Highly Multivariate Geo-Statistics Using Graphical Models

使用图形模型的高度多元地理统计

• 批准号: 1915803
• 负责人: Abhirup Datta
• 金额: $ 18万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1915803&HistoricalAwards=false
• 关键词: Highly; Multivariate; Geo; Statistics; Using

Researchers in forestry, ecology, climate sciences, environmental health, and many other fields routinely analyze geo-tagged data collected at thousands of locations using spatial statistics. Modern Geographical Information Systems (GIS) are empowered to simultaneously measure many different variables at each location. This heralds a shift towards a multivariate paradigm in spatial statistics. A joint analysis of all the variables help identify common geographical patterns and sources for the different variables. In this project, the PI pursues statistical methodology that can adequately address the emerging complexities of such highly-multivariate geospatial datasets. The innovations include a) utilizing available scientific information about the dependence among variables, b) ensuring computational scalability of the algorithms, and c) improving interpretability of findings from the multivariate analysis. The genesis of the proposed innovations lies in substantive questions related to climate modeling, air and water quality. These research domains study some of the most threatening challenges to the human society in the twenty-first century. The statistical methods developed in this project will enable practitioners in these fields to conduct highly-multivariate spatial analysis using modest computing resources. The project also provides the opportunity to train graduate students in many diverse and essential areas of statistics as well as in advanced statistical computing.Gaussian Processes (GPs) have long been used for modeling multivariate spatial surfaces. Multivariate GPs are often created by mixing univariate ones which obfuscate the individual spatial characteristics of each resultant surface. Direct constructions like the multivariate Matern GP are more interpretable but entail complex parameter constraints offering little flexibility to exploit prior information about inter-variable dependence. The PI proposes a novel procedure to create multivariate GPs that endows each surface with an interpretable GP measure with surface-specific variance, smoothness and spatial decay, but also enables incorporating the dependency network among the variables into the construction. A recurrent theme throughout is the versatile exploitation of graphical models. Graphs defined in space, time and variable domains are used to create multivariate GPs with desirable properties in terms of interpretation, computation and structure. Another accompanying theme is utilizing a standard decomposition of GPs to extend the discrete construction to well-defined continuous stochastic processes, thereby enabling predictions at any new location. Novel, simple, but efficient strategies will be explored for parameter estimation. Finally, the PI separately focuses on non-Euclidean spatial domains like estuaries and river networks. New univariate GPs will be devised that respect the complicated contours of these domains. Subsequently, harmonious application of graphical models will create multivariate locally smooth GPs to analyze multivariate spatial data on such domains.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.

林业、生态学、气候科学、环境健康和许多其他领域的研究人员经常使用空间统计分析在数千个地点收集的地理标记数据。现代地理信息系统（GIS）能够同时测量每个位置的许多不同变量。这预示着空间统计将转向多元范式。对所有变量进行联合分析有助于确定不同变量的共同地理模式和来源。在这个项目中，PI追求的统计方法，可以充分解决这种高度多元的地理空间数据集的新兴复杂性。创新包括a）利用有关变量之间依赖性的可用科学信息，B）确保算法的计算可扩展性，以及c）提高多变量分析结果的可解释性。这些创新的起源在于与气候建模、空气和水质量相关的实质性问题。这些研究领域研究的是21世纪世纪人类社会面临的一些最具威胁性的挑战。在这个项目中开发的统计方法将使这些领域的从业人员能够使用适度的计算资源进行高度多元的空间分析。该项目还提供了机会，培养研究生在统计学的许多不同的和重要的领域，以及在先进的统计计算。高斯过程（GP）长期以来一直用于建模多元空间曲面。多变量GP通常通过混合单变量GP来创建，这混淆了每个合成表面的个体空间特征。像多变量Matern GP这样的直接构造更易于解释，但需要复杂的参数约束，这使得利用关于变量间依赖性的先验信息的灵活性很小。PI提出了一种新的程序来创建多变量GP，赋予每个表面一个可解释的GP测量，具有表面特定的方差，平滑度和空间衰减，但也可以将变量之间的依赖网络纳入到构建中。贯穿始终的一个主题是图形模型的多功能开发。定义在空间，时间和变量域的图形被用来创建多变量GP与理想的属性在解释，计算和结构方面。另一个伴随的主题是利用GP的标准分解将离散构造扩展到定义良好的连续随机过程，从而实现在任何新位置的预测。新颖，简单，但有效的策略将探索参数估计。最后，PI分别关注非欧几里德空间域，如河口和河流网络。新的单变量GP将设计尊重这些领域的复杂轮廓。随后，图形模型的和谐应用将创建多变量局部平滑GP，以分析这些领域的多变量空间数据。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。

项目成果

Graphical Gaussian Process Models for Highly Multivariate Spatial Data.

高度多元空间数据的图形高斯过程模型。

• DOI: 10.1093/biomet/asab061
• 发表时间: 2022
• 期刊: Biometrika
• 影响因子: 2.7
• 作者: Dey,Debangan;Datta,Abhirup;Banerjee,Sudipto
• 通讯作者: Banerjee,Sudipto

Spatial disease mapping using directed acyclic graph auto-regressive (DAGAR) models.

• DOI: 10.1214/19-ba1177
• 发表时间: 2019-12
• 期刊: Bayesian analysis
• 影响因子: 4.4
• 作者: Datta A;Banerjee S;Hodges JS;Gao L
• 通讯作者: Gao L

Random Forests for Spatially Dependent Data

• DOI: 10.1080/01621459.2021.1950003
• 发表时间: 2021-08
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Arkajyoti Saha;Sumanta Basu;A. Datta

Spatial modeling for correlated cancers using bivariate directed graphs

使用二元有向图对相关癌症进行空间建模

• DOI: 10.21037/ace-19-41
• 发表时间: 2020
• 期刊: Annals of Cancer Epidemiology
• 作者: Gao, Leiwen;Banerjee, Sudipto;Datta, Abhirup
• 通讯作者: Datta, Abhirup

Hierarchical multivariate directed acyclic graph autoregressive models for spatial diseases mapping.

用于空间疾病映射的分层多元有向无环图自回归模型。

• DOI: 10.1002/sim.9404
• 发表时间: 2022
• 期刊: Statistics in medicine
• 影响因子: 2
• 作者: Gao,Leiwen;Datta,Abhirup;Banerjee,Sudipto
• 通讯作者: Banerjee,Sudipto