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wnoise comments on Why We Can't Take Expected Value Estimates Literally (Even When They're Unbiased) - Less Wrong
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That's true. Arbitrary means different things, from "not chosen by nature", to "not chosen by an outside standard".
In this case, the fact that it evidently was chosen to conform to scientific culture, and not for some ulterior motive, is bayesian evidence in favor of the validity of the frequentist methodology.
I think if we tabooed (taboo'd?) "arbitrary", we would all find ourselves in agreement about our actual predictions.