Mathematical Sciences: Random Coefficient Models and Robust Analysis

摘要：随机系数模型在建立相关性模型、纳入实验室或研究效应、发展贝叶斯估计和推论等方面有着广泛的应用。边际分析是另一种方法，其中直接为边际分布（在随机效应上集成）开发模型，推断是在总体平均效应水平上，而不是在单个实验单位的水平上。这些一般建模策略和稳健统计之间的联系和对比将被开发。其目的是为解决应用统计学中的难题提供新的思路。要解决的问题包括：鲁棒广义线性建模和图形数据分析；环境暴露风险评估，结合来自不同方案和终点测量的多个研究的信息；由光谱测量仪器产生的随机函数数据的推论。随着功能强大的计算机的广泛使用，越来越复杂的数据正在被收集。在分析化学中，用电子方法测定分离光谱已成为常规。在环境毒理学方面，正在建立关于潜在危险污染物的大型数据库。拟议的研究旨在为这类数据发展统计方法。在结合来自多重暴露反应研究的信息时，可以使用现代计算技术和新的统计范式来模拟由于实验室间效应或物种差异等因素造成的不确定性。在环境化学中，被测物质的量和测量仪器本身的波动会导致测量结果的额外随机性。调整这种影响对方法的成功至关重要，特别是当测量的特征数量（例如，质谱上的峰）变得很大时。拟议的研究将开发用于分析、推理和诊断的工具包。这项工作的关键组成部分是算法开发、模拟研究、渐近分析、方法测试和软件开发。推动这项研究的主要应用是环境风险评估（综合信息）和环境监测（光谱测量），针对国家在环境管理方面的战略关切。？?

Proposal: DMS 95-05290 Principal investigator: Douglas G. Simpson Institution: University of Illinois Title: RANDOM COEFFICIENT MODELS AND ROBUST ANALYSIS Abstract: Random coefficient models have found wide application for modeling correlation, incorporating laboratory or study effects, and in developing Bayesian estimates and inferences. Marginal analysis is an alternative approach in which models are developed directly for marginal distributions (integrated over random effects), and the inferences are at the level of population average effects rather than at the level of individual experimental units. Connections and contrasts between these general modeling strategies and robust statistics will be developed. The aim is to develop fresh ideas for attacking hard problems in applied statistics. Among the problems to be attacked: robust generalized linear modeling and graphical data analysis; environmental exposure risk assessment combining information from multiple studies with varying protocols and endpoint measurements; inferences for random function data arising from spectral measurement instruments. With the wide availability of powerful computers, increasingly complex data are being collected. In analytical chemistry it is now routine to qtore separation spectra electronically. In environmental toxicology large databases are being assembled on potentially hazardous pollutants. The proposed research is directed at the development of statistical methods for such data. In combining information from multiple exposure--response studies, it is possible to model uncertainty due to things such as interlaboratory effects or species differences using modern computational techniques and new statistical paradigms. In environmental chemistry, fluctuations in the amount of material assayed and in the measuring instrument itself lead to extra randomness in the measurement. Adjusting for this effect is critical to the success of the metho ds, particularly as the number of features measured, e.g., peaks on a mass spectrum, becomes large. The proposed research will develop toolkits for analysis, inference and diagnostics. Key components of the work are algorithm development, simulation studies, asymptotic analysis, testing of the methodology, and software development. The major applications driving this research are in environmental risk assessment (combining information) and environmental monitoring (spectral measurements), targeting strategic national concerns in environmental management. ??