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From: Luigi Salvatore Esposito <luigi.salvatore.esposito_at_cern.ch>

Date: Wed, 26 Oct 2016 14:18:02 +0000

Dear Emilio,

the result of the USRBIN is a random variable.

In order to evaluate its statistical uncertainties, one has to repeat each simulation for several batches.

As demonstration I ran FLUKA with N=1e5 primaries and with N=1e3 primaries. Both simulation repeated 5 batches.

The results are summarised in the following table.

As you can see by comparing the last two lines, the error of the mean and the expected uncertainties after simulated N primaries

are reasonably close having simulated only 5 batches. And moreover, they scale by the expected factor 10.

By the way, this is how the statistical uncertainties is evaluated in FLUKA when the results of several batches are merged

using the auxiliary programs in $FLUPRO/flutil.

Finally, you may want to a look at these slides<https://indico.cern.ch/event/442634/contributions/1096541/attachments/1185162/1717804/09_Statistics_and_sampling_2015.pdf> from the last FLUKA course (pp 32 and following)

Best, luigi

On 23 Oct 2016, at 11:42, emilio_at_impcas.ac.cn<mailto:emilio_at_impcas.ac.cn> wrote:

Dear FLUKA experts,

I am simulating the neutron production from a cylindrical W target using a 400 MeV proton beam; using the loop function, I change the radius R and the length L of the cylinder, scoring the total neutron produced.

At first, I tried with 10^5 proton; however I found some weird results (the neutron yield was decreasing and then increasing again changing L); for this reason I increased the primary particles up to 10^6, and the results were more consistent (you can find the imput cards in the attached files).

My problem is that the difference between the two bunch of simulations seems too large to be explained with statistical fluctuation: in the file "Neutron Yield 400 MeV.pdf" you can find the neutron yield n/p with 10^5 (solid curves) and 10^6 (dashed curves) protons; each color corresponds to a different radius. I also included the error bar due to the statistical fluctuation, calculated as Sqrt[n]/p, where n is the number of neutrons ! scored, p is the number of proton. There are several points at 6 and more sigma's, which is not possible with 30 datapoints. In general it looks like the statistical fluctuations are roughly 3 times larger than what expected with Sqrt[n].

Is it not correct to assume that the statistical error would be Sqrt[n]? Am I using some biasing that I am not aware of?

Thank you for your help

Emilio Ciuffoli

<Neutron Yield 400MeV.pdf><W-400MeV.inp><W-400MeV-2.inp>

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Received on Wed Oct 26 2016 - 17:55:21 CEST

Date: Wed, 26 Oct 2016 14:18:02 +0000

Dear Emilio,

the result of the USRBIN is a random variable.

In order to evaluate its statistical uncertainties, one has to repeat each simulation for several batches.

As demonstration I ran FLUKA with N=1e5 primaries and with N=1e3 primaries. Both simulation repeated 5 batches.

The results are summarised in the following table.

As you can see by comparing the last two lines, the error of the mean and the expected uncertainties after simulated N primaries

are reasonably close having simulated only 5 batches. And moreover, they scale by the expected factor 10.

By the way, this is how the statistical uncertainties is evaluated in FLUKA when the results of several batches are merged

using the auxiliary programs in $FLUPRO/flutil.

Finally, you may want to a look at these slides<https://indico.cern.ch/event/442634/contributions/1096541/attachments/1185162/1717804/09_Statistics_and_sampling_2015.pdf> from the last FLUKA course (pp 32 and following)

Best, luigi

On 23 Oct 2016, at 11:42, emilio_at_impcas.ac.cn<mailto:emilio_at_impcas.ac.cn> wrote:

Dear FLUKA experts,

I am simulating the neutron production from a cylindrical W target using a 400 MeV proton beam; using the loop function, I change the radius R and the length L of the cylinder, scoring the total neutron produced.

At first, I tried with 10^5 proton; however I found some weird results (the neutron yield was decreasing and then increasing again changing L); for this reason I increased the primary particles up to 10^6, and the results were more consistent (you can find the imput cards in the attached files).

My problem is that the difference between the two bunch of simulations seems too large to be explained with statistical fluctuation: in the file "Neutron Yield 400 MeV.pdf" you can find the neutron yield n/p with 10^5 (solid curves) and 10^6 (dashed curves) protons; each color corresponds to a different radius. I also included the error bar due to the statistical fluctuation, calculated as Sqrt[n]/p, where n is the number of neutrons ! scored, p is the number of proton. There are several points at 6 and more sigma's, which is not possible with 30 datapoints. In general it looks like the statistical fluctuations are roughly 3 times larger than what expected with Sqrt[n].

Is it not correct to assume that the statistical error would be Sqrt[n]? Am I using some biasing that I am not aware of?

Thank you for your help

Emilio Ciuffoli

<Neutron Yield 400MeV.pdf><W-400MeV.inp><W-400MeV-2.inp>

__________________________________________________________________________

You can manage unsubscription from this mailing list at https://www.fluka.org/fluka.php?id=acc_info

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