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PhilGoetz comments on You can't believe in Bayes - Less Wrong
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The probability value, which is what is being thrown away, is what is needed for a Bayesian analysis. Saying that that data is not useful means asserting that Bayesian analysis is not useful.
Precise Bayesian analysis is often impossible, and impossible can't be useful. A notch down, take the difficulty of analysis as a counterbalance. Only if you can show that in a given situation you can do better by including that additional info, that is justified, not in general.
It often isn't. Bayesianism isn't the be-all, end-all of logic. It's just another tool in the toolbox.