General Correlated Count Statistical Structures

该研究项目将侧重于分析在时间和/或空间上记录的有价值的数据的方法，例如，每日县COVID-19死亡人数、每月州龙卷风计数和每年北大西洋强烈飓风。这些数据在时间上可能是相关的，这意味着今天观测到的计数可能与刚刚过去发生的计数相关联，或者在空间上是相关的，这意味着相邻的观测相互关联。PI将开发统计方法，考虑到适合计数的特定类型的分布，例如泊松分布、几何分布和二项分布，使研究人员能够做出更准确的预测和推断。这里开发的模型和方法允许时间和空间上的正相关和负相关，这是许多当前统计计数模型无法实现的特征。例如，COVID-19病例往往聚集在一起，而橡树和松树不喜欢在彼此附近生长（负相关）。在这个项目中开发的模型将允许协变量的合并，并允许可能性推理。PI还将寻求建立加州气候中心，这是一个通过技术方法量化气候和环境问题的研究站。在技术层面上，PI将把高斯时空过程转换为具有期望的边际分布的计数过程。这项工作将证明这种设置产生了最灵活的计数结构。将探讨涉及非高斯过程的扩展，并通过粒子滤波和顺序蒙特卡罗方法开发通过最大似然技术拟合时空模型的方法。扩展到多元计数时间序列和将被检查和渐近推理的一些设置将被研究。将进行北半球积雪存在/不存在趋势的时空应用。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。

This research project will focus on methods for analyzing data recorded in time and/or space that is count-valued, for example, daily county COVID-19 deaths, monthly state tornado counts, and annual North Atlantic severe hurricanes. The data may be correlated in time, implying that counts observed today may be associated by counts occurring in the immediate past, or correlated in space, implying that adjacent observations are associated with each other. The PI will develop statistical methods that take into account the particular type of distribution appropriate for the counts, for example, Poisson, geometric, and binomial, enabling the researcher to make more accurate forecasts and inferences. The models and methods developed here allow both positive and negative correlations in time and space, a feature not achievable with many current statistical count models. For example, COVID-19 cases tend to cluster in groups, while oak and pine trees do not prefer to grow near one and other (negative correlation). The models to be developed in this project will permit the incorporation of covariates and allow for likelihood inference. The PI will also seek to construct the California Climate Center, a research station for climatic and environmental problems quantified by technical methods.On a technical level, the PI will transform a Gaussian space-time process into a count process having the desired marginal distribution(s). The work will prove that this setup produces the most flexible count structures achievable. Extensions involving non-Gaussian processes will be explored and methods to fit the spatio-temporal model via maximum likelihood techniques will be developed via particle filtering and sequential Monte Carlo methods. Extensions to multivariate count time series and will be examined and asymptotic inference for some setups will be studied. Space-time applications to snow presence/absence trends in the Northern Hemisphere will be conducted.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.