to a single event like
1) numerical precision error (how precise was the computation of the amplitude/Jacobian/...) this error is typically neglected.
2) theoretical error: those error are related to the renormalizaton and factorization scale. Those error are include by having more than one weight associated to the event.
3) PDF error: also include by associating multiple weight to the events (with a formula --PDF specific-- on how to estimate the error)

For the statistical error, those only make sense on a sample of events since this is an error of the integral, not of the function to integrate.
They are different estimator available (both for the cross-section and the associated error) and various part of the code can/are using different estimator.
So it is normal that you get different value of the cross-section reported in various place.

> It is not \sigma/\sqrt{N_evs}

This is one way to estimate the error based on the number of unweighted events.
We typically compute an error for each iteration baed on the weigthed events.
and the "final" error for that channel is based on the last three iterations (while the unweighted events are generated only for the last iteration)

> 1) The integrated weight in <MGGenerationInfo> is quite odd and is in contradiction with the events weight and the cross section result at the bottom of the file. What is going on? Is this the first MC estimate?

If you use the bias module, this number is likely the value of the cross-section computed with the biais. This is not then not the number that you want to use.

Cheers,

Olivier

> On 23 Nov 2023, at 21:00, Francesca Acanfora <email address hidden> wrote:
>
> New question #708522 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/708522
>
> Dear experts,
>
> I am trying to simulate e- e+ > e- e+ a a. I need to characterize it very accurately across the whole phase space. To do so I am performing multiple generations, which I would like to combine.
> Each generation has some cuts and/or a bias (implemented with my bias module).
> I need to know what error is to be associated to each event to properly track the fact that some phase space areas were populated more poorly than others.
>
> I copy-paste here some lines from one of my .lhe.gz biased files that are necessary for understanding my questions:
>
>
> <MGGenerationInfo>
> # Number of Events : 50000
> # Integrated weight (pb) : 6717840.124000001
> </MGGenerationInfo>
> </header>
> <init>
> 11 -11 5.290000e+00 5.290000e+00 0 0 0 0 -4 1
> +2.4515999e+00 +3.1964443e-03 +2.4515999e+00 1
> <generator name='MadGraph5_aMC@NLO' version='3.4.2'>please cite 1405.0301 </generator>
> </init>
> <event>
> 6 1 +5.2499286e-02 5.23715800e+00 7.54677100e-03 2.09571600e-01
>
>
>
> 1) The integrated weight in <MGGenerationInfo> is quite odd and is in contradiction with the events weight and the cross section result at the bottom of the file. What is going on? Is this the first MC estimate?
>
> 2) In the <init> I can see +2.4515999e+00 is the total cross section and +3.1964443e-03 is its error in pb. How is the error computed? It is not \sigma/\sqrt{N_evs} so there must be an information about each event error somewhere. Now, when an event starts (after <events>) I can read that the third entry of the row is the event weight multiplied by the number of events in the run, but there is no error with it. Is there a way to recover or at least estimate it?
>
> Thank you!
>
> Francesca
>
>
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.