beta_binomial

I think so. The ultimate question is who are you going to sue and who is going to sue you if something goes wrong? Imagine having to put your ML researcher on the stand and having him say "I can't say for sure that this or that didn't affect the outcome in a meaningful way"

There are legitimate reasons why stats wins out on interpretability. 1. Scaling is not hard 2. It is obvious to me "how to make these aggregations", but that is because I know statistics. Categories of variables treated as random effects can be interpreted both as a group (via variance parameters of the random effects) and individually via coefficients. 3. Bayesian estimation can even account for correlation of parameters and include it in the posterior prediction.

This does not make any sense to me and neither did OP's comment about NN's approximating the posterior. In fact, if p were the solution then that would simply be the maximum likelihood estimate, which would not include the p(theta), or the prior, and hence would not be Bayesian.