You can find Bayesian Neural Network examples starting here: http://pyro.ai/examples/bayesian_regression.html

I think the documentation and tutorials are thorough and laid out well to ease you into Bayesian NN and generally handling uncertainty with Neural Networks + Distributions. There's some Pyro-specific constructs in there, but it's the easiest way to get into BNNs without lots of prior knowledge.

This is a good example. There’s not much info I’ve been able to find - I’d be interested if anyone else has a solid tutorial.