标题： 具有未知特征数的多变量计数数据的贝叶斯非参数建模 显示英文标题

标题： Bayesian nonparametric modeling of multivariate count data with an unknown number of traits

摘要： 特征和特质分配模型是贝叶斯非参数学中的基本对象，在多个应用中起着重要作用。然而，现有的方法通常假设数据的完全可交换性，这在具有异质但相关组的设置中可能具有限制性。在本文中，我们引入了一类通用且易于处理的贝叶斯非参数先验，用于部分可交换的特质分配模型，依赖于完全随机向量。我们提供了全面的理论分析，包括边缘和后验分布的显式表达式，并在二元和泊松分布特质的情况下展示了我们框架的易处理性。我们方法的一个显著特点是特质的数量是一个随机量，从而允许我们对未观察到的特质进行建模和估计。基于这些结果，我们还开发了一个新颖的混合模型，从数据中推断群体划分结构，有效地对特质分配进行聚类。这种扩展推广了贝叶斯非参数潜在类别模型，并避免了当特质数量被假定为固定时出现的系统性过度聚类。我们通过一个应用到Operazione Infinito调查中的Ndrangheta犯罪网络，展示了我们方法的实用性，其中我们的模型提供了对非法活动组织的见解。 显示英文摘要

摘要： Feature and trait allocation models are fundamental objects in Bayesian nonparametrics and play a prominent role in several applications. Existing approaches, however, typically assume full exchangeability of the data, which may be restrictive in settings characterized by heterogeneous but related groups. In this paper, we introduce a general and tractable class of Bayesian nonparametric priors for partially exchangeable trait allocation models, relying on completely random vectors. We provide a comprehensive theoretical analysis, including closed-form expressions for marginal and posterior distributions, and illustrate the tractability of our framework in the cases of binary and Poisson-distributed traits. A distinctive aspect of our approach is that the number of traits is a random quantity, thereby allowing us to model and estimate unobserved traits. Building on these results, we also develop a novel mixture model that infers the group partition structure from the data, effectively clustering trait allocations. This extension generalizes Bayesian nonparametric latent class models and avoids the systematic overclustering that arises when the number of traits is assumed to be fixed. We demonstrate the practical usefulness of our methodology through an application to the `Ndrangheta criminal network from the Operazione Infinito investigation, where our model provides insights into the organization of illicit activities.