The verbal logic of Bayes’ rule is that whichever alternative gave the highest probability of seeing the evidence we actually observed is the one most supported by the evidence. “Support” means that the probability of the alternative increases from its prior.
That is precise enough to be wrong. The first half of the first sentence is about likelihood and the second sentence defines “support” to mean Bayes factor. They are not equal. I’m not sure if you got this from Arbital because it is hard to search. It does use the word “support,” but I don’t think it defines it.
You don’t seem to actually use this paragraph, instead talking about posteriors. That’s the right thing to do, but I think the quoted paragraph suggests “Bayesian hypothesis testing,” ie, using Bayes factors for hypothesis testing. Leaving aside your post, do any modern Bayesians actually advocate this? Jeffreys seems to mention it as at least plausible, but then he puts forward Lindley’s paradox, which shows that it is bad, at least when the prior is stupid. But people often do use uninformative priors.
That is precise enough to be wrong. The first half of the first sentence is about likelihood and the second sentence defines “support” to mean Bayes factor. They are not equal. I’m not sure if you got this from Arbital because it is hard to search. It does use the word “support,” but I don’t think it defines it.
You don’t seem to actually use this paragraph, instead talking about posteriors. That’s the right thing to do, but I think the quoted paragraph suggests “Bayesian hypothesis testing,” ie, using Bayes factors for hypothesis testing. Leaving aside your post, do any modern Bayesians actually advocate this? Jeffreys seems to mention it as at least plausible, but then he puts forward Lindley’s paradox, which shows that it is bad, at least when the prior is stupid. But people often do use uninformative priors.