Bayesian Analysis and Prediction of Gaussian Random Fields

高斯随机场的贝叶斯分析和预测

• 批准号: 0719508
• 负责人: Victor De Oliveira
• 金额: $ 7.34万
• 依托单位: University of Texas at San Antonio
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0719508&HistoricalAwards=false
• 关键词: Bayesian; Analysis; Prediction; Gaussian; Random

This project develops methodology for objective Bayesian analysis of spatial data, both geostatistical and lattice data, that arise in many of the social and earth sciences, such as economy, epidemiology, geography, geology and hydrology, as well as computationally efficient algorithms to perform Bayesian analysis and prediction based on moderate to large spatial datasets. On the methodological side, the investigator derives new automatic prior distributions for the parameters of different kinds of Gaussian random fields, specified either by their covariance matrices or by their precision matrices. The research explores the main statistical properties of Bayesian inferences based on these automatic priors, such as conditions for posterior propriety, frequentist properties of parameter andpredictive inferences, and existence of predictive summaries.A point of particular interest is the study of the pros and cons of the dependence of these automatic priors on the sampling design.On the computational side, the investigator derives methods to approximate these automatic priors distributions, since evaluation of these priors is in most cases computationally expensive, and develops new computationally efficient algorithms for Bayesian inference and prediction of spatial data that would make feasible Bayesian analysis based on moderate to large spatial datasets.The methodology proposed in this project serves as an initial step toward the development of objective Bayesian analysis for spatial hierarchical models used to describe non-Gaussian data, since most of these models use Gaussian random fields as building blocks.The statistical methodology developed during this project has practicalimpacts in many social and earth sciences, such as economy, epidemiology, geography, geology and hydrology, where the collection and analysis of spatial data have become common tasks.A paradigm of statistics called the Bayesian approach possesses several conceptual and methodological advantages when compared to traditional approaches for the analysis of spatial data, but technical and computational difficulties that arise during implementation have hindered its more widespread use among practitioners.This is particularly so for the analysis of some types large spatial datasets where current implementations of the Bayesian approach are too cumbersome or unfeasible to be carried out.The statistical methodology developed in this project would contribute to overcome some of these technical and computational hurdles, andconsequently to bridge the gap between methodology and practice for Bayesian analysis of spatial data.Graduate students would be engaged in the project, contributing to their statistical training as well as the enhancement of the Statistics program at the University of Arkansas.

该项目开发了对空间数据进行客观贝叶斯分析的方法，包括地质统计学和格点数据，这些数据出现在许多社会和地球科学中，如经济，流行病学，地理，地质学和水文学，以及计算效率高的算法，以基于中等到大型空间数据集进行贝叶斯分析和预测。在方法方面，研究人员推导出不同类型高斯随机场参数的新的自动先验分布，由其协方差矩阵或精度矩阵指定。研究了基于这些自动先验的贝叶斯推理的主要统计性质，如后验适当性的条件、参数和预测推理的频率论性质以及预测总结的存在性。特别感兴趣的一点是研究这些自动先验对抽样设计的依赖性的利弊。在计算方面，研究者推导出近似这些自动先验分布的方法，因为这些先验的评估在大多数情况下在计算上是昂贵的，并为贝叶斯推理和空间数据预测开发了新的计算效率高的算法，这些算法将使基于中到大空间数据的贝叶斯分析变得可行。数据集。该项目中提出的方法是为用于描述非高斯数据的空间分层模型开发客观贝叶斯分析的第一步，因为大多数这些模型使用高斯随机场作为构建块。该项目中开发的统计方法在许多社会和地球科学中具有实际影响，如经济，流行病学，地理，地质学和水文学，其中空间数据的收集和分析已成为常见的任务。与传统的空间数据分析方法相比，称为贝叶斯方法的统计学范式具有几个概念和方法上的优势，但在实施过程中出现的技术和计算困难阻碍了其在从业人员中的更广泛使用。因此，对于某些类型的大型空间数据集的分析，目前的贝叶斯方法的实现过于繁琐或不可行。在这个项目中开发的统计方法将有助于克服这些技术和计算障碍，从而弥合空间数据贝叶斯分析方法和实践之间的差距。研究生将参与这个项目，有助于他们的统计培训，以及在阿肯色州的统计程序的增强。