Hyperbolic models can reproduce the heavy-tailed degree distribution, high clustering, and hierarchical structure of empirical networks. Current algorithms for finding the hyperbolic coordinates of networks, however, do not quantify uncertainty in the inferred coordinates. We present BIGUE, a Markov chain Monte Carlo (MCMC) algorithm that samples the posterior distribution of a Bayesian hyperbolic random graph model. We show that combining random walk and random cluster transformations significantly improves mixing compared to the commonly used and state-of-the-art dynamic Hamiltonian Monte Carlo algorithm. Using this algorithm, we also provide evidence that the posterior distribution cannot be approximated by a multivariate normal distribution, thereby justifying the use of MCMC to quantify the uncertainty of the inferred parameters.

翻译：双曲模型能够复现实证网络中重尾的度分布、高聚类系数及层次化结构。然而，现有的网络双曲坐标求解算法未能量化推断坐标的不确定性。本文提出BIGUE——一种马尔可夫链蒙特卡洛（MCMC）算法，用于对贝叶斯双曲随机图模型的后验分布进行采样。研究表明，结合随机游走与随机簇变换的策略，相较于当前普遍采用且最先进的动态哈密顿蒙特卡洛算法，能显著提升混合效率。通过该算法，我们进一步证明后验分布无法用多元正态分布近似，从而论证了使用MCMC量化推断参数不确定性的必要性。