Statistical Analysis of Networked Point Processes

Case Western Reserve University, Cleveland OH

Investigators

Abstract

Motivated by problems arising in the analysis of neural data, the investigator and colleagues will develop new statistical methods for the analysis of functional data, and in particular to study multiple replications of point processes. The main question of interest is understanding the structure of the rate functions, and understanding how the rate functions relate to covariates. Particular attention will be given to the time distortion, or latency problem, where differences in the time scale among different replications are considered. Such time-scale differences are of particular interest in neural data applications, as they represent different speeds at which subjects complete tasks in response to a stimulus. The research will develop new methods, based on tools from extreme value theory, for functional regression and analysis of variance problems. Nerve cells, or neurons, are fundamental to communication between the brain and other parts of the body. When a subject receives an external stimulus, for example, a visual stimulus may consist of showing an object to the subject, nerve cells react and transmit information about the stimulus to the brain through a series of electrical pulses. The proposed research will advance understanding of this communication process by developing new methods for analyzing the neural signals. The statistical methods developed during the proposed research will study how the response to a stimulus differs among different subjects, and how these differences relate to factors such as species, age and gender. The proposed research has applications in product design. As an example, a warning device such as a traffic signal may be required to generate a stimulus to warn users of potential hazard. Understanding the response of different individuals to a given stimulus, and the different responses to different stimuli, will lead to improved products and safety for a wider variety of users.