Statistical Inference on Dynamic Networks

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With the fast development of information technology and the emergence of online networks, an increasing number of large scale dynamic network data sets become available. This project develops statistical analysis and modeling of dynamic networks. The model under study has the advantage of providing rich visualization of the dynamics of the network, allowing better understanding of the network structure as well as the behavior of individual nodes. The proposed inference procedure makes it possible to handle large scale dynamic network data, such as gene regulatory networks and disease transmission networks. The model can be used to analyze terrorist networks, study social interaction patterns, model disease transmission, and much more. The research project provides an ideal opportunity for involvement of students with a broad range of background and interests. Additional broader impacts include incorporation of the methods into relevant courses and dissemination of research results to the scientific community.This project develops statistical models and inference procedures for dynamic networks, including binary networks, weighted networks, and other complex networks. A state space model will be developed which embeds dynamic network data into a latent Euclidean space, allowing each node to have a temporal trajectory in this latent space. A Markov chain Monte Carlo algorithm is proposed to estimate the model parameters and latent positions of the nodes in the network. The model parameters provide insight into the structure of the network, and the visualization provided from the model gives insight into the network dynamics. In addition, the model can handle missing edge data and predict future edges between nodes. The methods will be applied to real network data from natural and social sciences.