Data for: S-values and Bayesian weighted all-subsets regressions

Abstract of associated article: This paper compares and contrasts Bayesian variable-exclusion methods proposed by Eduardo Ley and coauthors with methods proposed by Raftery and Sala-i-Martin et al. and with the s-values proposed by myself. A distinction is drawn between estimation uncertainty which is the focus of Ley׳s research and model ambiguity which arises in Ley׳s work and is the focus of my own recent proposal. The discussion is organized around the prior covariance matrix, which needs to be diagonal to support all-subsets regressions. The basic question addressed here is: what aspects of the prior covariance matrix can be taken as known, what aspects can be estimated and what aspects require a sensitivity analysis because they are neither known nor estimable. When diagonality is in doubt, we are more-or-less forced into a model ambiguity sensitivity mode because the data are never rich enough credibly to estimate the full prior covariance matrix. When diagonality is assumed, the data evidence, though very limited, can help to estimate the diagonal elements, but this literature has not yet produced a compelling conventional treatment which will necessarily include both estimation uncertainty and model ambiguity as they relate both to the diagonal values and to the rest of the prior covariance matrix. But there has been a lot of progress.

关联论文摘要：本文对比了爱德华多·莱伊（Eduardo Ley）及其合作者提出的贝叶斯变量排除法（Bayesian variable-exclusion methods），与拉夫蒂（Raftery）、萨拉-伊-马丁（Sala-i-Martin）等人提出的方法，以及笔者提出的s值（s-values）。本文厘清了莱伊研究的核心——估计不确定性（estimation uncertainty），与莱伊研究中出现且为笔者近期研究方案所聚焦的模型歧义（model ambiguity）之间的区别。讨论围绕先验协方差矩阵（prior covariance matrix）展开，该矩阵需满足对角化条件以支持全子集回归（all-subsets regressions）。本文旨在解答的核心问题为：先验协方差矩阵的哪些部分可视为已知，哪些可通过估计得到，又有哪些因既无法直接获知也无法估计，故而需要开展敏感性分析（sensitivity analysis）。当对角化假设存疑时，我们几乎不得不转向模型歧义敏感性分析框架，因为现有数据的信息量始终不足以可靠估计完整的先验协方差矩阵。若假设矩阵满足对角化条件，尽管数据证据仍较为有限，但可用于估计对角元素；不过现有相关研究尚未形成一套兼具说服力的标准处理框架，该框架需同时涵盖与对角元素及先验协方差矩阵其余部分相关的估计不确定性与模型歧义。不过目前该领域已取得诸多进展。