Mathematical Sciences: Foundations and Applications of Bayesian Inference and Decision Theory

数学科学：贝叶斯推理和决策理论的基础和应用

• 批准号: 8901234
• 负责人: Bruce Hill
• 金额: $ 16.18万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901234&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Foundations; Applications; Bayesian

The proposal examines four topics in Bayesian nonparametric statistics. They center about a procedure described as A subscript n which assumes that there are (n+1) observed values of (n+1) random quantities. The observable random quantities are assumed to be exchangeable and ties among them are assumed to have probability zero. Given n of the observations the probability that the (n+1)st observation falls in one of the open intervals created by the ranked given observations is assumed to be the inverse of the number of intervals. (There are (n+1) intervals.) The first topic involves the development of a version of this procedure for multivariate observations. The second topic involves extending the use of the procedure to the evaluation of the posterior expectation of future observations. The fourth topic involves extending results for the procedure to the analysis of mixture data in the context of Bayesian data analysis. The third topic is the development of a theory of randomization from a Bayesian viewpoint.

该提案考察了贝叶斯非参数统计中的四个主题。它们围绕着一个被描述为A下标n的过程，该过程假设有(n+1)个随机量的(n+1)个观测值。假设可观测的随机变量是可交换的，并且假设它们之间的联系的概率为零。给定n个观测值，假设第(n+1)个观测值落入由已排名的给定观测值创建的开放区间之一的概率与区间数成反比。(有(n+1)个间隔。)第一个主题涉及为多变量观测开发该程序的一个版本。第二个主题涉及将该程序的使用扩展到对未来观测的后验期望的评估。第四个主题涉及将程序的结果扩展到贝叶斯数据分析中的混合数据分析。第三个主题是从贝叶斯观点发展随机化理论。