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Uncertainties of numerical results

  1. Apr 21, 2013 #1
    How do people generally determine uncertainties on results that are based on Monte Carlo simulations? Take this fictive example, just so we have something specific to talk about:

    I look at 106 particles, confined to a box. There is a small hole in one of the walls, and at some time t0 I am interested in knowing how many particles N have diffused out of the box. This can be simulated by a Monte Carlo approach (Brownian motion).

    This number N will vary each time I perform the simulation, but it will converge the larger I make the initial sample. Nonetheless, I guess an uncertainty is still present - how can we determine that in general?

    Thanks for input in advance.
  2. jcsd
  3. Apr 21, 2013 #2
    I'm not sure if there's a more elegant method, but I'd repeat the simulation multiple times and take the standard deviation of the results. Perhaps if it's too computationally expensive to do this with a very high N, you can repeat it for a few low N and extrapolate the uncertainty as a function of N using a curve fit? I assume it would be 1/sqrt(N)?
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