Bayesian Statistics: The three cultures

I never liked the clubs you were expected to put yourself in, what "side" you were on, or the idea that problems in science that we see today could somehow be reduced to the inferential philosophy you adopt. In a lot of ways I see myself as information-theoretic in orientation, so maybe objective Bayesian, although it's really neither frequentist nor Bayesian.

This three cultures idea is a bit of slight of hand in my opinion, as the "pragmatic" culture isn't really exclusive of subjective or objective Bayesianism and in that sense says nothing about how you should approach prior specification or interpretation or anything. Maybe Gelman would say a better term is "flexibility" or something but then that leaves the question of when you go objective and when you go subjective and why. Seems better to formalize that than leave it as a bit of smoke and mirrors. I'm not saying some flexibility about prior interpretation and specification isn't a good idea, just that I'm not sure that approaching theoretical basics with the answer "we'll just ignore the issues and pretend we're doing something different" is quite the right answer.

Playing a bit of devil's advocate too, the "pragmatic" culture reveals a bit about why Bayesianism is looked at with a bit of skepticism and doubt. "Choosing a prior" followed by "seeing how well everything fits" and then "repeating" looks a lot like model tweaking or p-hacking. I know that's not the intent, and it's impossible to do modeling without tweaking, but if you approach things that way, the prior just looks like one more degree of freedom to nudge things around and fish with.

I've published and edited papers on Bayesian inference, and my feeling is that the problems with it have never been in the theory, which is solid. It's in how people use and abuse it in practice.