One of the major challenges in modern day statistics is to formulate models and develop inferential procedures to understand the complex multivariate relationships present in high-dimensional datasets. In this paper, we address the issue of model determination for DAGs, with respect to a given ordering of the variables, together with the corresponding parameter estimation. For this, we use a hierarchical mixture prior and develop a Gibbs sampling algorithm to carry out the posterior computations. We first focus on the Gaussian DAG models and calculate the posterior probability of being the edge between two nodes. We then extend our idea to construct a DAG for discrete data under the assumption that the data generated by discretization of the marginal distributions of a latent multivariate Gaussian distribution via a set of predetermined threshold values. Results show that the proposed method has high accuracy. The source code is available at http://bs.ipm.ac.ir/softwares/Gibbs/code.rar

现代统计学的主要挑战之一是制定模型并开发推理程序来理解高维数据集中存在的复杂多元关系。在本文中，我们针对给定的变量排序以及相应的参数估计来解决 DAG 的模型确定问题。为此，我们使用分层混合先验并开发吉布斯采样算法来执行后验计算。我们首先关注高斯 DAG 模型并计算成为两个节点之间边缘的后验概率。然后，我们扩展我们的想法，在假设数据是通过一组预定阈值对潜在多元高斯分布的边缘分布进行离散化生成的数据的情况下，为离散数据构建 DAG。结果表明，所提出的方法具有较高的准确率。源代码可在 http://bs.ipm.ac.ir/softwares/Gibbs/code.rar