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\"{o}s-R\'{e}nyi (ER) model, independent edge (IE) model, and a special one-parameter low-rank stochastic blockmodel (SBM) with known memberships. The Erd\"{o}s-R\'{e}nyi 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：我们考察证据/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经验一致性。该模型选择框架包括：确定一组候选模型，通过包含先验方法为每个模型参数配备先验分布，并计算或近似每个模型的证据。我们演示如何利用该准则在埃尔德什–雷尼（ER）模型、独立边（IE）模型以及一个成员已知的单参数低秩随机块模型（SBM）中选取最合适的模型。埃尔德什–雷尼模型可视为线性嵌套于IE模型内，这一事实允许应用指数族结果。单参数SBM并非如此理想，因此我们提出一种数值方法来近似证据。我们将此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分布，以便将其纳入该范式。