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My question is simple. Which are the general conditions for which a Monte Carlo simulation can be used to represent a statistical system? Or conversely, which are the statistical system that cannot be represented, even in principle, by a Monte Carlo simulation?

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    $\begingroup$ When you can't write down a plausible model. Then the question becomes which systems are not amenable to statistical modeling? $\endgroup$ Commented Dec 12, 2013 at 20:20

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Monte carlo simulation is intended to reproduce the behavior of any random variable you use...it is as close as you can get to actually running an experiment without actually doing so. As such, there are really no limits to what you could use it for apart from the need to actually specify a model to simulate.

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