Statistical Network Analysis: Beyond Block Models.

Network data represent​ ​ connections between units of analysis and lead to many interesting research questions​ with diverse applications​. In this thesis, we focus on inferring the structure underlying an observed network, which can be thought of as a noisy random realization of the unobserved true structure. ​Different applications focus on different types of underlying structure; one question of broad interest is finding a community structure, with communities typically defined as groups of nodes that share similar connectivity patterns. ​One common and widely used model for describing​ a community structure​ in a network is the stochastic block model. This model has attracted a lot of attention because of its tractable theoretical properties, but it is also well known to oversimplify the structure observed in real world networks and often does not fit the data well. Thus there has been a recent push to expand the stochastic block model in various ways to make it closer to what we observe in the real world, and this thesis makes several contributions to this effort.PhDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133476/1/yzhanghf_1.pd