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 rank-1 stochastic blockmodel (SBM). The Erd\"{o}s-R\'{e}nyi may be considered as being linearly nested within IE, a fact which permits exponential family results. The rank-1 SBM is not so ideal, so we propose a numerical method to approximate its 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：我们研究了证据/灵活性（即“奥卡姆”）范式，并证明了贝叶斯证据在确定网络数据合适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：确定候选模型集合，通过包含先验方法为每个模型参数赋予先验分布，以及计算或近似每个模型的证据。我们展示了如何利用该准则在埃尔德什-雷尼（ER）模型、独立边（IE）模型和秩-1随机块模型（SBM）中选择最合适的模型。埃尔德什-雷尼模型可视为线性嵌套于独立边模型中，这一事实允许利用指数族结果。秩-1随机块模型则不具备如此理想的性质，因此我们提出了一种数值方法来近似其证据。我们将此范式应用于脑连接组数据。未来工作需要为更多候选随机图模型推导并赋予合适的先验分布，使其能够纳入该范式。