Bayesian analysis of product feature allocation models

• 成果类型: Article; Early Access
• 署名作者: Ghilotti, Lorenzo; Camerlenghi, Federico; Rigon, Tommaso
• 署名单位: University of Milano-Bicocca
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf058
• 发表日期: 2025
• 关键词: indian buffet process; FINITE APPROXIMATIONS; Dirichlet process; species richness; beta processes; probability; estimators; Extrapolation; rarefaction; variants

摘要

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 alpha-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.