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

该研究项目将推进分析结构化人类活动数据的理论和方法。由于最近的技术进步，各种来源正在收集大量实时人类活动数据，例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新的统计建模工具。在这个项目中开发的方法是由动机，并可用于进一步了解人类行为。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学和社会科学界之间建立桥梁。开源R包将通过CRAN开发并提供给公众使用。研究人员将开发一系列新的非参数和半参数点过程模型，用于描述结构化人类活动的时间点模式。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)一种同时建模和聚类方法，用于日常人类活动模式，这些模式不仅是结构化的，而且在不同的子人群中是异质的;以及（3）一类新的双变量点过程模型，用于对现代社交媒体用户的复杂行为进行建模，并对用户的内容生成行为提供有意义的见解。对于前两个目标，流行的函数数据分析工具将被引入到模型点过程的复杂结构。有效的计算算法将被开发和这些算法的理论特性将被调查。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模拟社交媒体发帖行为，其中发帖强度函数用样条基函数近似。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.