Yeah but in this case it's really a wrong way to think about it.
If you have a DAG based on wrong assumptions, it doesn't matter whether you get a point estimate based on null hypothesis thinking or whether you get a posterior distribution based on some prior. The problem is that the way in which you combine variables is wrong, and bayesian analysis will just be more detailed and precise in being wrong.
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)
