Our interest is in multiplex network data with multiple network samples observed across the same set of nodes. Examples originate from a variety of fields, including brain connectivity, international trade networks, and social networks, among others. Our goal is to infer a hierarchical structure of the nodes at a population level, while performing multi-resolution clustering of the individual replicates. To accomplish this, we propose a Bayesian hierarchical model, provide theoretical support in terms of identifiability and posterior consistency, and design efficient methods for posterior computation. We provide novel technical tools for proving model identifiability, which are of independent interest. Our proposed methodology is demonstrated through numerical simulation and an application to brain connectome data.

翻译：摘要：本文关注在相同节点集上观测到多个网络样本的多层网络数据。实例源于脑连接、国际贸易网络和社交网络等多个领域。我们的目标是在种群层面推断节点的层次结构，同时对个体副本进行多分辨率聚类。为此，我们提出一种贝叶斯层次模型，在可识别性和后验一致性方面提供理论支撑，并设计高效的后验计算方法。我们提供了证明模型可识别性的新颖技术工具，这些工具本身具有独立研究价值。通过数值模拟和脑连接组数据的应用，我们验证了所提出方法的有效性。