High Dimensional Model Averaging and Model Selection

摘要：Merlise A Clyde提议：0406115研究人员提出了变量和模型选择问题的新进展，这是统计学中最基本和最普遍的问题之一。 贝叶斯方法是吸引人的这个问题，由于自然的概率框架，解决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，其中大量数据集提供了许多潜在的预测因子。 PI和co-PI研究了贝叶斯模型选择和模型平均的两个主要挑战：先验规范和后验计算。 他们调查新的家庭自动客观先验，具有理想的风险属性，适应未知程度的稀疏性，也允许易于处理的计算大规模模型搜索。 为了实现新的方法，他们开发了有效的软件，用于随机搜索和高维模型空间的模型平均。 在工业和生物问题中的应用将使用新的方法来开发。发现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中的一个基本问题。 贝叶斯方法已被证明是非常成功的这个问题，然而，贝叶斯方法的实施变得具有挑战性的应用中，可能的模型的数量是天文数字。 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所驱动的。 研究人员提出的选择和组合模型的自动程序适用于许多其他重要的应用领域，其中变量选择是利用。

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.