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

-----------------------------------------------------------------------提案编号：DMS Pi：Merlise A.Clyde Institution：杜克大学项目：模式不确定性、模型选择和稳健性，及其在环境科学中的应用摘要：寻找描述数据和变量之间关系的模型是统计学和科学中的一个基本问题。线性回归及其推广是数据分析中最常用的一些统计方法。随着科学家收集越来越大的数据集，对使用所有测量的协变量对数据进行过度拟合的恐惧导致了标准方法，即根据协变量的子集选择一个“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括哪些变量的不确定性，这可能会导致过度自信的推断。模型的不确定性往往远远超过问题中的其他不确定性来源，但在标准的统计实践和教学中通常被忽视。本研究侧重于将模型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，预测和推断基于一组模型，而不是单个模型；每个模型按比例贡献它从观测数据中获得的支持。研究了识别用于贝叶斯模型平均的有前景的模型的新方法。这些都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。这项研究的主要应用之一是评估颗粒物对老年人口死亡率的影响，并评估环境保护局新的国家环境空气质量颗粒物标准的潜在影响。这个和其他案例研究将被用来为杜克大学的环境和生物科学专业的学生开发一门现代贝叶斯统计方法的新课程。

----------------------------------------------------------------------- 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.