A Bayesian approach is proposed that unifies Gaussian Bayesian network constructions and comparisons between two networks (identical or differential) for data with graph ordering unknown. When sampling graph ordering, to escape from local maximums, an adjusted single queue equi-energy algorithm is applied. The conditional posterior probability mass function for network differentiation is derived and its asymptotic proposition is theoretically assessed. Simulations are used to demonstrate the approach and compare with existing methods. Based on epigenetic data at a set of DNA methylation sites (CpG sites), the proposed approach is further examined on its ability to detect network differentiations. Findings from theoretical assessment, simulations, and real data applications support the efficacy and efficiency of the proposed method for network comparisons.

中文翻译：

---

高斯贝叶斯网络与图排序未知的比较

提出了一种贝叶斯方法，该方法将高斯贝叶斯网络结构和两个网络（相同或差分）之间的比较用于图形排序未知的数据。在对图排序进行采样时，为了摆脱局部最大值，应用了调整后的单队列等能量算法。推导了网络微分的条件后验概率质量函数，并对其渐近命题进行了理论评估。模拟用于演示该方法并与现有方法进行比较。基于一组 DNA 甲基化位点（CpG 位点）的表观遗传数据，进一步检查了所提出的方法检测网络分化的能力。理论评估、模拟的结果，