[srean]

Why are you talking about priors ? Nonparametric vs parametric is an axis completely orthogonal to Bayesian vs Frequentist.

We weren't talking about the "success" though, I was responding to the question "where in the body of stats literature would a neural net model lie".

I argue that would be non-parametric stats. In parametric stats the limit (#params/#data) goes to 0. For models where this is not the case, statisticians and probabilists call them non-parametric (and in certain cases semi-parametric models). Neural net, especially the deep kind (and certainly not the single layer kind) have the property that #params/#data is finite and large.