Mathematical Sciences: Statistical Inference for General Models

数学科学：一般模型的统计推断

• 批准号: 8902667
• 负责人: Stephen Stigler
• 金额: $ 37.29万
• 依托单位: University of Chicago
• 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 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902667&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Inference; General

This work consists of research in mathematical statistics. The problems involve inference for spatial processes including the properties of predictors based on estimated covariance functions and prediction problems for non-Gaussian spatial processes. The relationship between prediction and estimation for general stochastic processes will be studied. Researchers will examine the ways a regression interpretation of James-Stein shrinkage estimators permits a unified treatment of a broad class of problems in cluster analysis from a decision theoretic perspective. Previous historical investigations will be extended to cover main themes in the first half of this century. The asymptotic theory of estimation will be studied with particular attention to the behavior of maximum likelihood estimators on infinite dimensional parameter spaces. The application of algorithms for the computation of posterior distributions to problems of image reconstruction will be examined with particular attention to images generated by positron emission tomography. The computation of probability distributions over graphical structures will be investigated with applications to genetics.

这项工作包括数理统计研究。 这些问题涉及空间过程的推理，包括 基于估计协方差的预测量的性质 函数和预测问题的非高斯空间 流程. 预测与估计的关系 一般随机过程将被研究。 研究人员 我将研究如何回归解释詹姆斯-斯坦 收缩估计允许一个广泛的类的统一处理 从决策论角度分析聚类分析中的问题 perspective. 此前的历史调查将延长 涵盖本世纪上半叶的主要主题。 的 估计的渐近理论将特别研究 注意最大似然估计量的行为 无限维参数空间 的应用 后验分布的计算算法， 图像重建的问题将被检查， 特别注意正电子发射产生的图像 断层扫描 概率分布的计算 图形结构将与应用程序进行研究， 遗传学