Mathematical Sciences: Model-based Statistical Inference and Data Analysis

主要研究人员：Stephen M. Stigler， xiaoli b孟机构：芝加哥大学题目：基于模型的统计推断和数据分析摘要研究人员的研究主题是关于复杂数据集分析中涉及潜在结构的统计模型的构建和研究。Stigler的研究涉及通信网络的模型，其中可用的数据是以定向交易的频率计数的形式出现的。所研究的模型与成对比较的标准线性模型不同，因为它们不是传递的-它们表现出循环-并且它们与计数分散的标准多项模型相背离。b孟的研究涉及贝叶斯过程的频率特性，并与他对多重归算方法的研究有关，多重归算方法是一种通用而有效的推理工具，用于处理样本调查中无响应的复杂问题，特别是那些产生将被许多用户分析的公共数据文件的问题。孟将寻求建立贝叶斯过程在多重归因推理中的鲁棒频率性，具体涉及不一致多重归因推理下的置信度效度、后验预测p值的频率评估、无偏归因和单观测无偏先验。本研究分为两部分。一部分研究科学交流的本质，试图建立统计模型，以便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必然形成一个层次结构，或者它们是否表现出更复杂的思想“交易”模式）。另一部分涉及到在无应答情况下对调查结果进行分析的统计模型的构建。当潜在的调查对象因为与他们给出的答案相关的原因而拒绝参与时，所有的调查都可能容易产生偏见，研究的方法将改善复杂调查（如美国人口普查）的这个问题，在这些调查中，最好准备公共使用的数据文件来解决这个问题，并且对所做的统计假设不过于敏感。

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.