Mathematical Sciences: Random Coefficient Models and Robust Analysis

提案：DMS 95-05290主要研究者：道格拉斯G.辛普森机构：伊利诺伊大学题目：随机系数模型和稳健分析 摘要： 随机系数模型已广泛应用于 建模相关性，结合实验室或研究 影响，并在发展贝叶斯估计和推断。 边际分析是一种替代方法， 是直接为边缘分布开发的（在随机效应上集成），并且推断是在总体平均效应水平上，而不是在 个别实验单位。这些通用建模策略和鲁棒性建模策略之间的联系和对比 将进行统计。目的是开发新鲜的 解决应用统计学难题的思路。 在要攻击的问题中：鲁棒广义线性 建模和图形数据分析;环境暴露 结合多项研究信息的风险评估 具有不同的协议和端点测量;推断 对于由光谱测量产生的随机函数数据 仪器. 随着功能强大的计算机的广泛使用， 正在收集越来越复杂的数据。在 分析化学现在， 电子分离光谱。在环境 毒理学大型数据库正在组装 潜在的有害污染物。拟议研究 旨在发展统计方法 对于这样的数据。在结合来自多个 暴露-反应研究，有可能建立模型 由于实验室间效应等因素造成的不确定性 或物种差异， 技术和新的统计范式。在 由于环境化学因素的影响，所分析的材料量和测量仪器本身的波动导致测量中的额外随机性。调整 因为这种效果对于该方法的成功是至关重要的， 特别是当测量的特征的数量，例如，峰 在质谱图上，变得很大。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， 仿真研究，渐近分析，测试的 方法论和软件开发。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），针对战略国家 关注环境管理。 ??

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. ??