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

该研究项目将推进结构化人类活动数据分析的理论和方法。由于最近的技术进步，大量的实时人类活动数据，如社交媒体数据和交易数据，正在被各种来源收集。这些新数据的复杂性和规模需要新的统计建模工具。在这个项目中开发的方法是由人类行为驱动的，可以用来进一步理解人类行为。通过与领域专家积极的跨学科合作，该项目将在统计界与行为金融学和社会科学界之间建立一座桥梁。开源R包将通过CRAN开发并提供给公众使用。该项目的关键材料将被纳入高级研究生课程。研究人员将为结构化人类活动的时间点模式开发一系列新的非参数和半参数点过程模型。特别是，他们将开发(1)一个多层次的功能主成分分析框架，用于模拟人类活动，如股票交易等；(2)对不同亚种群间既有结构又有异质的人类日常活动模式进行同步建模和聚类；(3)一类新的二元点过程模型，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对具有复杂结构的点过程进行建模。高效的计算算法将被开发，这些算法的理论性质将被研究。对于第三个目标，将使用半参数状态切换多类型点过程模型来建模社交媒体发布行为，其中发布强度函数近似为样条基函数。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.