Uncertainty of MonteCarlo Simulations: Weight and Error Bars

In summary, the conversation discusses the uncertainty of a MonteCarlo simulation of particle collisions at LHC. The speaker has plotted variables and normalized the data with a weight, but is unsure about the correct method for calculating error bars. They question whether the weight should be taken into consideration and if the square root of the number of events is the proper calculation. The response clarifies that if the original events are without weights, the error bars should be calculated using the square root of the number of events, while the luminosity is just a constant scaling factor. If the original events have weights, the calculation can become more complex.
  • #1
Aleolomorfo
73
4
Hello everybody,
I need a help, primarly a confirmation about my reasoning. I have data from a MonteCarlo simulation of collisions between particles at LHC (made with Madgraph). I have plotted some variables, for example the angle between two final leptons. Then I have normalized the plot to a determined integrated luminosity, so I have applied a weight to the histogram. I'd like to put error bars due to the uncertainty of the generated event from the MonteCarlo, which is a poisson error. So I have taken the content of each bin and then made the square root. But I have some doubt. First of all, shouldn't I take into consideration the weight in some way? Secondly, I'm not so sure about ##\sqrt{N}##, because maybe it should be something like ##\frac{\sqrt{N}}{N-1}.##
Thanks in advance
 
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  • #2
Are your original events without weights?
In that case the error bars on the original distribution should be sqrt(N). The luminosity is just a constant scaling for both central value and uncertainties (no uncertainty on the luminosity in MC).

If your original events have weights things can get more complicated. Luminosity stays a constant factor, however.
 
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Likes Aleolomorfo
  • #3
Yes, my original events are without weights.
Thank you very much for the answer!
 

1. What is Monte Carlo simulation and how does it relate to uncertainty?

Monte Carlo simulation is a computational method used to estimate the probability of outcomes by running a large number of simulations using random sampling. It relates to uncertainty because it takes into account the variability and randomness of the input parameters, resulting in a range of possible outcomes rather than a single point estimate.

2. What is the significance of weight in Monte Carlo simulations?

The weight in Monte Carlo simulations represents the relative importance of a particular sample or input parameter. It is used to adjust the contribution of each sample to the overall results, giving more weight to samples that are more representative of the population. This helps to improve the accuracy of the simulation results.

3. How are error bars calculated in Monte Carlo simulations?

Error bars in Monte Carlo simulations are typically calculated using statistical methods such as standard deviation or confidence intervals. These methods take into account the variability of the simulation results and provide a range of values that the true result is likely to fall within, with a certain level of confidence.

4. What are some sources of uncertainty in Monte Carlo simulations?

Some sources of uncertainty in Monte Carlo simulations include the randomness of input parameters, the accuracy of the simulation model, and the number of simulations performed. Other sources may include assumptions made in the model, human error in inputting data, and limitations of the software or hardware used.

5. How can one improve the accuracy of Monte Carlo simulation results?

To improve the accuracy of Monte Carlo simulation results, one can increase the number of simulations performed, use more representative samples, and refine the simulation model to better match the real-world scenario. It is also important to identify and reduce sources of uncertainty, and to carefully consider the assumptions and limitations of the simulation. Validating the results with real-world data can also help improve accuracy.

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