Abstract This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical challenges revolve around dealing with the unknown mean and variance functions and in particular, the correlation matrix. To tackle these problems, we have developed priors over the smooth functions and a Markov chain Monte Carlo algorithm for inference and model selection. Specifically, Dirichlet process mixtures of Gaussian distributions are used as the basis for a cluster-inducing prior over the elements of the correlation matrix. The smooth, multidimensional means and variances are represented using radial basis function expansions. The complexity of the model, in terms of variable selection and smoothness, is then controlled by spike-slab priors. A simulation study is presented, demonstrating performance as the response dimension increases. Finally, the model is fit to a number of real world datasets. An R package, scripts for replicating synthetic and real data examples, and a detailed description of the MCMC sampler are available in the supplementary materials online.

中文翻译：

---

带变量选择的多元连续响应的贝叶斯半参数分析

摘要 本文提出了一种对高斯多元响应回归进行贝叶斯半参数推理的方法。我们受到来自物理和社会科学的各种中小维度问题的启发。统计挑战围绕着处理未知的均值和方差函数，尤其是相关矩阵。为了解决这些问题，我们开发了平滑函数的先验和用于推理和模型选择的马尔可夫链蒙特卡罗算法。具体而言，高斯分布的狄利克雷过程混合用作相关矩阵元素上的聚类诱导先验的基础。使用径向基函数展开来表示平滑的多维均值和方差。模型的复杂性，在变量选择和平滑度方面，然后由尖峰板先验控制。提出了一项模拟研究，展示了响应维度增加时的性能。最后，该模型适用于许多真实世界的数据集。在线补充材料中提供了 R 包、用于复制合成和真实数据示例的脚本以及 MCMC 采样器的详细说明。