Statistical uncertainties Monte Carlo

In summary, the conversation discusses the statistical uncertainties of simulations in Monte Carlo. The speaker asks if they can calculate the uncertainties based on the number of events they ran and the resulting distributions. It is suggested to move to a statistics forum for a more accurate estimate of uncertainty. It is also mentioned that the uncertainty will be limited by shot noise and will depend on the number of particles and how the distribution is represented.
  • #1
Lian1985
1
0
Hi!

I'm newbie in Monte Carlo. My question concerns the statistical uncertainties of my simulations.

Let's say that the result of my Monte Carlo is a certain distribution A (e.g. number of particles as a function of the depth in a target) and I have run NA events to generate that distribution. Then, I run the same code with NB events and I obtain the distribution B.
Can I calculate the statistical uncertainties of my results based on only on these information?

Thank you for your help!
 
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  • #2
You can get an estimate of statistical uncertainty, although there will be question of how good it is. It will depend partly on how large NA and NB are - the larger the better.

Suggestion: move to the statistics forum.
 
  • #3
At the very least, you will be limited by shot noise due to quantized number of particles. Typically, this gives you a Poisson distributed noise, with error which scales as sqrt(N), with N the number of particles. Details will depend on what your code is doing. If your distribution is represented as a number of particles per bin, then the error is at least sqrt(number of particles in that bin) unless some averaging was done in the code.
 

1. What is Monte Carlo simulation?

Monte Carlo simulation is a computational technique used in statistical analysis to model complex systems or processes that involve random variables. It involves using random sampling to generate a large number of possible outcomes and analyzing the results to estimate the likelihood of various outcomes or to understand the behavior of a system.

2. How are Monte Carlo simulations used to estimate statistical uncertainties?

Monte Carlo simulations use repeated random sampling to generate a large number of possible outcomes for a given system or process. By analyzing the distribution of these outcomes, statistical uncertainties can be estimated, including measures such as mean, variance, and confidence intervals.

3. What are statistical uncertainties?

Statistical uncertainties refer to the range of possible values that a parameter or measurement can take. They arise due to random variations and errors in data. These uncertainties can be quantified using statistical methods such as standard deviation, confidence intervals, and hypothesis testing.

4. How can Monte Carlo simulations help in decision making?

Monte Carlo simulations can provide valuable insights and information for decision making by generating a large number of possible outcomes and their associated probabilities. This allows decision-makers to assess the risks and uncertainties associated with different options and make informed decisions based on the available data.

5. What are some limitations of Monte Carlo simulations?

One limitation of Monte Carlo simulations is that they rely on random sampling, which may not always accurately represent the real-world system or process being studied. Additionally, the accuracy of the results depends on the quality and quantity of data used in the simulation. Other limitations may include computational costs and assumptions made in the modeling process.

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