Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) vector with a few non-zero components, those covariates that are most important. This article extends the global-local shrinkage idea to a scenario where one wishes to model multiple response variables simultaneously. Here, we have developed a variable selection method for a K-outcome model (multivariate regression) that identifies the most important covariates across all outcomes. The prior for all regression coefficients is a mean zero normal with coefficient-specific variance term that consists of a predictor-specific factor (shared local shrinkage parameter) and a model-specific factor (global shrinkage term) that differs in each model. The performance of our modeling approach is evaluated through simulation studies and a data example.

中文翻译：

---

通过共享收缩为多结果模型选择贝叶斯变量

在线性模型中对潜在的大量协变量进行变量选择非常流行。在贝叶斯上下文中，常见的先验选择可能导致回归系数的后验期望，即具有一些非零分量（最重要的协变量）的稀疏（或接近稀疏）向量。本文将全局-局部收缩的想法扩展到希望同时对多个响应变量建模的场景。在这里，我们为 K-结果模型（多元回归）开发了一种变量选择方法，该方法可识别所有结果中最重要的协变量。所有回归系数的先验是具有系数特定方差项的均值零正态，该方差项由预测变量特定因子（共享局部收缩参数）和模型特定因子（全局收缩项）组成，每个模型都不同。我们的建模方法的性能通过模拟研究和数据示例进行评估。