In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The proposed approach involves modeling of related conditional distributions of a response vector given the covariates using a Dependent Dirichlet Process (DDP) prior. The DDP is used to introduce dependence across covariates. The flexible covariate-dependent mixture of multivariate Gaussian kernels gives rise to an induced posterior for the desired multivariate quantile. For posterior computations, we use a truncated stick-breaking representation of the DDP, and use a block Gibbs sampler for estimating the model parameters. We illustrate our method with simulation studies, and a data containing blood pressures of 40 women. Finally, we provide a theoretical justification for the proposed method through posterior consistency and support properties of the prior.

在本文中，我们考虑了非参数贝叶斯方法进行多元分位数回归。所提出的方法涉及使用先验从属狄利克雷过程（DDP）在给定协变量的情况下对响应向量的相关条件分布进行建模。DDP用于引入协变量之间的依赖性。多元高斯核的灵活的依赖于协变量的混合产生了所需多元分位数的诱导后验。对于后验计算，我们使用DDP的截断式折断表示，并使用块Gibbs采样器估计模型参数。我们通过仿真研究和包含40位女性血压的数据来说明我们的方法。最后，