Statistical Inference on Dynamic Networks

随着信息技术的快速发展和在线网络的出现，越来越多的大规模动态网络数据集成为可能。该项目开发动态网络的统计分析和建模。所研究的模型具有提供丰富的网络动态可视化的优点，可以更好地理解网络结构以及单个节点的行为。所提出的推理过程使得处理大规模动态网络数据成为可能，例如基因调控网络和疾病传播网络。该模型可用于分析恐怖主义网络，研究社会互动模式，疾病传播模型等等。该研究项目为具有广泛背景和兴趣的学生提供了理想的参与机会。此外，还将该方法纳入相关课程，并向科学界传播研究成果。该项目开发了动态网络（包括二进制网络、加权网络和其他复杂网络）的统计模型和推理程序。将开发一个状态空间模型，该模型将动态网络数据嵌入到潜在的欧几里得空间中，允许每个节点在该潜在空间中具有时间轨迹。提出了一种马尔可夫链蒙特卡罗算法来估计模型参数和网络中节点的潜在位置。模型参数提供了对网络结构的洞察，模型提供的可视化提供了对网络动态的洞察。此外，该模型可以处理缺失的边缘数据并预测节点之间的未来边缘。该方法将应用于自然科学和社会科学领域的真实的网络数据。

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.