IS INFINITY THAT FAR? A BAYESIAN NONPARAMETRIC PERSPECTIVE OF FINITE MIXTURE MODELS

• 成果类型: Article
• 署名作者: Argiento, Raffaele; De Iorio, Maria
• 署名单位: University of Bergamo; National University of Singapore
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2201
• 发表日期: 2022
• 页码: 2641-2663
• 关键词: population-structure; unknown number; posterior distribution; DENSITY-ESTIMATION; sampling methods; inference; components

摘要

Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. Following a Bayesian nonparametric perspective, we introduce a new class of priors: the Normalized Independent Point Process. We investigate the probabilistic properties of this new class and present many special cases. In particular, we provide an explicit formula for the distribution of the implied partition, as well as the posterior characterization of the new process in terms of the superposition of two discrete measures. We also provide consistency results. Moreover, we design both a marginal and a conditional algorithm for finite mixture models with a random number of components. These schemes are based on an auxiliary variable MCMC, which allows handling the otherwise intractable posterior distribution and overcomes the challenges associated with the Reversible Jump algorithm. We illustrate the performance and the potential of our model in a simulation study and on real data applications.