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Variance Reduction

Posted By: Timothy Chow
Date: Friday, 18 July 2014, at 10:27 p.m.

In Response To: Variance Reduction (rambiz)

Bob is right that I sometimes quibble about this, but it's not as bad as you're making it out to be. The use of the normal distribution is based on the central limit theorem. The central limit theorem is remarkably robust. It doesn't just apply to the Bernoulli distribution. It applies to any sum of independent random variables. Variance reduction just adds another random variable to the mix.

There are two ways you can quibble. (1) You can question the independence assumption. But if you're worried about this, then you should be worried about the non-variance reduced calculation as well, because you can question the independence assumption there too. I could be wrong but I don't think the variance reduction violates the independence assumption significantly more than the non-variance-reduced case does. (2) You can worry about the rate of convergence. I'm not sure about this either, but I suspect that variance reduction actually causes faster convergence, so that the normal distribution may actually be a better approximation in the variance-reduced case. After all, high variance is one of the usual culprits for slow convergence.

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