We investigate the evidence/flexibility (i.e., "Occam") paradigm and demonstrate the theoretical and empirical consistency of Bayesian evidence for the task of determining an appropriate generative model for network data. This model selection framework involves determining a collection of candidate models, equipping each of these models' parameters with prior distributions derived via the encompassing priors method, and computing or approximating each models' evidence. We demonstrate how such a criterion may be used to select the most suitable model among the Erd\H{o}s-R\'enyi (ER) model, independent edge (IE) model, and a special one-parameter low-rank stochastic blockmodel (SBM) with known memberships. The Erd\H{o}s-R\'enyi may be considered as being linearly nested within IE, a fact which permits exponential family results. The uniparametric SBM is not so ideal, so we propose a numerical method to approximate the evidence. We apply this paradigm to brain connectome data. Future work necessitates deriving and equipping additional candidate random graph models with appropriate priors so they may be included in the paradigm.

翻译：我们研究证据/灵活性（即“奥卡姆”）范式，并展示贝叶斯证据在确定网络数据适当生成模型任务中的理论与实证一致性。该模型选择框架包括：确定候选模型集合，通过包容先验方法为每个模型的参数赋予先验分布，并计算或近似每个模型的证据。我们演示如何利用此类准则在厄尔多斯-雷尼（ER）模型、独立边（IE）模型及一种具有已知成员关系的特殊单参数低秩随机块模型（SBM）中选取最适模型。厄尔多斯-雷尼模型可被视为线性嵌套于IE模型中，这一事实使得指数族结果得以应用。单参数SBM的理想性不及前者，因此我们提出一种数值方法近似其证据。我们将该范式应用于脑连接组数据。未来工作需要推导并为更多候选随机图模型配备适当的先验，使其得以纳入该范式。