Point Processes and time Series: Mutual Information Analyses

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Proposal: DMS-0203921 PI: David Brillinger Title: Point processes and time series: mutual information analysis ABSTRACT 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.