Mathematical Sciences: Model-based Statistical Inference and Data Analysis

数学科学：基于模型的统计推断和数据分析

• 批准号: 9505043
• 负责人: Stephen Stigler
• 金额: $ 6万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505043&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Model; based; Statistical

Proposal DMS 95-05043 Principal Investigators: Stephen M. Stigler, Xiao-Li Meng Institution: University of Chicago Title: Model-based Statistical Inference and Data Analysis Abstract The investigators study topics that concern the construction and investigation of statistical models involving latent structure for the analysis of complex data sets. Stigler's research involves models for communications networks where the available data is in the form of frequency counts of directed transactions. The models studied depart from standard linear models for paired comparisons in that they are not transitive - they exhibit cycles - and they incorporate departures from standard multinomial models for the dispersion of counts. Meng's research involves frequentist properties of Bayesian procedures, and is related to his research on multiple imputation methodology, a general and efficient inferential tool for handling the complex problem of nonresponse in sample surveys, especially those that produce public-use data files which will be analyzed by many users. Meng will seek to establish robust frequentist properties of Bayesian procedures in multiple imputation inference, with specific reference to confidence validity under uncongenial multiple imputation inferences, frequency evaluations of posterior predictive p-values, and unbiased imputations and single observation unbiased priors. The research is of two parts. One part studies the nature of scientific communication, seeking to build statistical models to understand better the relationship between theoretical research and applied research (in particular the degrees to which they influence each other), and the relationships between different fields of science (for example, do different but related disciplines necessarily form a hierarchy, or do they exhibit more complicated patterns of "trade" in ideas.) The other part involves the construction of statistical models for analyzing survey results when nonresponse is a problem. All surveys may be susceptible to bias when potential respondents decline to participate for reasons related to the answer they would have given, and the methods studied will ameliorate this problem for complex surveys such as the U. S. Census, where it is desirable to prepare public-use data files that address this problem and are not overly sensitive to the statistical assumptions made.

提案DMS 95-05043主要研究者：Stephen M.施蒂格勒， 孟晓丽研究机构：芝加哥大学研究方向：基于模型的统计推断与数据分析 摘要 调查人员研究与建筑有关的主题， 包含潜在结构的统计模型研究 用于分析复杂的数据集。 斯蒂格勒的研究涉及到 通信网络的模型，其中可用数据在 定向事务的频率计数形式。 研究的模型 与配对比较的标准线性模型不同， 它们不是传递性的--它们表现出循环--并且它们包含 偏离标准多项式模型的分散 道理 孟的研究涉及贝叶斯的频率论性质 程序，并与他对多重插补的研究有关 方法论，一个通用的和有效的推理工具，处理 抽样调查中的无答复这一复杂问题，特别是 那些产生公共使用的数据文件，这些文件将被许多 用户. 孟将寻求建立鲁棒的频率属性， 多重插补推断中的贝叶斯程序， 不一致多重插补下的参考信度效度 推断，后验预测p值的频率评估， 无偏估算和单观察无偏先验。 本研究分为两部分。 第一部分研究科学的本质 沟通，寻求建立统计模型，以更好地了解 理论研究与应用研究的关系 (in（特别是它们相互影响的程度），以及 不同科学领域之间的关系（例如， 不同但相关的学科是否必然形成一个等级制度， 还是他们展示了更复杂的思想“交易”模式。） 另一部分涉及统计模型的构建， 分析调查结果时，无响应是一个问题。 所有调查 当潜在的受访者拒绝 参与的原因与他们会给出的答案有关， 所研究的方法将改善复杂调查的这一问题 例如美国，S.人口普查，在需要准备公共用途的情况下 解决此问题的数据文件，并且对 统计假设。