Uncertainties of numerical results

1. Apr 21, 2013

Niles

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?