We propose a new highly flexible and tractable Bayesian approach to undertake variable selection in non-Gaussian regression models. It uses a copula decomposition for the joint distribution of observations on the dependent variable. This allows the marginal distribution of the dependent variable to be calibrated accurately using a nonparametric or other estimator. The family of copulas employed are “implicit copulas” that are constructed from existing hierarchical Bayesian models widely used for variable selection, and we establish some of their properties. Even though the copulas are high dimensional, they can be estimated efficiently and quickly using Markov chain Monte Carlo. A simulation study shows that when the responses are non-Gaussian, the approach selects variables more accurately than contemporary benchmarks. A real data example in the Web Appendix illustrates that accounting for even mild deviations from normality can lead to a substantial increase in accuracy. To illustrate the full potential of our approach, we extend it to spatial variable selection for fMRI. Using real data, we show our method allows for voxel-specific marginal calibration of the magnetic resonance signal at over 6000 voxels, leading to an increase in the quality of the activation maps.

中文翻译：

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非高斯响应的贝叶斯变量选择：边缘校准的 copula 方法

我们提出了一种新的高度灵活且易于处理的贝叶斯方法来在非高斯回归模型中进行变量选择。它对因变量上的观测值的联合分布使用 copula 分解。这允许使用非参数或其他估计器准确校准因变量的边际分布。所使用的 copula 家族是“隐式 copula”，它们是从广泛用于变量选择的现有分层贝叶斯模型构建的，我们建立了它们的一些属性。尽管 copula 是高维的，但可以使用马尔可夫链蒙特卡罗来高效快速地估计它们。模拟研究表明，当响应为非高斯响应时，该方法比当代基准更准确地选择变量。Web 附录中的一个真实数据示例说明，即使考虑到与正态性的轻微偏差，也可以显着提高准确性。为了说明我们方法的全部潜力，我们将其扩展到 fMRI 的空间变量选择。使用真实数据，我们展示了我们的方法允许对超过 6000 个体素的磁共振信号进行体素特定的边缘校准，从而提高激活图的质量。