Statistical Analysis of Networked Point Processes

受神经数据分析中出现的问题的启发，研究人员及其同事将开发新的统计方法来分析功能数据，特别是研究点过程的多次重复。兴趣的主要问题是理解利率函数的结构，以及利率函数与协变量的关系。将特别注意时间失真或延迟问题，其中考虑不同复制之间的时间尺度差异。这种时间尺度差异在神经数据应用中特别感兴趣，因为它们代表受试者响应刺激完成任务的不同速度。这项研究将开发新的方法，基于极值理论的工具，用于函数回归和方差分析问题。神经细胞，或神经元，是大脑和身体其他部位之间交流的基础。当受试者接收到外部刺激时，例如，视觉刺激可以包括向受试者显示物体，神经细胞做出反应并通过一系列电脉冲将关于刺激的信息传输到大脑。这项研究将通过开发分析神经信号的新方法来促进对这种通信过程的理解。在拟议的研究中开发的统计方法将研究不同受试者对刺激的反应如何不同，以及这些差异如何与物种，年龄和性别等因素相关。所提出的研究在产品设计中具有应用价值。作为示例，可能需要诸如交通信号的警告设备来生成刺激以警告用户潜在的危险。了解不同个体对给定刺激的反应，以及对不同刺激的不同反应，将为更广泛的用户带来更好的产品和安全性。

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.