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It does not seem fair to say that frequentists do not update their beliefs based on new evidence. This does not seem to accurately capture what the difference between Bayesians and frequentists (or anyone else) is.
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What's the difference as you see it?

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Everyone updates their belief in hypotheses based on the perceived strength of evidence they observe. That's just science.

Frequentists and Bayesians differ in which sets of statistical tools they prefer for measuring the strength of evidence.

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> Everyone updates their belief

Uh oh. How does frequentist model define "belief" and "updating a belief"?

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