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Let's say that I want to calculate the probability of achieving more than 8 heads in 10 coin tosses. The easiest and most accurate way will be to simply use the binomial distribution and sum the probability of getting 9 an 10 heads.

However, it is also possible to simulate numerous coin tosses and then see which proportion of those answers our question. In which general scenario (doesn't have to be restricted to coin tosses) would this method of simulation be better than using the binomial and why?

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Some advantages of simulation:

  • you can use it when you don't know how to do the exact calculation

  • you can use it to check you got the exact calculation correct

  • you can generalize the situation and examine sensitivity of the exact solution to changes in the circumstances (what if there's heterogeneity or dependence, for example?); often the simple situation can be done exactly but the more general cases may be somewhat trickier.

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If you know how to calculate what you want to know, by some known formula or otherwise, there can be no advantage to simulation, except from learning effect, and sometimes, as a check on the theoretical calculation. The real advantage of simulation is that it can be used when you do not know how to solve theoretically, and even in some cases, even if you know, simulation could be faster.

Another advantage is that it is easier to vary the assumptions, to check on sensitivity of the conclusions to the underlying assumptions.

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