Statistical Distances, Estimating Functions, and Mixture Models

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The principal investigator and his colleagues study important topics in three major areas of statistics. The work on statistical distances, the first area, is focused on developing understanding of distances as measures of loss when one is building a statistical model. Important considerations in developing this theory include the tradeoff between statistical sensitivity and robustness of interpretation. The results have wide implications in model building. The research on estimating equations, area two, targets the development of the generalized method of moment methodology into wider statistical contexts than current knowledge allows. A second topic in this area concerns the reconciliation of fixed and random effects modeling. The final area is mixture models, where a number of important applications in bioinformatics are leading to demands for improved mixture model tools.This research work focuses on both theoretical and applied problems. Statistics has always relied heavily on the building of appropriate statistical models. The use of computational power has allowed statisticians to handle larger and larger data sets with increasingly sophisticated models. In the process, there is increased need for understanding the extent to which a simplified but restrictive model might be a very good description of reality without being strictly correct; this is the basis for the investigation of statistical distances. Although theoretical in nature, this has implications throughout statistics and could lead to a more meaningful use of models. A second investigation is focused on a class of statistical methods that allow one to reduce the restrictiveness of model building assumptions; the goal is to expand the range of applicability of these methods. There are many potential applications in social sciences and medicine. The final subject of investigation springs from an increased demand for statistical tools in the area of biology, especially in genomic research; the principal investigator is applying expertise in his modeling area to three different applications. In each application the statistical model used, the mixture model, has direct scientific meaning as a tool for measuring the heterogeneity in biological processes.