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Does it? I don't think I've ever seen the phrase "without evidence" used sloppily by anyone whose definition of evidence is "B s.t. P(B|A)/P(B) > 0".
Wouldn’t the definition of “A is Bayesian evidence of B” be “P(B|A) > P(B)”
I typed >0 when I meant to type >1, yes. That's very embarrassing.
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It's not being sloppy with the phrase "without evidence", as @RenOS pointed it's more about elevating your position to the null hypothesis.
The whole Bayesian reasoning thing always felt like a gimmick to me anyway. You can claim to be a good Bayesian no matter the outcome of any particular case.
One of the key differences between Bayesian and frequentist statistics is that the latter has a "null hypothesis" and the former does not. Priors aren't the same thing; in Bayesian-speak an experiment leads to an update that's a real number, not a binary acceptance/rejection.
Yeah, but you can also claim to be a good non-Bayesian pundit regardless. The biggest difference from my point of view is that I've seen the best rationalists publish graphs of how well their past predictions, as declared in advance, turned out to be calibrated. I've never seen anybody more mainstream than Nate Silver do the same, even though "my punditry is my profession and public service and livelihood" would seem to entail a much stronger case for doing so than "I like blogging", so I'm going to doubt that rationalism has led to much of anything in the mainstream media.
... which is a shame, because an admission of "that's evidence but not enough to budge my priors" really is a big step up from a declaration of "without evidence". When not moving far from your priors is a good idea (which it often is - I've seen legitimate evidence for Flat Earth Theory!) you at least gain a little humility from having to openly admit what you're doing. And when your conclusions resembling your priors is a bad idea, you're more likely to notice that eventually if you have to acknowledge every time when you're dismissing Not Enough Evidence rather than Not Real Evidence.
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People can claim to be good anything regardless of facts on the ground. Talk and unfounded claims are cheap and may even be free (ignoring opportunity costs).
I'd expect anyone who outright calls themselves a Bayesian to do better on that front.*
*Going off Bayesian priors about what the kind of people nerdy enough to have even heard of the idea are like, let alone self professed ones
I mean that the whole framework is designed so that you never end up having to eat crow. "My priors for this are very low. Oh, it happened anyway? Oh well, I promise to bump up my priors somewhat for the next time this non-repeatable event happens!".
Uh.. That's the worst way of reasoning from evidence that's ever been tried, barring all the others.
Absent logical omniscience, you are occasionally going to be wrong, and then you try to be less wrong. Taken deeply enough, no macroscopic events in the history of the universe are likely to ever be truly alike or repeatable, so sorting out reference classes is unavoidably important.
"I was wrong about World War 3 not happening. Well, we can't have a World War 3 2.0 happen for me to be right about, but at least I can adjust my priors for massive wars happening in the future".
Besides. You can very much eat crow when you are confidently wrong. It just takes intellectual honesty, and Bayesians at least pay lip service to the notion we learn from our mistakes. Keep being bad at updating, and people will stop considering what you say to be informative (and that's not unique to self-professed Bayesians, because in practise most humans apply the concepts implicitly, some are more disciplined and explicit than others).
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