Point Processes and time Series: Mutual Information Analyses

建议：DMS-0203921PI：David Brillinger标题：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。在其他量中，互信息系数将成为时间、空间或频率的函数。将开发各种类型估计的统计特性，包括基于核的估计、具有收缩的小波、重复时间。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年提出了熵和互信息的概念。这些都使我们的技术社会的发展方式发生了革命性的变化，并推动了这种发展。互信息表征了变量之间的相关性和科学关系的强度。其目的是将该思想扩展到随机函数和随机散布。这项工作将是理论和数据驱动的。这项工作可能会有重要的回报，因为科学是关于定律和关系的。

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.