Dirichlet Process Mixtures of Block g Priors for Model Selection and Prediction in Linear Models

• 成果类型: Article; Early Access
• 署名作者: Porwal, Anupreet; Rodriguez, Abel
• 署名单位: Alphabet Inc.; Google Incorporated; University of Washington; University of Washington Seattle
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2681993
• 发表日期: 2026-07-11
• 关键词: Conditional Lindley paradox; Continuous shrinkage prior; g prior; Linear Model; model selection; variable-selection; prior distributions; regression; horseshoe; definition; rules

摘要

This article introduces Dirichlet process mixtures of block g priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of g priors that allow for differential shrinkage for various (data-selected) blocks of parameters while fully accounting for the predictors' correlation structure, providing a bridge between the literatures on model selection and continuous shrinkage priors. We show that Dirichlet process mixtures of block g priors are consistent in various senses and, in particular, that they avoid the conditional Lindley paradox highlighted by Som, Hans, and MacEachern. Further, we develop a Markov chain Monte Carlo algorithm for posterior inference that requires only minimal ad-hoc tuning. Finally, we investigate the empirical performance of the prior in various real and simulated datasets. In the presence of a small number of very large effects, Dirichlet process mixtures of block g priors lead to higher power for detecting smaller but significant effects with only a minimal increase in the number of false discoveries. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.