Bayesian Nonparametric Modeling of Network Data

Network data representing relationship structures among a set of nodes are available in many fields of applications covering social science, neuroscience, business intelligence and broader relational settings. Although early probability models for networks date back almost sixty years, this field of research is still an object of intense and dynamic interest. A primary reason for the recent growth of statistical methodologies in modeling of networks is that the routine collection of such data is a recent development. Online social networks, novel neuroimaging technologies, improved business intelligence analyses and sophisticated computer algorithms monitoring world news media, currently provide increasingly complex network data sets along with novel motivating applications and new methodological questions. A challenging issue in such settings is that data are available via multiple network observations and hence the rich literature in modeling of a single network falls far short of the goal of providing flexible inference in this scenario. Statistical modeling of replicated network data is still on its infancy and several questions remain about coherence of inference, flexibility, computational tractability and other key issues. Motivated by complex applications from different domains, this thesis aims to take a sizable step towards addressing these issues via Bayesian nonparametric modeling. The thesis is organized in two main frameworks, further divided in different topics. The first thread develops flexible and computationally tractable stochastic processes for modeling dynamic networks, which incorporate temporal dependence and exploit latent network structures. The second focuses on defining a provably flexible representation for the probabilistic generative mechanism underlying a network-valued random variable, which is able to provide valuable insights both on shared and subject -- or phenotype -- specific sources of variability in the network structur