[math_dandy]

Uncertainty estimates in traditional parametric statistics are facilitated by strong assumptions on the distribution of the data being analyzed.

In traditional nonparametric statistics, uncertainty estimates are obtained by a process called bootstrapping. But there's a trade-off. There's no free lunch!) If you want to eschew strong distributional hypotheses, you need to pay for it with more data and more compute. The "more compute" typically involves fitting variants of the model in question to many subsets of the original dataset. In deep learning applications in which each fit of the model is extremely expensive, this is impractical.