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

arXiv: https://arxiv.org/abs/1909.06753 · HTML: https://mlsanity.com/paper/1909.06753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inference](https://mlsanity.com/paper/2107.03920/) (2021)
- [Approximate Bayesian inference and forecasting in huge-dimensional multi-country VARs](https://mlsanity.com/paper/2103.04944/) (2021)

## Abstract (arXiv)

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.