Variable Selection and Related Problems

拟议的研究将开发和评估多元回归和相关问题的变量选择程序。 贝叶斯和频率论的观点都将被考虑。 从贝叶斯的角度来看，重点将是随机搜索变量选择方法，使用分层混合模型来指导变量选择。 这些方法将包括一个快速贝叶斯变量选择的程序，以处理数百个变量一次，一个程序的广义线性模型中的变量选择，一个程序的变量选择在可交换回归，并同时进行变量选择和离群值删除的程序。 从频率论的角度来看，重点将放在一个新的标准，用于评估选择标准称为风险通货膨胀。 这项研究将需要应用和推广的风险膨胀的一系列广泛的模型选择问题，其中包括广义线性模型，时间序列模型的顺序选择程序，和变点选择估计的变点问题。 风险膨胀也将被用来衡量使用变量选择程序结合启发式搜索方法的偏差。 一类新的变量选择程序，使用自适应维数处罚也将被开发。 现代统计方法的主要目标之一是提供将输入变量与感兴趣的输出相关联的统计模型。 例如，这些模型被用来预测和解释农业中的年度作物产量，商业和经济学中的利率，医学中的癌症发病率以及社会学中的犯罪率。 建立这种模型的一个关键组成部分是选择包含强预测性和解释性信息的输入变量。 这一组成部分特别重要，因为最近包含大量潜在输入变量的大型数据库激增。 拟议的艾德的研究将提供强大的新方法，选择这样的输入变量，为各种各样的建模情况。

The proposed research will develop and evaluate variable selection procedures for multiple regression and related problems. Both the Bayesian and the frequentist points of view will be considered. From the Bayesian perspective, the focus will be on stochastic search variable selection methods which use a hierarchical mixture model to guide variable selection. These methods will include a procedure for fast Bayes variable selection to handle hundreds of variables at once, a procedure for variable selection in generalized linear models, a procedure for variable selection across exchangeable regressions, and a procedure for performing simultaneous variable selection and outlier removal. From the frequentist perspective, the focus will be on a new criterion for evaluating selection criteria called risk inflation. This research will entail the application and generalization of risk inflation to a broad set of model selection problems which includes generalized linear models, order selection procedures for time series models, and change-point selection for estimation in change-point problems. Risk inflation will also be used to gauge the bias of using variable selection procedures in conjunction with heuristic search methods. A new class of variable selection procedures which use adaptive dimensionality penalties will also be developed. One of the main goals of modern statistical methods is to provide statistical models which relate input variables to outputs of interest. For example, such models are used to predict and explain annual crop production in agriculture, interest rates in business and economics, cancer incidence in medicine, and crime rates in sociology. A key component in building such models is the selection of input variables which contain strong predictive and explanatory information. This component is especially important because of the recent proliferation of large databases containing vast numbers of potential input variables. The propos ed research will provide powerful new methods for selecting such input variables for a wide variety of model building situations.