New Development in Point Process Theory, Methods and Applications

点过程理论、方法与应用的新进展

• 批准号: 1810591
• 负责人: Yongtao Guan
• 金额: $ 10万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-15 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1810591&HistoricalAwards=false
• 关键词: New; Development; Point; Process; Theory

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.

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出现。这些新数据的复杂性和规模要求新的统计建模工具。拟议的研究将开发新的建模工具，可用于分析复杂和大型数据。 本项目将研究新方法的应用，以回答流行病学、金融学、社会学等学科中出现的科学问题。本项目将开发点过程的新理论和方法。特别是，该项目将开发（1）更有效的估计程序的基础上拟似然拟合点过程模型和（2）一个新的框架进行主成分分析的标记点过程。对于第一个目标，有效的计算算法将开发和这些算法的理论特性进行研究。对于第二个目标，标记点过程的标记和点通过两个潜在相关的潜在过程联系起来，并对两个潜在过程中的每一个进行主成分分析。将研究所提出的方法的理论特性。将开发数据驱动程序来选择调整参数。该奖项反映了NSF的法定使命，并且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。

项目成果

Nonparametric estimation of the pair correlation function of replicated inhomogeneous point processes

• DOI: 10.1214/20-ejs1755
• 发表时间: 2020
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Ganggang Xu;Chong Zhao;A. Jalilian;R. Waagepetersen;Jingfei Zhang;Yongtao Guan

Semiparametric Multinomial Logistic Regression for Multivariate Point Pattern Data

多元点模式数据的半参数多项式Lo​​gistic回归

• DOI: 10.1080/01621459.2020.1863812
• 发表时间: 2021
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Hessellund, Kristian Bjørn;Xu, Ganggang;Guan, Yongtao;Waagepetersen, Rasmus
• 通讯作者: Waagepetersen, Rasmus