Default Bayesian Analysis of Spatial Data

空间数据的默认贝叶斯分析

• 批准号: 2113375
• 负责人: Victor De Oliveira
• 金额: $ 16万
• 依托单位: University of Texas at San Antonio
• 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: 2021-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2113375&HistoricalAwards=false
• 关键词: Default; Bayesian; Analysis; Spatial; Data

The collection and analysis of spatial data are ubiquitous in most natural and earth sciences, such as ecology, epidemiology, geology and hydrology. This research project will develop statistical methodology for automatic Bayesian analysis of Gaussian models that does not require any subjective input. These models play a prominent role due to their versatility to model spatially varying phenomena, and because they serve as building blocks for the construction of more elaborate models. The Bayesian approach is especially appealing when the main goal is spatial interpolation, but implementing it for such models faces two big challenges: (i) Automatic formulation of sensible prior distributions that are adapted to the scale of the data under investigation and (ii) Analysis of massive data sets that are the norm nowadays. The project aims at developing theory and practice to overcome both challenges, which will make practicably feasible the automatic Bayesian analysis of large spatial data sets. In addition, the project will train graduate students in spatial statistics in general, and the topics of this project in particular. The results derived from the project will be disseminated in diverse outlets, and software to implement the methodology will be made publicly available.The research project will make practicably feasible default Bayesian analyses of large spatial data sets, by contributing innovations to the two parts of the Bayesian model. First, approximate reference priors for the parameters of covariance models will be developed that allow carrying out Bayesian analyses for these models in an automatic fashion, not requiring subjective elicitation. These will be based on the spectral approximation of stationary random fields. Second, likelihood approximations feasible for large spatial data sets will be elaborated by developing strategies to tune a recently proposed approximation for stationary covariance functions. The tuning of the approximation aims at striking a balance between accuracy and computational effort. Both approximations rely on the spectral density, rather than the covariance function, of the model. Together, the reference prior and likelihood approximations will make possible carrying out default Bayesian analyses that include model selection and assessment. In addition, the project will critically assess the common practice of fixing the smoothness of the random field at a value, chosen by convention or tradition, that bears no relation to the data under analysis. The project will investigate methods to quantify the information content in spatial data about smoothness parameters, and uncover how this depends on the sample design. The methodology will be tested on diverse data sets from the earth sciences, with special focus on spatial rainfall 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.

空间数据的收集和分析在大多数自然和地球科学中都是普遍存在的，例如生态学，流行病学，地质和水文学。该研究项目将开发统计方法，用于自动对不需要任何主观输入的高斯模型分析。这些模型由于其具有多功能性而在空间变化的现象上起着重要作用，并且由于它们是建造更精细模型的基础。当主要目标是空间插值时，贝叶斯的方法尤其吸引人，但针对此类模型实施它面临两个大挑战：（i）自动提出明智的先前分布，这些分布适用于所研究的数据规模以及（ii）（ii）分析当今常态的大规模数据集。该项目旨在发展理论和实践来克服这两个挑战，这将使实际上可行的贝叶斯对大空间数据集的分析。此外，该项目一般将培训研究生的空间统计数据，尤其是该项目的主题。从项目中得出的结果将在各种渠道中传播，并且将公开提供该方法的软件。该研究项目将通过为贝叶斯模型的两个部分贡献创新，从而使可行的大型空间数据集对大型空间数据集进行可行的默认贝叶斯分析。首先，将开发有关协方差模型参数的近似参考先验，以自动进行这些模型进行贝叶斯分析，而不需要主观启发。这些将基于固定随机场的光谱近似。其次，通过制定策略来调整最近提出的固定协方差函数近似值，可以详细阐述大型空间数据集可行的可能性近似值。近似的调整旨在达到准确性和计算工作之间的平衡。两种近似值都取决于模型的光谱密度，而不是协方差函数。共同的参考之前和可能性近似将使进行默认的贝叶斯分析，包括模型选择和评估。此外，该项目将批判性地评估以约定或传统选择的价值固定随机字段的平滑度的共同实践，该价值与所分析的数据无关。该项目将研究用于量化有关平滑度参数的空间数据中信息内容的方法，并发现这是如何取决于样本设计的。该方法将对地球科学的各种数据集进行测试，特别关注空间降雨数据。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响评估标准，认为值得通过评估来获得支持。