In this paper, we propose novel strategies based on Gibbs sampling for the estimation of the coefficients and topology of a graphical network represented by a first-order vector autoregressive model. As the topology and the coefficients are closely related, obtaining their Markov chains together is a nontrivial task. When incorporating both in a Gibbs-based sampler, the topology samples at each iteration are decisive factors in how information for the corresponding coefficient samples is propagated. We propose new Gibbs-based samplers that differ in the sampling strategies and scanning order used for their operation. We ran a series of experiments on simulated data to analyze and compare the samplers’ performances with dimension of data, data size, and choice of prior. The best performing sampler was also applied to real data related to a financial network. Converged Markov chains of coefficient and topology elements of the network attest to the method’s validity, and plots illustrating posterior distributions of the predicted data against the observed data indicate promising inference for real data applications.

在本文中，我们提出了基于吉布斯采样的新策略，用于估计由一阶向量自回归模型表示的图形网络的系数和拓扑。由于拓扑和系数密切相关，因此将它们的马尔可夫链一起获得是一项非常重要的任务。当将两者结合到基于 Gibbs 的采样器中时，每次迭代的拓扑样本是相应系数样本的信息如何传播的决定性因素。我们提出了新的基于 Gibbs 的采样器，它们在用于其操作的采样策略和扫描顺序上有所不同。我们对模拟数据进行了一系列实验，通过数据维度、数据大小和先验选择来分析和比较采样器的性能。性能最好的采样器也被应用于与金融网络相关的真实数据。网络的系数和拓扑元素的收敛马尔可夫链证明了该方法的有效性，并且说明预测数据与观察数据的后验分布的图表明对实际数据应用的推断很有前景。