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Bayesian Nonparametric Modeling and Inference Methods for Point Processes

点过程的贝叶斯非参数建模和推理方法

基本信息

批准号：
1950902
负责人：
Athanasios Kottas
金额：
$ 28.99万
依托单位：
University of California-Santa Cruz
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1950902&HistoricalAwards=false
关键词：
Bayesian Nonparametric Modeling Inference Methods

项目摘要

This research project will develop flexible statistical models and corresponding inference methods for different classes of point processes. The theory of point processes was developed to study the distribution of events that occur at random times and/or spatial locations. This project will advance statistical methodology for a range of problems involving data that arise from point processes. A key objective will be to increase the scope of several classes of point processes by developing statistical models that relax the restrictive assumptions of state-of-the-art methods. Point process methods are important for the field of statistics and have applications in a variety of areas, including climatology, criminology, finance, and seismology. The new models will be applied to important societal problems including the study of clustering patterns for different types of crime and the analysis of earthquake occurrences. To facilitate use of the methods by practitioners and researchers from other fields, publicly available software will be developed for implementing several of the statistical models. The project also will create educational opportunities for graduate students and seek to increase the participation of women and underrepresented groups in the research.This research project will develop a general model-based framework for point processes over time or space, including Poisson processes and Hawkes processes. The modeling framework involves structured mixture representations for point process intensities that achieve a balance between model flexibility and computational efficiency in implementation of statistical inference and prediction. The project will develop tractable inference methods for spatial point processes observed over irregular domains; for instance, city, state, or country boundaries. It also will increase the inferential scope for marked Hawkes processes, a versatile class of stochastic point process models that have been applied in diverse areas, including earthquake modeling, finance, criminology, and analysis of social networks. Even though the theory for Hawkes processes is well studied, statistical inference methods are relatively less developed, especially under general settings that allow for non-standard data features and for full uncertainty quantification. The research project has a substantial analytic component with regards to methodological development for the various point process models, as well as a significant computational component with regards to achieving efficient model fitting that can be scaled to large amounts of data. The practical utility of the new methods will be investigated with several simulation studies and through substantive applications involving analysis of earthquake and crime data.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.

本研究计画将针对不同类别的点过程，发展弹性的统计模式与对应的推论方法。点过程理论是为了研究在随机时间和/或空间位置发生的事件的分布而开发的。该项目将推进一系列问题的统计方法，这些问题涉及点过程产生的数据。一个关键的目标将是增加几类点过程的范围，通过开发统计模型，放松国家的最先进的方法的限制性假设。点过程方法在统计学领域很重要，在气候学、犯罪学、金融学和地震学等领域都有应用。新的模型将应用于重要的社会问题，包括研究不同类型犯罪的聚类模式和分析地震发生。为便利其他领域的从业人员和研究人员使用这些方法，将开发可公开获得的软件，以实施若干统计模型。该项目还将为研究生创造教育机会，并寻求增加女性和代表性不足群体在研究中的参与。该研究项目将为时间或空间上的点过程（包括Poisson过程和Hawkes过程）开发一个基于模型的通用框架。建模框架涉及点过程强度的结构化混合表示，在统计推断和预测的实施中实现模型灵活性和计算效率之间的平衡。该项目将为在不规则域上观察到的空间点过程开发易于处理的推理方法;例如，城市，州或国家边界。它还将增加标记霍克斯过程的推理范围，这是一类多功能的随机点过程模型，已应用于不同领域，包括地震建模，金融，犯罪学和社交网络分析。尽管霍克斯过程的理论研究得很好，统计推断方法相对较少，特别是在允许非标准数据特征和完全不确定性量化的一般设置下。该研究项目有一个实质性的分析部分，涉及各种点过程模型的方法开发，以及一个重要的计算部分，涉及实现可扩展到大量数据的有效模型拟合。新方法的实际效用将通过几个模拟研究和地震和犯罪数据分析的实质性应用进行调查。该奖项反映了NSF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。