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

该项目支持的研究福尔斯在三个方面 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稳健贝叶斯分析 分析（特别是对先验和损失的敏感性）， 贝叶斯设计，多层贝叶斯估计和选择， 低维假设检验和稳健检验， 密度估计、无信息和参考先验 发展“自动”贝叶斯方法，并消除 的参数。 在统计决策理论中， 该研究涉及多变量估计（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。 的 计算问题包括蒙特卡罗积分， 贝叶斯计算和随机变量的生成。

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.