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neq1 comments on Bayes' rule =/= Bayesian inference - Less Wrong
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Wait a minute - when the Bayesian says "I think the coin probably has a chance near 50% of being heads", she's using data from prior observations of coin flips to say that. Which means that the frequentist might get the same answer if he added those prior observations to his dataset.
Yes, that's a good point. Tthat would be considered using a data augmentation prior (Sander Greenland has advocated such an approach).