Mathematical Sciences: Investigations in Bayesian Analysis, Statistical Decision Theory and Computation

数学科学：贝叶斯分析、统计决策理论和计算研究

• 批准号: 8923071
• 负责人: James Berger
• 金额: $ 53.67万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8923071&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Investigations; Bayesian; Analysis

The research supported on this project falls within three related areas of statistics: Bayesian analysis, statistical decision theory, and computation. The research in Bayesian analysis includes robust Bayesian analysis (in particular, sensitivity to the prior and the loss), Bayesian design, hierarchical Bayesian estimation and selection, testing of lower dimensional hypotheses and robust testing, density estimation, noninformative and reference prior development for "automatic" Bayesian methodology, and elimination of nuisance parameters. Within the statistical decision theory, the research involves multivariate estimation (with emphasis on covariance matrix and discriminant function estimation), empirical Bayes and robust Bayes selection procedures, and sequential and multi-stage selection procedures. The computational problems include Monte Carlo integration for Bayesian calculation and generation of random variables.

该项目支持的研究属于统计学的三个相关领域：贝叶斯分析、统计决策理论和计算。 贝叶斯分析的研究包括鲁棒贝叶斯分析（特别是对先验和损失的敏感性）、贝叶斯设计、分层贝叶斯估计和选择、低维假设检验和鲁棒测试、密度估计、“自动”贝叶斯方法的非信息和参考先验开发，以及消除干扰参数。 在统计决策理论中，研究涉及多元估计（重点是协方差矩阵和判别函数估计）、经验贝叶斯和稳健贝叶斯选择程序以及顺序和多阶段选择程序。 计算问题包括贝叶斯计算的蒙特卡罗积分和随机变量的生成。