  We present a Bayesian formulation of weighted stochastic block models that
can be used to infer the large-scale modular structure of weighted networks,
including their hierarchical organization. Our method is nonparametric, and
thus does not require the prior knowledge of the number of groups or other
dimensions of the model, which are instead inferred from data. We give a
comprehensive treatment of different kinds of edge weights (i.e. continuous or
discrete, signed or unsigned, bounded or unbounded), as well as arbitrary
weight transformations, and describe an unsupervised model selection approach
to choose the best network description. We illustrate the application of our
method to a variety of empirical weighted networks, such as global migrations,
voting patterns in congress, and neural connections in the human brain.
