Now, the biggest difference that I can see is that, within machine learning contexts, people are more concerned with the quality of the predictions than the interpretation of the independent variables. That’s not hard and fast, but it seems to be a common thread.
And for some problems, making a good prediction is really the right thing. In other cases, understanding the mechanisms you might use to effect an outcome is more important. Both are valid uses of statistical methods, depending on the problem.
I think within the realm of classical statistics, Bayesian methods’ super power is in being able to generate results that are much easier to communicate to lay people. Also Bayesian methods are nice if you want to do sensitivity analysis in a principled up front kind of way.
But I could imagine using those methods in an ML context even if they aren’t the current darlings of the methodological pantheon.
Having worked with Oracle's version, and seen entire systems buult out of that, I dread it.
Just because Bayesian isn’t over-hyped doesn’t mean it doesn’t solve real problems. Not everything can be solved with ML, unless the problem is getting more investor money.