Stick-Breaking Processes With Exchangeable Length Variables

• 成果类型: Article
• 署名作者: Gil-Leyva, Maria F.; Mena, Ramses H.
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1941054
• 发表日期: 2023
• 页码: 537-550
• 关键词: representation; distributions; probability; SEQUENCES

摘要

Our object of study is the general class of stick-breaking processes with exchangeable length variables. These generalize well-known Bayesian nonparametric priors in an unexplored direction. We give conditions to assure the respective species sampling process is proper and the corresponding prior has full support. For a rich subclass we explain how, by tuning a single [0,1]-valued parameter, the stochastic ordering of the weights can be modulated, and Dirichlet and Geometric priors can be recovered. A general formula for the distribution of the latent allocation variables is derived and an MCMC algorithm is proposed for density estimation purposes.