Conditional Inference Algorithms for Graphs, Tables, and Point Processes

离散值矩阵数据（如列联表、共现表、图和网络的邻接矩阵以及多元二进制时间序列）带来的统计挑战通常可以通过关注矩阵中条目模式的条件分布来大大减少，并给定矩阵的边界。尽管这种条件作用简化了统计挑战，但它极大地增加了任何相关统计过程的计算挑战。该项目有两个主要目标：(1)设计实用的方法和算法，用于对给定边界的矩阵的条件分布进行统计推断；(2)将这些方法和算法专门用于各种学科的科学需求，包括神经科学、生态学、网络分析、教育测试和组合近似。随着收集和存储大量复杂数据的新技术的出现，统计在科学、技术、工程、医学和商业中发挥着越来越重要的作用。这些新的数据来源需要新的统计思维和改进的统计算法。该项目开发了新的网络统计分析算法，如社会网络、生态网络和大脑网络。初步结果已经被神经科学合作者用来更好地理解人类癫痫发作的结构。该项目还资助研究生的培训，他们将成为科学和工程领域的下一代创新者。

The statistical challenges posed by discrete-valued matrix data (such as contingency tables, co-occurrence tables, adjacency matrices of graphs and networks, and multivariate binary time series) can often be greatly reduced by focusing on the conditional distribution of the pattern of entries in the matrix, given the margins of the matrix. Although this conditioning simplifies the statistical challenges, it greatly increases the computational challenges of any associated statistical procedures. This project has two principle aims: (1) to design practical methods and algorithms for statistical inference about the conditional distribution of a matrix given its margins, and (2) to specialize these methods and algorithms to the scientific needs of a variety of disciplines, including neuroscience, ecology, network analysis, educational testing, and combinatorial approximation.With the advent of new technologies for gathering and storing large amounts of complex data, statistics is playing an increasingly central role in science, technology, engineering, medicine and commerce. These new data sources require new types of statistical thinking and improved statistical algorithms. This project develops new algorithms for the statistical analysis of networks, such as social networks, ecological networks, and brain networks. Preliminary results are already being used by neuroscience collaborators to better understand the structure of human seizures. This project also funds the training of graduate students who will become the next generation of innovators in science and engineering.