We introduce and study a unified Bayesian framework for extended feature allocations which flexibly captures interactions -- such as repulsion or attraction -- among features and their associated weights. We provide a complete Bayesian analysis of the proposed model and specialize our general theory to noteworthy classes of priors. This includes a novel prior based on determinantal point processes, for which we show promising results in a spatial statistics application. Within the general class of extended feature allocations, we further characterize those priors that yield predictive probabilities of discovering new features depending either solely on the sample size or on both the sample size and the distinct number of observed features. These predictive characterizations, known as "sufficientness" postulates, have been extensively studied in the literature on species sampling models starting from the seminal contribution of the English philosopher W.E. Johnson for the Dirichlet distribution. Within the feature allocation setting, existing predictive characterizations are limited to very specific examples; in contrast, our results are general, providing practical guidance for prior selection. Additionally, our approach, based on Palm calculus, is analytical in nature and yields a novel characterization of the Poisson point process through its reduced Palm kernel.

翻译：本文提出并研究了一个统一的贝叶斯框架，用于处理扩展特征分配问题。该框架能够灵活捕捉特征及其关联权重之间的相互作用（例如排斥或吸引）。我们对所提出的模型进行了完整的贝叶斯分析，并将一般理论具体应用于若干值得关注的先验分布类别。这包括一种基于行列式点过程的新型先验分布，我们在空间统计应用中展示了其优异性能。在扩展特征分配的一般类别中，我们进一步刻画了那些能够产生预测概率的先验分布——这些概率要么仅依赖于样本量，要么同时依赖于样本量和观测到的不同特征数量。这类被称为"充分性"公设的预测刻画，自英国哲学家W.E.约翰逊关于狄利克雷分布的开创性工作以来，已在物种抽样模型文献中得到广泛研究。在特征分配的研究背景下，现有的预测刻画仅限于非常特殊的案例；相比之下，我们的结果具有普适性，为先验选择提供了实用指导。此外，我们基于帕姆演算的研究方法本质上是解析性的，通过约化帕姆核给出了泊松点过程的新颖刻画。