Our interest is in replicated network data with multiple networks observed across the same set of nodes. Examples include brain connection networks, in which nodes corresponds to brain regions and replicates to different individuals, and ecological networks, in which nodes correspond to species and replicates to samples collected at different locations and/or times. Our goal is to infer a hierarchical structure of the nodes at a population level, while performing multi-resolution clustering of the individual replicates. In brain connectomics, the focus is on inferring common relationships among the brain regions, while characterizing inter-individual variability in an easily interpretable manner. To accomplish this, we propose a Bayesian hierarchical model, while providing 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 simulations and application to brain connectome data provide support for the proposed methodology.

翻译：本文关注于重复网络数据，其中多个网络在同一组节点上被观测到。例如，脑连接网络，其中节点对应脑区，重复样本对应不同个体；以及生态网络，其中节点对应物种，重复样本对应在不同地点和/或时间收集的样本。我们的目标是在群体水平上推断节点的层次结构，同时对个体重复样本进行多分辨率聚类。在脑连接组学中，重点在于推断脑区之间的共同关系，同时以易于解释的方式表征个体间的变异性。为此，我们提出了一个贝叶斯层次模型，并在可识别性和后验一致性方面提供了理论支持，同时设计了高效的后验计算方法。我们提出了证明模型可识别性的新技术工具，这些工具本身具有独立的研究价值。我们的模拟实验及在脑连接组数据上的应用为所提出的方法提供了支持。