We ask: when do Bayesian model averaging (BMA) weights over decision trees carry sufficient epistemic information to justify committed exploitation of the averaging distribution? We answer this question in closed form for Bayesian decision trees (BDTs) with Dirichlet-Multinomial leaf models and a Catalan-exponential tree-size prior (Schetinin&Jakaite, 2025), establishing a complete non-asymptotic theory of rational commitment thresholds.

翻译：我们提出一个问题：当决策树上的贝叶斯模型平均（BMA）权重承载足够的认知信息，足以证明对平均分布进行承诺性利用的合理性时，这一条件如何成立？我们针对具有狄利克雷-多项叶模型和卡塔兰-指数树规模先验（Schetinin & Jakaite, 2025）的贝叶斯决策树（BDT），以闭式解形式回答了这个问题，从而建立了一套关于理性承诺阈值的完整非渐近理论。