Collaborative Research: Non- and Semi-Parametric Modeling of Structured Human Activity Patterns Using Point Processes

这一研究项目将为结构化人类活动数据的分析提供理论和方法的支持。由于最近的技术进步，各种来源正在收集大量的实时人类活动数据，如社交媒体数据和交易数据。这些新数据的复杂性和规模要求使用新的统计建模工具。这个项目中将要开发的方法是由对人类行为的进一步理解所驱动的，并且可以用来进一步理解人类行为。通过与领域专家的积极跨学科合作，该项目将在统计界与行为金融界和社会科学界之间建立一座桥梁。将开发开源R包，并通过CRAN提供给公众使用。该项目的关键材料将纳入研究生高级课程。研究人员将开发一系列新的非参数和半参数点过程模型，用于结构化人类活动的时间点模式。特别是，他们将开发(1)用于模拟股票交易等人类活动的多层次功能主成分分析框架；(2)用于日常人类活动模式的同步建模和聚类方法，这些模式不仅是结构化的，而且跨不同的子群是异质的；以及(3)一类新的双变量点过程模型，用于模拟现代社交媒体用户的复杂行为，并为用户的内容生成行为提供有意义的见解。对于前两个目标，将引入流行的功能数据分析工具来模拟具有复杂结构的点过程。将开发高效的计算算法，并研究这些算法的理论性质。对于第三个目标，将使用半参数制度转换多类型点过程模型来模拟社交媒体发布行为，其中发布强度函数用样条基函数来近似。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will advance theory and methods for analyzing structured human-activity data. Because of recent technological advances, large amounts of real-time human-activity data, such as social media data and transaction data, are being collected by various sources. The complexity and magnitude of these new data call for new statistical modeling tools. The methods to be developed in this project are motivated by and can be used to further understanding of human behaviors. Through active interdisciplinary collaborations with domain experts, the project will establish a bridge between the statistics community and the behavioral finance and social science communities. Open-source R packages will be developed and made available for public use through CRAN. Key materials from the project will be incorporated into the advanced graduate student courses.The investigators will develop a series of new non- and semi-parametric point process models for temporal point patterns of structured human activities. In particular, they will develop (1) a multi-level functional principal component analysis framework for modeling human activities such as stock trading etc.; (2) a simultaneous modeling and clustering approach for daily human activity patterns that are not only structured but also heterogeneous across different sub-populations; and (3) a new class of bivariate point process models to model the complex behaviors of modern social media users and provide meaningful insights into a user's content generating behavior. For the first two aims, popular functional data analysis tools will be introduced to model point processes with complex structures. Efficient computational algorithms will be developed and theoretical properties of these algorithms will be investigated. For the third aim, a semi-parametric regime-switching multi-type point process model will be used to model social media posting behaviors, where the posting intensity functions are approximated with spline basis functions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.