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Is XG confidence confident?

Posted By: Timothy Chow
Date: Thursday, 6 May 2010, at 8:50 p.m.

In Response To: Is XG confidence confident? (Daniel Murphy)

Daniel Murphy wrote:

Rephrase, please. The 1k, 2k, 5k and 10k rollouts are all of one play.

In the case of just one play, the term "confidence" in "95% confidence" is somewhat sloppy usage. "Confidence" is usually used in statistical hypothesis testing, and with just one play, you're not really testing any hypothesis; you're performing statistical estimation of a parameter (the equity). The interval that is being reported as a 95% confidence interval is just two sample standard deviations around the sample mean, and can be interpreted as saying that if you had a Gaussian random variable whose mean were equal to the sample mean and whose standard deviation were equal to the sample standard deviation, then 95% of the time it would lie within that interval.

In particular, it's not statistically legitimate to assert that you can be "95% confident that the true equity lies in this interval." If that's the kind of statement you're hoping to make at the end of a rollout then I think you'd need to adopt a Bayesian framework, which the bots don't currently do.

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