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

TL;DR

This paper introduces a novel Gaussian approximation method for efficiently computing posteriors in regression models with high-dimensional nuisance parameters, improving accuracy over existing methods.

Contribution

The paper proposes a new integrated rotated Gaussian approximation technique that effectively separates and integrates out nuisance parameters in high-dimensional Bayesian regression models.

Findings

Outperforms existing posterior approximation methods in simulations.

Provides theoretical guarantees on approximation accuracy.

Demonstrates effectiveness on real data sets.

Abstract

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 data sets shows that it can outperform state-of-the-art posterior approximation approaches.