Statistical Analysis of Networked Point Processes

由于神经数据分析中出现的问题，研究人员和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。感兴趣的主要问题是了解利率函数的结构，以及了解利率函数如何与协变量相关。将特别注意时间扭曲或延迟问题，其中考虑到不同复制之间在时间尺度上的差异。这种时标差异在神经数据应用中特别令人感兴趣，因为它们代表了受试者完成任务对刺激做出反应的不同速度。这项研究将开发基于极值理论的工具，用于功能回归和方差问题分析的新方法。神经细胞，或称神经元，是大脑和身体其他部位交流的基础。例如，当受试者受到外部刺激时，视觉刺激可能包括向受试者展示物体，神经细胞做出反应，并通过一系列电脉冲将有关刺激的信息传输到大脑。这项拟议的研究将通过开发分析神经信号的新方法来促进对这一交流过程的理解。在拟议的研究期间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、年龄和性别等因素有关。所提出的研究在产品设计中具有应用价值。例如，可能需要诸如交通信号灯之类的警告设备来产生刺激以警告用户潜在的危险。了解不同个体对特定刺激的反应，以及对不同刺激的不同反应，将为更广泛的用户改进产品和安全性。

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.