General Correlated Count Statistical Structures

一般相关计数统计结构

• 批准号: 2113592
• 负责人: Robert Lund
• 金额: $ 22万
• 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: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2113592&HistoricalAwards=false
• 关键词: General; Correlated; Count; Statistical; Structures

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.

该研究项目将专注于分析在计数值的时间和/或空间中记录的数据的方法，例如，每日县新冠肺炎死亡人数、每月州龙卷风计数和年度北大西洋严重飓风。这些数据在时间上可能是相关的，这意味着今天观察到的计数可能与最近发生的计数相关，或者在空间上相关，这意味着相邻的观测彼此关联。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、几何和二项式，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，新冠肺炎病例倾向于成群生长，而橡树和松树不喜欢生长在一个或另一个附近(负相关)。本项目将开发的模型将允许纳入协变量，并允许进行似然推断。国际气候中心还将寻求建设加州气候中心，这是一个用技术方法量化的气候和环境问题研究站。在技术层面上，国际气候中心将把高斯时空过程转化为具有所需边际分布的计数过程(S)。这项工作将证明，这种设置产生了可实现的最灵活的计数结构。将探索涉及非高斯过程的扩展，并将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来拟合时空模型的方法。对多元计数时间序列的推广进行了研究，并研究了一些设置的渐近推断。该奖项反映了NSF的法定使命，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，被认为是值得支持的。

项目成果

Poisson Count Time Series

泊松计数时间序列

• 发表时间: 2024
• 期刊: Journal of Time Series Analysis
• 影响因子: 0.9
• 作者: Kong Jiajie;Lund, Robert
• 通讯作者: Lund, Robert

Seasonal count time series

• DOI: 10.1111/jtsa.12651
• 发表时间: 2022-06-22
• 期刊: JOURNAL OF TIME SERIES ANALYSIS
• 影响因子: 0.9
• 作者: KONG, J. I. A. J. I. E.;LUND, R. O. B. E. R. T.
• 通讯作者: LUND, R. O. B. E. R. T.

High-dimensional latent Gaussian count time series: Concentration results for autocovariances and applications

高维潜在高斯计数时间序列：自协方差和应用的集中结果

• 发表时间: 2024
• 期刊: Electronic journal of statistics
• 影响因子: 1.1
• 作者: Düker, Marie-Christine;Lund, Robert;Pipiras, Vladas
• 通讯作者: Pipiras, Vladas

Statistical Inference for Lindley Random Walks with Correlated Increments

具有相关增量的 Lindley 随机游走的统计推断

• 发表时间: 2024
• 期刊: Journal of statistical computation and simulation
• 影响因子: 1.2
• 作者: Grant, John;Kong, Jiajie;Liu, Xin;Lund, Robert;Wood, Jonathan
• 通讯作者: Wood, Jonathan

A Comparison of Changepoint Techniques for Time Series Data

时间序列数据变点技术的比较

• 发表时间: 2022
• 期刊: Computational statistics data analysis
• 作者: Shi, X.;Gallagher, C.M;Lund, R.B;Killick, R.
• 通讯作者: Killick, R.