Annoyance comments on You can't believe in Bayes - Less Wrong

4 Post author: PhilGoetz 09 June 2009 06:03PM

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Comment author: Annoyance 10 June 2009 04:53:30PM 0 points [-]

It's not useless, not by any means.

A threshold can be contradicted by a contrary-to-expectation observation. A statement of probability cannot, as long as it's not an absolute.

If you believe that there's only one-in-a-hundred chance of something happening, and it happens, were you right or wrong?

Comment author: orthonormal 10 June 2009 08:06:34PM 1 point [-]

Neither, you just take a hit according to your scoring rule; but if you're properly calibrated, it'll be compensated for on average by 99 times that your 1-in-a-hundred chances don't happen.

If I repeatedly claim I have a 1-in-2 chance of rolling snake eyes, you'd probably see me take repeated blows by a logarithmic scoring rule, which would suffice for bystanders to put less trust in my probability estimates. Eventually I should admit I'm poorly calibrated.

Of course if you're talking about a probability 1 minus epsilon threshold, a miss on that claim is a huge penalty by a log scoring rule.