Replicated network data are increasingly available in many research fields.In connectomic applications, inter-connections among brain regions arecollected for each patient under study, motivating statistical models which canflexibly characterize the probabilistic generative mechanism underlying thesenetwork-valued data. Available models for a single network are not designedspecifically for inference on the entire probability mass function of anetwork-valued random variable and therefore lack flexibility in characterizingthe distribution of relevant topological structures. We propose a flexibleBayesian nonparametric approach for modeling the population distribution ofnetwork-valued data. The joint distribution of the edges is defined via amixture model which reduces dimensionality and efficiently incorporates networkinformation within each mixture component by leveraging latent spacerepresentations. The formulation leads to an efficient Gibbs sampler andprovides simple and coherent strategies for inference and goodness-of-fitassessments. We provide theoretical results on the flexibility of our model andillustrate improved performance --- compared to state-of-the-art models --- insimulations and application to human brain networks.
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