Does frequentist/bayesian matters to anything but quasi-religious beliefs?
I mean, that's maths, either approach has to give the same results, as they come from the same theory. The Bayes theorem is just a theorem, use it explicitly or not, the numbers will be the same because the axioms are the same.
No, they are linked to beliefs (like anything else), but the canonical forms do differ a lot. Most importantly:
- bayesian methods give you posterior distributions rather than point estimates and SEs
- bayesian methods natively offer prior and posterior predictive checks
- with bayesian methods, it's evidently easier to combine knowledge from multiple sources, which null-hypothesis testing struggles with (best way is probably still meta-analyses)
I mean, that's maths, either approach has to give the same results, as they come from the same theory. The Bayes theorem is just a theorem, use it explicitly or not, the numbers will be the same because the axioms are the same.