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What is the best way to sample from a Poisson-Binomial distributed random variable $Z$? Since $Z = \operatorname{Bern}(p_1) + \operatorname{Bern}(p_2) + ...$ we could sample from each Bernoulli random variable and total the number of successes. Or, we could calculate the CDF of $Z$ via convolution: https://stats.stackexchange.com/a/25161/22199, and sample from $Z$ directly using the inverse transform. Are there any other good ways to do this?

kjetil b halvorsen
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Alex
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    When they're a good approximation, various approximations could be used to approximately sample -- there's a reference with relevant information relating to a number of aspects of Poisson binomial calculations here. Note that if you have a good approximation to the cdf you could apply inverse transform type sampling. – Glen_b Oct 12 '16 at 01:28

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