Collaborative Research: Specification and Estimation of Exponential Family Random Graph Models for Weighted Networks

了解网络协同效应对动态关系过程的影响在许多现实世界的研究环境中扮演着重要的角色。例如，了解哪些形式的货币和社会政策可以减少国际金融传染的可能性，以及不同生理条件对人脑不同相互关联区域的活动水平的作用。对这类领域的统计洞察需要分析方法，既要处理联系的存在和不存在，也要处理网络中各单元之间的联系强度。该项目的重点是开发和实施统计方法和软件，用于分析加权(即纽带强度)网络数据。广义指数随机图模型(GERGM)是建立和检验网络假说的有力工具。该项目将通过以下方式推进GERGM的发展现状：(1)更好地了解可用GERGM表示的网络概率分布空间；开发马尔可夫链蒙特卡罗估计方法，这将拓宽GERGM可进行估计的规范的类别；(3)开发特殊情况的GERGM约束，以促进将相关矩阵作为网络进行研究；以及(4)发展关于GERGM族性质的渐近理论。作为这项研究的一部分，将开发GERGM的两个说明性应用。第一部分是对全球环境公共政策网络的分析，揭示了全球环境派别与合作的网络属性。第二个应用涉及对人类神经活动网络的分析，旨在了解连接大脑各区域的复杂依赖关系。鉴于最近统计网络模型在社会学、遗传学、神经科学、政治学、物理学、金融学、语言学和生态学等领域的应用出现爆炸性增长，预计本项目中开发的统计方法将与许多不同的领域相关。就加权网络数据的重要性而言，神经科学是领先的领域之一。该项目的目标之一是通过推进创新的神经技术，为脑研究的多机构倡议做出贡献。该项目提供了另外两项贡献，将促进加权网络的统计研究。首先，该项目将促进和传播免费和开放源码的统计软件，使其能够使用方便的应用程序。第二，在这个项目中开发的材料将被纳入研究生水平的研究方法课程和研讨会。

Understanding the effect of network synergies on dynamic relational processes plays an important role in a number of real-world research settings. Examples include understanding what forms of monetary and social policy reduce the instance of international financial contagion, and the role of different physiological conditions on the activity levels of different interconnected regions in the human brain. Statistical insights into areas such as these require analytical methods which deal with both the presence and absence of ties as well as tie strengths between units in networks. This project focuses on the development and implementation of statistical methods and software for the analysis of weighted (i.e., tie strength) network data. The generalized exponential random graph model (GERGM) is a powerful tool for formulating and testing hypotheses about networks. The project will advance the current state of development of the GERGM by (1) developing a better understanding of the space of network probability distributions that can be formulated with the GERGM; developing Markov Chain Monte Carlo methods for estimation, which will broaden the class of GERGM specifications for which estimation is feasible; (3) developing special-case GERGM constraints that facilitate the study of correlation matrices as networks; and (4) developing asymptotic theory regarding the properties of the GERGM family. As part of this research, two illustrative applications of the GERGM will be developed. The first one involves the analysis of global environmental public policy networks, which offers insight into the network properties of global environmental faction and cooperation. The second application involves the analysis of neural activity networks in humans, which aims to understand complex dependencies connecting regions of the brain. Given the recent explosion in the application of statistical network models in fields as diverse as sociology, genetics, neuroscience, political science, physics, finance, linguistics, and ecology, it is expected that the statistical methods developed in this project will be relevant to a number of different fields. One of the leading fields, in terms of the prominence of weighted network data, is neuroscience. One of the aims of this project is to contribute to the multi-agency initiative on Brain Research through Advancing Innovative Neurotechnologies. This project offers two additional contributions that will facilitate the statistical study of weighted networks. First, this project will contribute and disseminate free and open-source statistical software that permits user-friendly applications. Second, the material developed in this project will be incorporated into graduate-level research methods coursework and workshops.