Bayesian Learning for Spatial Point Processes: Theory, Methods, Computation, and Applications

科学家、工程师、经济学家和体育从业者越来越意识到，在试图恢复随时间和空间变化的复杂模式时，准确理解潜在集群的重要性。这种模式的例子包括北美发生的地震、巴罗科罗拉多岛的树木位置、职业球员在篮球场上的投篮尝试，以及来自直播流的弹幕评论。在对这种复杂的点过程模式进行统计分析时，科学目标通常涉及强度估计或聚类学习。为了帮助实现科学目标，本项目将开发揭示空间点过程中隐藏的空间同质性以及不同单变量或多变量过程之间潜在异质性的方法。该项目将促进统计科学领域的知识，并为政府机构、环境科学家、社会科学家和体育产业从业人员的工作提供有用的工具。该项目还将为本科生和研究生提供培训机会。该项目将填补非参数贝叶斯方法和空间点过程之间的空白，包括单变量和多变量过程的强度估计和异质性学习。研究将集中在三个主题的基础上，非参数贝叶斯框架应用于不同的社会经济问题。在第一个课题中，研究者将构建一个马尔可夫约束非参数贝叶斯先验来学习具有空间同质性的点过程强度面。研究者将在第二个主题中开发一种联合估计多点过程的强度表面和潜在组信息的方法。最后，研究人员将开发一个具有复杂强度函数和潜在群体结构的多变量点过程模型。研究者将建立新的估计量的一致性和渐近分布，并与公开可用的软件一起开发有效的算法。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。

Scientists, engineers, economists, and sports practitioners are increasingly aware of the importance of accurately understanding underlying clusters when trying to recover complex patterns that vary across time and space. Examples of such patterns include earthquake occurrences over North America, tree locations in Barro Colorado Island, field goal attempts of professional players over basketball courts, and bullet-screen comments from live streams. When performing statistical analysis on such complex point process patterns, the scientific goals often involve either intensity estimation or cluster learning. To help achieve the scientific goals, this project will develop methods to reveal hidden spatial homogeneity within spatial point processes and underlying heterogeneity among different univariate or multivariate processes. The project will advance knowledge within the statistical sciences and contribute useful tools to the work of government agencies, environmental scientists, social scientists, and practitioners in the sports industry. The project will also provide training opportunities to undergraduate and graduate students. This project will fill the gap between nonparametric Bayesian methods and spatial point processes, including intensity estimation and heterogeneity learning for univariate and multivariate processes. The research will focus on three topics based on a nonparametric Bayesian framework with applications to different socio-economic problems. In the first topic, the investigator will construct a Markov constraint nonparametric Bayesian prior to learn the point process’s intensity surface of with spatial homogeneity. The investigator will develop a method for jointly estimating intensity surfaces and latent group information for multiple point processes in the second topic. Lastly, the investigator will develop a multivariate point process model with complex intensity function and latent group structure for each type of points. The investigator will establish consistency and asymptotic distributions of the new estimators and develop efficient algorithms together with publicly available software.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.