Model Uncertainty, Model Selection, and Robustness with Applications in Environmental Sciences

-- 主要研究者：Merlise A.克莱德机构：杜克大学项目：模式不确定性，模型选择和鲁棒性， 在环境科学中的应用 摘要： 寻找模型来描述数据和变量之间的关系是统计学和科学中的一个基本问题。线性 回归及其推广是一些最常用的 数据分析的统计方法。 当科学家们收集 越来越大的数据集，过度拟合数据的恐惧， 使用所有测量的协变量导致标准方法，即根据协变量的子集选择单个“最佳”模型，然后继续进行科学推断和预测，就好像这是真正的模型一样。 这种典型的分析忽略了模型中应包含哪些变量的不确定性，可能导致过度自信的推断。 模型的不确定性往往大大超过其他来源的不确定性的问题，但通常被忽视的标准统计实践和教学。 本研究的重点是将模型的不确定性纳入数据分析和决策的贝叶斯方法。 在贝叶斯模型平均中，预测和推断是基于一组模型而不是单个模型;每个模型都按比例从观察数据中获得支持。 研究了贝叶斯模型平均中有前途模型的识别方法。 这些可以增加贝叶斯方法对涉及大量变量的现实问题的适用性。 该研究的主要应用之一是估计颗粒物对老年人死亡率的影响，并评估EPA新的国家环境空气质量标准对颗粒物的潜在影响。 这个和其他案例研究将用于开发一个新的课程，在现代贝叶斯统计方法的环境和生物科学的学生在杜克大学。

----------------------------------------------------------------------- Proposal Number: DMS PI: Merlise A. Clyde Institution: Duke University Project: Mode Uncertainty, Model Selection, and Robustness, with Applications in Environmental Sciences Abstract: Finding models to describe data and relationships among variables is a fundamental problem in statistics and science. Linear regression and its generalizations are some of the most commonly used statistical methods for data analysis. As scientists collect increasingly larger data sets, the fear of over-fitting the data by using all measured covariates leads to the standard approach of selecting a single ``best'' model based on a subset of the covariates, and then proceeding with scientific inferences and predictions as if that were the true model. This typical analysis ignores the uncertainty about which variables should be included in the model, potentially leading to overconfident inferences. Model uncertainty often significantly outweighs other sources of uncertainty in problems, but is generally ignored in standard statistical practice and teaching. This research focuses on Bayesian methods for incorporating model uncertainty into data analysis and decision making. In Bayesian model averaging, predictions and inferences are based on a set of models rather than a single model; each model contributes proportionally to the support it receives from the observed data. Novel methods of identifying promising models for use in Bayesian model averaging are studied. These can increase the applicability of Bayesian methods to realistic problems that involve a large number of variables. One of the major applications of the research is to estimate the effect of particulate matter on mortality in the elderly population and assess the potential impact of the EPA's new National Ambient Air Quality Standards for particulates. This and other case studies will be used to develop a new course in modern Baye sian statistical methods for environmental and biological science students at Duke University.