  Replicated network data are increasingly available in many research fields.
In connectomic applications, inter-connections among brain regions are
collected for each patient under study, motivating statistical models which can
flexibly characterize the probabilistic generative mechanism underlying these
network-valued data. Available models for a single network are not designed
specifically for inference on the entire probability mass function of a
network-valued random variable and therefore lack flexibility in characterizing
the distribution of relevant topological structures. We propose a flexible
Bayesian nonparametric approach for modeling the population distribution of
network-valued data. The joint distribution of the edges is defined via a
mixture model which reduces dimensionality and efficiently incorporates network
information within each mixture component by leveraging latent space
representations. The formulation leads to an efficient Gibbs sampler and
provides simple and coherent strategies for inference and goodness-of-fit
assessments. We provide theoretical results on the flexibility of our model and
illustrate improved performance --- compared to state-of-the-art models --- in
simulations and application to human brain networks.
