abnormalities of calculated uncertainties of Xsec

[Kevin Kwok]

I used MG5 with Higgs Characterisation model (http://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/HiggsCharacterisation/HC_UFO_v4.1.zip @ http://feynrules.irmp.ucl.ac.be/wiki/HiggsCharacterisation) to simulate p p > x0 , x0 > mu+ mu- mu+ mu-. There are some unusual behaviours on the uncertainties of cross sections. I have attached the banner file below for reference. There are the problems:

1. I found that the cross section is quite sensitive to the seed. I used the same set of values of parameters but different seeds to generate N=100,000 samples 7 times, and the cross sections were quite different:
>> 0.003563 ± 3.2e-06 [seed = 21]
>> 0.003550 ± 2.8e-06 [seed = 30]
>> 0.003544 ± 2.8e-06 [seed = 39]
>> 0.003574 ± 3.6e-06 [seed = 48]
>> 0.003543 ± 2.7e-06 [seed = 57]
>> 0.003575 ± 3.3e-06 [seed = 66]
>> 0.003568 ± 3.0e-06 [seed = 75]
These numbers with the uncertainties taken into account did not overlap. Is it a problem for the generator, or something else?

2. I found the uncertainties in cross section for N=1,000,000 were larger then that for N=100,000, so I generate N=1,000,000 samples with different seeds, again the MC sample is very sensitive to the seed and even worse than N=100,000
>> 0.003570 ± 9.1e-07 [seed = 84]
>> 0.003575 ± 0.00013 [seed = 66]
>> 0.003577 ± 0.00011 [seed = 75]
>> 0.003570 ± 9.1e-07 [seed = 84]
It is clear that the seed had important effect (compare seeds = 66,75 with seed = 84). The same seed did give the same cross section, as it should be (compare the results between two seed=84 cases). Note that the bad seeds in N=1,000,000 (seeds = 66,75) had no problem in N=100,000. Again, is it a problem for the generator, or something else?

3. The (pseudo-)random number seeds seemed not to be pseudo-random, they has a fix pattern: 21 -> 30 -> 39 -> (48) -> 57 -> 66 -> 75 -> 84 -> (94) -> ... That is, every time I run MG5 the random seed for the first run is the same, 21, and 30 for the second run, and so on. This will lead to a bias while the results are being cross-checked, and it becomes serious when the results are sensitive to the seed. Can this be rectified by programming algorithm means?

====================================================================
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#*********************************************************************
# *
# MadGraph5_aMC@NLO *
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# http://madgraph.hep.uiuc.edu *
# http://madgraph.phys.ucl.ac.be *
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#* Command File for MadGraph5_aMC@NLO *
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set group_subprocesses Auto
set ignore_six_quark_processes False
set loop_optimized_output True
set low_mem_multicore_nlo_generation False
set loop_color_flows False
set gauge unitary
set complex_mass_scheme False
set max_npoint_for_channel 0
import model sm
define p = g u c d s u~ c~ d~ s~
define j = g u c d s u~ c~ d~ s~
define l+ = e+ mu+
define l- = e- mu-
define vl = ve vm vt
define vl~ = ve~ vm~ vt~
import model ./HC_UFO
generate p p > x0 , x0 > mu+ mu- mu+ mu-
output ~/Final/
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HC_UFO
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[Olivier Mattelaer (olivier-mattelaer)]

Hi,

> These numbers with the uncertainties taken into account did not overlap. Is it a problem for the generator, or something else?

You should never trust too much the statistical uncertainties quoted by MC integrator.
First we can not proof that the estimator of the error is going to converge trough the real statistical error or not.
In practise, it seems that such error is often under-estimate by a factor of close to 5.

Now, this is not problematic since this is a LO computation where the cross-section is affected by theoretical uncertainty which are in the best case scenario of the order of 20% (typically much larger than that).

> It is clear that the seed had important effect (compare seeds = 66,75 with seed = 84). The same seed did give the same cross section, as it should be (compare the results between two seed=84 cases).

Looks like something bad happens for seed 66 and 75. Maybe some overtraining of the grid which can happens sometimes when you request too many events in one go. The fact that the error is (slightly) higher
should not be seen as problematic in this case as this is still much smaller than the other type of error.

> Note that the bad seeds in N=1,000,000 (seeds = 66,75) had no problem in N=100,000. Again, is it a problem for the generator, or something else?

You can not compare the same seed with two different N, this is as different as using two different seed.
They are obviously a correlation within the first iteration of the code but this correlation attenuates iteration after iteration.

> 3. The (pseudo-)random number seeds seemed not to be pseudo-random, they
> has a fix pattern: 21 -> 30 -> 39 -> (48) -> 57 -> 66 -> 75 -> 84 ->
> (94) -> ... That is, every time I run MG5 the random seed for the first
> run is the same, 21, and 30 for the second run, and so on. This will
> lead to a bias while the results are being cross-checked, and it becomes
> serious when the results are sensitive to the seed. Can this be
> rectified by programming algorithm means?

Well we do not choose the seed in a random way (as you spot it out).
We could do it obviously but then they are always a risk that if you run N times that you
can have two samples with the same seed (which would be bad).
This method ensures that you never have twice the same seed.

If you want to run on multiple directory simultaneously. The advised method is either
1) use gridpack in READONLY mode (such that you limit IO) [but where you have to set the seed manually]
2) you can define your starting seed for each of the directory with enough gap to ensure that they do not overlap.
(i.e. if you do
> launch
> set seed 100k
> launch
> launch
the seed of the second and third will be
100009 and 100018

Cheers,

Olivier

> On 17 May 2018, at 15:50, Kevin Kwok <email address hidden> wrote:
>
> Public bug reported:
>
> I used MG5 with Higgs Characterisation model
> (http://feynrules.irmp.ucl.ac.be/raw-
> attachment/wiki/HiggsCharacterisation/HC_UFO_v4.1.zip @
> http://feynrules.irmp.ucl.ac.be/wiki/HiggsCharacterisation) to simulate
> p p > x0 , x0 > mu+ mu- mu+ mu-. There are some unusual b...