Mathematical Sciences: Model-based Statistical Inference and Data Analysis

建议DMS95-05043主要研究人员：斯蒂格勒，肖李蒙研究所：芝加哥大学标题：基于模型的统计推理和数据分析摘要研究人员研究涉及复杂数据集分析的潜在结构的统计模型的构建和调查。斯蒂格勒的研究涉及通信网络的模型，其中可用的数据以定向交易的频率计数的形式存在。所研究的模型不同于配对比较的标准线性模型，因为它们不是可传递的--它们表现出循环--它们包含了与标准多项式模型的背离，用于计数的分散。孟的研究涉及贝叶斯过程的频率性质，并与他对多重归因法的研究有关，多重归因法是一种通用而有效的推理工具，用于处理抽样调查中复杂的无回答问题，特别是那些产生公共使用的数据文件的抽样调查，这些文件将被许多用户分析。孟晚舟将寻求建立贝叶斯过程在多重归罪推理中的稳健频率性质，特别是在不相称的多重归罪推断、后验预测p值的频率评估、无偏归结和单一观察无偏先验下的置信度有效性。本研究分为两个部分。第一部分研究科学交流的性质，试图建立统计模型，以更好地理解理论研究和应用研究之间的关系(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一定形成一个层次结构，或者它们是否表现出更复杂的思想“交易”模式。)另一个部分涉及构建统计模型，用于分析无回答问题时的调查结果。当潜在受访者出于与他们将给出的答案相关的原因而拒绝参与时，所有调查都可能容易受到偏差的影响，所研究的方法将改善美国人口普查等复杂调查的这一问题，在美国人口普查中，最好准备公共使用的数据文件来解决这一问题，并且对所作的统计假设不太敏感。

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.