UCLA

In network data, such as those representing social and economic relationships, the connections between entities depend on one another. Exponential-family random graph models (ERGMs) are the standard tool for capturing this dependence. They are difficult to fit because their parameter space has a challenging geometry. Large regions of it produce networks that are either nearly empty or nearly complete, neither of which is wanted by practitioners. Common Bayesian methods either ignore this geometry or work around it inefficiently. This dissertation develops methodology that respects it. The first chapter shows that a recent variational method for ERGM estimation introduces a formulation that neglects tie dependence and works poorly in realistic settings. The second chapter proposes a new prior distribution for Bayesian ERGM inference. Unlike standard priors, it concentrates on parameter values that produce realistic networks. The third chapter shows that the new prior generalizes to modern sampling methods that use auxiliary samples. The methods are demonstrated through simulations and applied to a tailor shop network from a 1972 study.