Spike and slab variable selection: Frequentist and Bayesian strategies
Spike and slab variable selection: Frequentist and Bayesian strategies
复制标题
DOI：
10.1214/009053604000001147
复制
发表时间：
2005-04-01
影响因子：
4.5
通讯作者：
Rao, JS
中科院分区：
文献类型：
--
作者：
Ishwaran, H;Rao, JS
从频数和贝叶斯的角度来看，线性回归模型中的变量选择有许多明显的特点。在本文中，我们介绍了一种变量选择方法，称为重新缩放的钉子和板条模型。我们研究了先验分层规范的重要性，并将其与频率广义岭回归估计联系起来。具体地说，我们研究了连续双峰先验对超方差参数建模的有用性，以及标度通过其与惩罚的关系对后验均值的影响。提出了几种模型选择策略，并从理论上对其进行了研究，其中包括一些频度策略和一些贝叶斯策略。我们从风险误分类的角度论证了选择性收缩对于有效变量选择的重要性，并证明了这是使用重新缩放的尖峰和板条模型的后验来实现的。我们还展示了如何使用专门的向前选择策略来验证程序在有限样本中减少模型不确定性的能力。使用该工具，我们展示了重新缩放的尖峰和板条模型在降低模型不确定性方面的有效性。
Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the effect scaling has on the posterior mean through its relationship to penalization. Several model selection strategies, some frequentist and some Bayesian in nature, are developed and studied theoretically. We demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification, and show this is achieved using the posterior from a rescaled spike and slab model. We also show how to verify a procedure's ability to reduce model uncertainty in finite samples using a specialized forward selection strategy. Using this tool, we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty.