Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximation. (26th August 2020)

• Record Type: Journal Article
• Authors: van den Boom, W; Reeves, G; Dunson, D B
• Is Part Of: Biometrika. Volume 108:Number 2(2021)
• Page Start: 269
• Page End: 282
• Publication Date: 2020-08-26
• Subjects: Bayesian statistics -- Dimensionality reduction -- Marginal inclusion probability -- Nuisance parameter -- Posterior approximation -- Support recovery -- Variable selection; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asaa068
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: 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.