High Dimensional Model Averaging and Model Selection

摘要：研究人员对统计学中最基本和最广泛的问题之一——变量和模型选择问题提出了新的进展。贝叶斯方法对这个问题很有吸引力，因为它的自然概率框架同时解决了模型和参数的不确定性。然而，随着模型或变量数量的增加，贝叶斯方法的实现变得具有挑战性，这是一个非常常见的问题，大量数据集提供了许多潜在的预测器。PI和co-PI研究了贝叶斯模型选择和模型平均实现中的两个主要挑战：先验规范和后验计算。他们研究了新的自动客观先验族，这些先验族具有理想的风险特性，适应未知的稀疏度，并且还允许大规模模型搜索的易于处理的计算。为了实现新的方法，他们开发了高效的软件，用于高维模型空间的随机搜索和模型平均。在工业和生物问题上的应用将采用新的方法。寻找和使用模型来描述大量数据集中变量之间的关系是统计学和科学的一个基本问题。贝叶斯方法已经被证明在这个问题上是非常成功的，然而，在可能的模型数量是天文数字的应用中，贝叶斯方法的实现变得具有挑战性。PI和co-PI在统计计算和建模方面开发创新的新方法和软件，用于选择和组合模型。这些方法的发展是由工业和生物问题的应用驱动的。研究者提出的自动选择和组合模型的程序也适用于使用变量选择的许多其他重要应用领域。

ABSTRACTPI: Merlise A ClydePROPOSAL: 0406115The investigators propose new advancements for the problem of variable and model selection, one of the most fundamental and widespread problems in statistics. Bayesian methods are appealing for this problem, due to the natural probabilistic framework which addresses both model and parameter uncertainty. The implementation of Bayesian methods, however, becomes challenging as the number of models or variables grows, an all too common problem where massive data sets provide many potential predictors. The PI and co-PI investigate two major challenges in the implementation of Bayesian model selection and model averaging: prior specification and posterior calculation. They investigate new families of automatic objective priors that have desirable risk properties, adapt to unknown degree of sparsity and also permit tractable computation for large scale model search. To implement the new methodology, they develop efficient software for stochastic search and model averaging for high dimensional model spaces. Applications in industrial and biological problems will be developed using the new methodology.Finding and using models to describe relationships between variables in massive datasets is a fundamental problem in both statistics and the sciences. Bayesian methods have been shown to be very successful for this problem, however, the implementation of Bayesian methods becomes challenging in applications where the number of possible models is astronomical. The PI and co-PI develop innovative new methods and software in statistical computing and modeling for selecting and combining models. These methodological developments are driven by applications in industrial and biological problems. The automatic procedures proposed by the investigators for selecting and combining models have applicability to many other important application areas where variable selection is utilized.