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buybuydandavis comments on (Subjective Bayesianism vs. Frequentism) VS. Formalism - Less Wrong
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Comments (106)
I mostly agree, finding why/how it is isomorphic is the important thing. But it is still isomorphic to more than one thing, frequency and subjective degree of belief included.
The two are still locked in a debate which is ultimately the result of interpreting one question in two different ways, and then answering the two seperate questions as if they were exclusive answers to one question. Exactly as the two argue about sound being there in the absence of observers.
The bayesian would give the same answer as the frequentist if he interpreted the question as the frequentist. Same goes for the sound realist, for the same reasons.
How isormorphic it is remains to be seen. The infinite set digressions have not been particularly helpful to real problems.
The objective bayesian is free to estimate frequencies, and has done so, a la Jaynes. He explicitly identifies that both questions are answering different questions, and answers both.
I'm not aware of anyone doing this, but I think a frequentist could just as well interpret subjective degrees of belief in frequentist terms, but the sample space would be in informational terms, looking for transformation groups in states of knowledge.
Sometimes. I think if we're trying to keep terms straight, you should separate probability_SubjectiveBayes, probability_Math, probability_Frequentist, and probability_HumanLanguage. You seem to conflate probability_Math and probability_HumanLanguage.
probability\_SubjectiveBayes, probability\_Math, probability\_Frequentist, and probability\_HumanLanguage. You seem to conflate probability\_Math and probability\_HumanLanguage.
Corrected. Thanks.