New Development in Point Process Theory, Methods and Applications

近年来，随着现代数据采集技术的快速发展，高分辨率的空间、时间和时空数据以前所未有的速度得到了应用。这些新数据的复杂性和规模要求使用新的统计建模工具。这项拟议的研究将开发可用于分析复杂和大型数据的新建模工具。该项目将考虑应用新的方法来回答流行病学、金融学和社会学等学科中出现的科学问题。这个项目将在点过程中开发新的理论和方法。特别是，该项目将开发(1)基于拟似然的更有效的估计程序来拟合点过程模型，以及(2)对标记点过程进行主成分分析的新框架。对于第一个目标，我们将开发高效的计算算法，并研究这些算法的理论性质。对于第二个目标，通过两个潜在相关的潜在过程将标记点过程的标记和点联系起来，并对这两个潜在过程分别进行主成分分析。将对所提出方法的理论性质进行研究。将开发数据驱动的程序来选择调整参数。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。

With the rapid development of modern data collection technologies, high-resolution spatial, temporal, and spatial-temporal data have become available at an unprecedented speed in recent years. The complexity and magnitude of these new data call for new statistical modeling tools. The proposed research will develop new modeling tools that can be used to analyze complex and large data. Novel applications of the proposed methods will be considered to answer scientific questions arising in disciplines such as epidemiology, finance, and sociology.This project will develop new theory and methods in point processes. In particular, the project will develop (1) more efficient estimation procedures based on quasi-likelihood to fit point process models and (2) a novel framework to conduct principle component analysis for marked point processes. For the first aim, efficient computational algorithms will be developed and theoretical properties of these algorithms will be investigated. For the second aim, the marks and points of the marked point process are linked through two potentially correlated latent processes, and principle component analysis is conducted for each of the two latent processes. Theoretical properties of the proposed method will be investigated. Data driven procedures will be developed to select the tuning parameters.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.