Mathematical Sciences: Model-based Statistical Inference and Data Analysis

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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.