They all seem to represent random variables by the nodes and (in)dependence via the (possibly directed) edges. I'm esp interested in a bayesian's point-of-view.
Causality – Relation Between Hierarchical Models, Neural Networks, Graphical Models, and Bayesian Networks
causalitygraphical-modelmultilevel-analysisneural networks
Best Answer
A Bayesian network is a type of graphical model. The other "big" type of graphical model is a Markov Random Field (MRF). Graphical models are used for inference, estimation and in general, to model the world.
The term hierarchical model is used to mean many things in different areas.
While neural networks come with "graphs" they generally don't encode dependence information, and the nodes don't represent random variables. NNs are different because they are discriminative. Popular neural networks are used for classification and regression.
Kevin Murphy has an excellent introduction to these topics available here.