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BGonline.org Forums
A better approch?
Posted By: Timothy Chow In Response To: A better approch? (Maik Stiebler)
Date: Wednesday, 4 November 2009, at 10:09 p.m.
Maik Stiebler wrote:
If you assume that the trial results for each move are normally distributed with a known variance sigma^2 (brushing over that technicality again for now) and unknown mean mu, and your prior distribution of mu is uniform, the posterior distribution of mu after n trials is the familiar looking (m, sigma^2/n) normal distribution, where m is the sample mean.
This is still a Bayesian viewpoint, so it does nothing to stop an "anti-frequentist rant."
Also, I think you meant to say that the posterior distribution converges to a normal distribution, rather than is a normal distribution.
However, I think your main point is this: One can give an argument that calculating multivariate Gaussian tail probabilities will give you the right answer in the limit, and therefore its closeness to the correct answer is not an "accident." I'd have to check the details to be sure, but this sounds right.
It still strikes me as an odd thing to do, since I suspect that it leads you to invest more computational effort for a less accurate result, and the inaccuracies are hard to estimate. I think it also leads to conceptual confusion, as this thread has indicated. So I would still recommend computing posterior probabilities the way I have been indicating all along. Otherwise, once you start adding extra complications (e.g., variance reduction), it will be all too easy to make a mistake.
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