  Water pollution is a major global environmental problem, and it poses a great
environmental risk to public health and biological diversity. This work is
motivated by assessing the potential environmental threat of coal mining
through increased sulfate concentrations in river networks, which do not belong
to any simple parametric distribution. However, existing network models mainly
focus on binary or discrete networks and weighted networks with known
parametric weight distributions. We propose a principled nonparametric weighted
network model based on exponential-family random graph models and local
likelihood estimation and study its model-based clustering with application to
large-scale water pollution network analysis. We do not require any parametric
distribution assumption on network weights. The proposed method greatly extends
the methodology and applicability of statistical network models. Furthermore,
it is scalable to large and complex networks in large-scale environmental
studies. The power of our proposed methods is demonstrated in simulation
studies and a real application to sulfate pollution network analysis in Ohio
watershed located in Pennsylvania, United States.
