I really appreciate Andrew Gelman's way of defining 'probability' that transcends the frequentist/Bayesian schism: Probability is a mathematical concept encoded in the Kolmogorov axioms. That's it. No need to argue over a canonical interpretation. It's just math!
This suggests that questions like the following are ill-posed and not worth arguing over:https://twitter.com/3blue1brown/status/1074415844715782144 …
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This doesn't mean that we can't advocate for Bayesianism. I think science should use more Bayesian methods (because it concerns our subjective beliefs about the world). It's just that there isn't One True Way, definitionally speaking.
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But then someone comes along and says: How much would you bet on X? And bayes comes back.
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By “ill-posed” I meant that it’s wrong to ask about the “probability” of this thing, as if that had a well-defined answer. Instead it would be better to ask, “At what odds would you bet that...?” But then the question isn’t interesting :P
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On the contrary, finding a rigorous framework in which those questions can be asked and answered precisely can yield deep theories.
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Unification matters. When the exact same mathematical apparatus lets you describe the behavior of long term frequencies, betting odds, gas particles, it tells you some deep underlying principle is at play. If you go "gee, what a versatile tool" you're missing out.
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This paper talks about one principled approach to such questions:https://intelligence.org/2016/09/12/new-paper-logical-induction/ …
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Agree it's ill-posed, disagree about it being not worth arguing over. Have you seen
@MIRIBerkeley's research on logical induction?Thanks. Twitter will use this to make your timeline better. UndoUndo
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What if you have to bet money on it and that Nth digit answer will comeup in few years if you start calculating now?
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