Abstract We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather than relying on a stochastic search through the high-dimensional model space, we develop an ECM algorithm similar to the EMVS procedure of Ročková and George targeting modal estimates of the matrix of regression coefficients and residual precision matrix. Varying the scale of the continuous spike densities facilitates dynamic posterior exploration and allows us to filter out negligible regression coefficients and partial covariances gradually. Our method is seen to substantially outperform regularization competitors on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several later-life cognition, psychological, and socio-economic outcomes. An R package, scripts for replicating examples in this article, and results from further simulation studies are provided in the supplementary materials available online.

中文翻译：

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使用多变量 Spike-and-Slab LASSO 同时选择变量和协方差

摘要 我们提出了一种贝叶斯程序，用于在多元线性回归模型中使用连续尖峰和板坯先验同时选择变量和协方差，其中 q 可能相关的响应被回归到 p 预测变量上。我们不依赖于通过高维模型空间的随机搜索，而是开发了一种类似于 Ročková 和 George 的 EMVS 过程的 ECM 算法，目标是回归系数矩阵和残差精度矩阵的模态估计。改变连续尖峰密度的规模有利于动态后验探索，并允许我们逐渐过滤掉可忽略不计的回归系数和部分协方差。我们的方法在模拟数据上明显优于正则化竞争对手。我们通过重新检查最近的一项观察性研究中的数据来证明我们的方法，该观察性研究是关于踢高中足球对几种晚年认知、心理和社会经济结果的影响。在线提供的补充材料中提供了 R 包、用于复制本文示例的脚本以及进一步模拟研究的结果。