Point Processes and time Series: Mutual Information Analyses

题目：点过程和时间序列：互信息分析摘要：本研究涉及互信息系数的理论和实证研究。它将普通的相关系数推广到随机过程的情况。要研究的过程包括：点过程、时间序列、时空过程和随机网络。互信息系数将成为时间、空间或频率的函数。各种类型估计的统计性质，包括基于核的，具有收缩的小波，递归时间将被开发。将使用强逼近、极限定理、遍历理论和非参数估计等工具。克劳德·香农在1948年引入了熵和互信息的概念。这些都彻底改变并推动了我们技术社会的发展方式。相互信息表征了变量之间和科学关系之间的依赖强度。它的目的是发展的思想扩展到随机函数和随机散射。这项工作将由理论和数据驱动。这项工作可能有重要的回报，因为科学是关于规律和关系的。

Proposal: DMS-0203921PI: David BrillingerTitle: Point processes and time series: mutual information analysisABSTRACT This research concerns the theoretical and empirical investigation of the mutual information coefficient. It extends the ordinary correlation coefficient to the case of random processes. The processes to be studied include: point processes, time series, spatial-temporal processes and random networks. The mutual information coefficient will become a function of time or space or frequency amongst other quantities. The statistical properties of a variety of types of estimates, including kernel-based, wavelets with shrinkage, recurrence times will be developed. The tools of strong approximations, limit theorems, ergodic theory and nonparametric estimation will be employed. Claude Shannon introduced the concepts of entropy and mutual information in 1948. These have both revolutionized and driven the way that our technological society has developed. Mutual information characterizes the strength of dependence between variates and of scientific relationships. It is intended to develop extensions of the idea to random functions and random scatter. The work will be both theory and data driven. The work may have important payoffs for science is about laws and relationships.