Network data arises through observation of relational information between a collection of entities. Recent work in the literature has independently considered when (i) one observes a sample of networks, connectome data in neuroscience being a ubiquitous example, and (ii) the units of observation within a network are edges or paths, such as emails between people or a series of page visits to a website by a user, often referred to as interaction network data. The intersection of these two cases, however, is yet to be considered. In this paper, we propose a new Bayesian modelling framework to analyse such data. Given a practitioner-specified distance metric between observations, we define families of models through location and scale parameters, akin to a Gaussian distribution, with subsequent inference of model parameters providing reasoned statistical summaries for this non-standard data structure. To facilitate inference, we propose specialised Markov chain Monte Carlo (MCMC) schemes capable of sampling from doubly-intractable posterior distributions over discrete and multi-dimensional parameter spaces. Through simulation studies we confirm the efficacy of our methodology and inference scheme, whilst its application we illustrate via an example analysis of a location-based social network (LSBN) data set.
翻译:文献中最近的工作独立地考虑了以下几个方面:(一)观察网络样本,神经科学中的连接数据是一个普遍的例子,以及(二)网络中的观测单位是边缘或路径,例如人与人之间的电子邮件或用户对网站的一系列页面访问,通常称为互动网络数据。然而,这两个案例的交叉还有待考虑。在本文件中,我们提出一个新的巴耶西亚模型框架,以分析这些数据。根据从业者指定的观测距离指标,我们通过位置和尺度参数界定模型的组别,类似于高斯分布,随后对模型参数进行推论,为这种非标准数据结构提供合理的统计摘要。为了便于推断,我们建议采用专门的Markov连锁蒙特卡洛(MCMC)计划,从离散和多维参数空间的可加倍吸引的远地点分布中取样。我们通过模拟研究,确认了我们的方法和推论方法的功效,同时通过应用模型参数为这种非标准数据结构提供合理的统计摘要。我们用一个基于社会定位网络的模型来说明其应用情况。