Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation

• 成果类型: Article
• 署名作者: Van den Boom, W.; Reeves, G.; Dunson, D. B.
• 署名单位: Yale NUS College; National University of Singapore; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa068
• 发表日期: 2021
• 页码: 269282
• 关键词: bayesian variable selection; projections; distributions; estimators; inference; priors

摘要

Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a high-dimensional or otherwise computationally challenging nuisance parameter. The focus is on regression models and the key idea is to separate the likelihood into two components through a rotation. One component involves only the nuisance parameters, which can then be integrated out using a novel type of Gaussian approximation. We provide theory on approximation accuracy that holds for a broad class of forms of the nuisance component and priors. Applying our method to simulated and real datasets shows that it can outperform state-of-the-art posterior approximation approaches.