Bayesian analysis of product feature allocation models
研究了一类乘积形式的特征分配模型，推导出预测结构和后验分布的闭式表达式，并应用于生态学中物种丰富度估计，通过丹麦森林和巴罗科罗拉多岛的植物数据验证。
Abstract Feature allocation models are an extension of Bayesian nonparametric clustering models, where individuals can share multiple features. We study a broad class of models whose probability distribution has a product form, which includes the popular Indian buffet process. This class plays a prominent role among existing priors, and it shares structural characteristics with Gibbs-type priors in the species sampling framework. We develop a general theory for the entire class, obtaining closed form expressions for the predictive structure and the posterior law of the underlying stochastic process. Additionally, we describe the distribution for the number of features and the number of hitherto unseen features in a future sample, leading to the α-diversity for feature models. We also examine notable novel examples, such as mixtures of Indian buffet processes and beta Bernoulli models, where the latter entails a finite random number of features. This methodology finds significant applications in ecology, allowing the estimation of species richness for incidence data, as we demonstrate by analyzing plant diversity in Danish forests and trees in Barro Colorado Island.