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.

该项目开发了在许多社会和地球科学（例如经济，流行病学，地理学，地质学和水文学）等许多社会和地球科学中出现的对空间数据的目标贝叶斯分析的方法论，以及计算上有效的算法，以基于中度至大量的散布数据集，以执行贝叶斯分析和预测。在方法论方面，研究者为不同类型的高斯随机场的参数提供了新的自动先验分布，该分布由其协方差矩阵或其精度矩阵指定。该研究探讨了基于这些自动先验的贝叶斯推论的主要统计特性，例如后置术的条件，参数的频繁属性和预测性的推断以及预测性摘要的存在，一个特定的兴趣点是对这些自动偏向分布的依赖性的研究的研究。由于对这些先验的评估在计算上是昂贵的，并且为贝叶斯推论和预测空间数据开发了新的计算有效算法，这些算法将根据中等到大空间数据集进行可行的贝叶斯分析。该项目中提出的中等至大的方法学是针对这些项目的初始模型，用于这些模型的最初范围，以描述这些模型，以描述spatial spatial spatial hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark hierark a inst a specy的初始步骤。高斯随机领域作为基础。在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，例如经济，流行病学，地理学，地质和水文学，空间数据的收集和分析已成为常见任务。在统计数据中，拜访和方法对传统方法进行了与传统方法进行比较时的统计范围，但要对传统的分析进行了比较。在实施过程中，这尤其是为了分析某些类型的大型空间数据集的分析，在这种分析中，贝叶斯方法的当前实施太笨拙或不可行，无法进行。将参与该项目，为他们的统计培训以及阿肯色大学的统计计划的增强做出了贡献。