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steven0461 comments on The ideas you're not ready to post - Less Wrong
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Great thread idea.
Frequentist Pitfalls:
Bayesianism vs Frequentism is one thing, but there are a lot of frequentist-inspired misinterpretations of the language of hypothesis testing that all statistically competent people agree are wrong. For example, note that: p-values are not posteriors (interpreting them this way usually overstates the evidence against the null, see also Lindley's paradox), p-values are not likelihoods, confidence doesn't mean confidence, likelihood doesn't mean likelihood, statistical significance is a property of test results not hypotheses, statistical significance is not effect size, statistical significance is not effect importance, p-values aren't error probabilities, the 5% threshold isn't magical.
In a full post I'd flesh all of these out, but I'm considering not doing so because it's kind of basic and it turns out Wikipedia already discusses most of this surprisingly well.
More generally, semantics of the posteriors, and of probability in general, comes from the semantics of the rest of the model, of prior/state space/variables/etc. It's incorrect to attribute any kind of inherent semantics to a model, which as you note happens quite often, when frequentist semantics suddenly "emerges" in probabilistic models. It is a kind of mind projection fallacy, where the role of the territory is played by math of the mind.
To return to something we discussed in the IRC meetup: there's a simple argument why commonly-known rationalists with common priors cannot offer each other deals in a zero-sum game. The strategy "offer the deal iff you have evidence of at least strength X saying the deal benefits you" is defeated by all strategies of the form "accept the deal iff you have evidence of at least strength Y > X saying the deal benefits you", so never offering and never accepting if offered should be the only equilibrium.
This is completely off-topic unless anyone thinks it would make an interesting top-level post.
ETA: oops, sorry, this of course assumes independent evidence; I think it can probably be fixed?