Dear Ricardo,
Thanks for your reply. I have gone through the pdf and some of my doubts
are not cleared.
1. In FLUKA, suppose, no of histories (N) = 1E+5. The spawn value
= 10 and no of cycles = 5.
So, when spawn = 1, cycle = 1, these 1E+5 no of histories will not be
simulated together. Rather, it will be divided into X no of batches with
N/X histories. For each batch, we will get a mean value of our
estimator. So, for X no of batches, we will get X no of means which if
we plot, we will get a sampling distribution of sample (or batch) means.
Is my concept correct?
If it is correct, then we can call this X as sample size. Now, since, in
FLUKA input, we are giving only total no history, not the batch size,
what does FLUKA decide as batch size? Is there any predefined parameter
assigned for batch size? For central limit theorem to be valid, the
sample size should be greater than 30 so that whatever be the population
distribution, the sampling distribution of sample means will always be a
normal distribution.
2. For each sampling distribution of sample (or batch) means, the
central limit theorem is valid. Also, each distribution has their own
mean ()(mean of sampling distribution of sample means) and standard
deviation () (SD of sampling distribution of sample means).
Each SD satisfy the relation where x = a random variable of our
estimator, X = no of batches (or sample size), σ = SD of population
distribution. Now for spawn = 1, generally we give 5 cycles. So we will
get 5 and 5 . Then what is the method to get the final SD of our estimator?
For spawns > 1, many such and will be generated. How can we merge
those results to get a single value of and for our estimator?
Thanks and Regards
Jyoti
----- Original Message -----
From: "r s augusto" <r.s.augusto_at_cern.ch>
To: fluka-discuss_at_fluka.org
Sent: Thursday, December 19, 2019 4:20:06 AM
Subject: [fluka-discuss]: RE: What is the relation between sample size
and particle
history in FLUKA
Date: Wed, 18 Dec 2019 18:46:14 +0000
Dear Jyoti,
Sender: owner-fluka-discuss_at_mi.infn.it
The sample size is indeed related to the number of histories. In FLUKA
it generally involves a batch-by-batch approach, in which instead of
running a simulation of N histories, X simulations of N/X histories are
run instead. Each simulation has its own random seed and is therefore
independent.
You can find more information in:
https://indico.cern.ch/event/694979/contributions/2927088/attachments/1657637/2654305/Fundamentals_of_MC_simulations_of_radiation_transport_2018.pdf
(Statistical uncertainty in MC simulations).
Best regards,
Ricardo
//Ricardo dos Santos Augusto
TRIUMF-EH&S TRL Rr-7
Office: +1 604 222 10 47 (6375)
Mobile: +1 604 338 50 57
4004 Wesbrook Mall,
Vancouver, BC V6T 2A3, Canada//
________________________________________
De : owner-fluka-discuss_at_mi.infn.it [owner-fluka-discuss_at_mi.infn.it] de
la part de Giuseppe Battistoni [Giuseppe.Battistoni_at_mi.infn.it]
Envoyé : mardi 17 décembre 2019 8:50
À : fluka-discuss_at_fluka.org
Objet :
Date: Tue, 17 Dec 2019 12:01:33 +0530 (IST)
From: Jyoti <jyoti.grg_at_britatom.gov.in>
To: "fluka-discuss" <fluka-discuss_at_fluka.org>
Subject: What is the relation between sample size and particle history in
FLUKA
Dear Fluka Experts,
The central limit theorem states that the standard deviation of
distribution of sample means = standard deviation of population
distribution / square root of (sample size).
In the context of FLUKA Monte Carlo simulation, we repeat our
simulations by large number of histories.
What is the sample size in case of our FLUKA simulation? Is it related
with the particle history?
With Regards,
Jyoti
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Received on Thu Dec 19 2019 - 13:40:15 CET