In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each component one by one. This is particularly true for complex traits having multiple correlated components. A Bayesian multivariate variable selection (BMVS) approach is proposed to select important predictors influencing the multivariate response from a candidate pool with ultrahigh dimension. By applying the sample-size-dependent spike and slab priors, the BMVS approach satisfies the strong selection consistency property under certain conditions, which represents the advantages of BMVS over other existing Bayesian multivariate regression-based approaches. The proposed approach considers the covariance structure of multiple responses without assuming independence and integrates the estimation of covariance-related parameters together with all regression parameters into one framework through a fast-updating Markov chain Monte Carlo (MCMC) procedure. It is demonstrated through simulations that the BMVS approach outperforms some other relevant frequentist and Bayesian approaches. The proposed BMVS approach possesses a flexibility of wide applications, including genome-wide association studies with multiple correlated phenotypes and a large scale of genetic variants and/or environmental variables, as demonstrated in the real data analyses section. The computer code and test data of the proposed method are available as an R package.

中文翻译：

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一种超高维多元回归的贝叶斯变量选择方法

在许多实践中，科学家们对检测哪些预测变量真正与多变量响应相关联特别感兴趣。将多个响应建模为一个向量比将每个组件一一分离更准确。对于具有多个相关成分的复杂性状尤其如此。提出了一种贝叶斯多元变量选择 (BMVS) 方法，用于从具有超高维度的候选池中选择影响多元响应的重要预测因子。通过应用与样本大小相关的尖峰和平板先验，BMVS 方法在特定条件下满足强选择一致性属性，这代表了 BMVS 相对于其他现有的基于贝叶斯多元回归的方法的优势。所提出的方法在不假设独立性的情况下考虑了多个响应的协方差结构，并通过快速更新的马尔可夫链蒙特卡罗 (MCMC) 程序将协方差相关参数的估计与所有回归参数集成到一个框架中。通过模拟证明，BMVS 方法优于其他一些相关的常客和贝叶斯方法。所提出的 BMVS 方法具有广泛应用的灵活性，包括具有多种相关表型和大量遗传变异和/或环境变量的全基因组关联研究，如真实数据分析部分所示。所提出方法的计算机代码和测试数据可作为 R 包获得。