Statistical Distances, Estimating Functions, and Mixture Models

首席研究员和他的同事研究统计学的三个主要领域的重要课题。关于统计距离的工作是第一个领域，重点是在建立统计模型时发展对距离作为损失度量的理解。发展这一理论的重要考虑因素包括统计敏感性和解释稳健性之间的权衡。研究结果在模型构建中具有广泛的意义。对估计方程的研究，区域二，目标是将矩方法学的广义方法发展到比当前知识允许的更广泛的统计背景中。该领域的第二个主题涉及固定效应和随机效应建模的协调。最后一个领域是混合模型，生物信息学中的一些重要应用导致了对改进的混合模型工具的需求。本研究工作的重点是理论问题和应用问题。统计一直在很大程度上依赖于建立适当的统计模型。计算能力的使用使统计学家能够用越来越复杂的模型处理越来越大的数据集。在这个过程中，越来越需要了解一个简化但限制性的模型在多大程度上可能是对现实的很好的描述，而不是严格正确的；这是研究统计距离的基础。虽然本质上是理论性的，但这对整个统计学都有影响，并可能导致更有意义的模型使用。第二项调查集中在一类统计方法上，这些方法允许人们减少模型构建假设的限制性；目标是扩大这些方法的适用范围。在社会科学和医学领域有许多潜在的应用。调查的最后一个主题源于对生物学领域，特别是基因组研究领域统计工具的需求增加；首席研究员正在将他的建模领域的专业知识应用到三个不同的应用中。在每个应用中使用的统计模型，即混合模型，作为测量生物过程异质性的工具，具有直接的科学意义。

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.