Point Processes and time Series: Mutual Information Analyses

点过程和时间序列：互信息分析

• 批准号: 0203921
• 负责人: David Brillinger
• 金额: $ 26.1万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-15 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0203921&HistoricalAwards=false
• 关键词: Point; Processes; time; Series; Mutual

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.

提案：DMS-0203921 PI：大卫布里林格标题：点过程和时间序列：互信息分析摘要 本研究对互信息系数进行了理论和实证研究。它将普通相关系数推广到随机过程的情形。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或空间或频率以及其他量的函数。各种类型的估计，包括基于核，小波收缩，递归时间的统计特性将被开发。强逼近，极限定理，遍历理论和非参数估计的工具将被采用。 克劳德·香农在1948年提出了熵和互信息的概念。这些都彻底改变和推动了我们的技术社会的发展方式。互信息表征变量之间和科学关系的依赖强度。它的目的是发展扩展的想法，随机函数和随机散射。这项工作将是理论和数据驱动的。这项工作可能有重要的回报，因为科学是关于法律和关系的。