1 vote
Accepted

What is the difference between an input and observed data in a Bayesian neural network?

You're pretty close: $x,y$ correspond to a single data point $\mathcal{D}$ is the whole dataset Given this, you can read the posterior $p(y|x,D)$ as " what's the distribution of $y$ given that ...
Alberto's user avatar
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1 vote

What are the main benefits of using Bayesian networks?

Yes, you are correct that one of the key benefits of Bayesian networks is that they allow you to calculate joint probability distributions without directly using the chain rule of probability. ...
Hans-Peter Schrei's user avatar

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