# Approximation Properties of Variational Bayes for Vector Autoregressions

arXiv: https://arxiv.org/abs/1903.00617 · HTML: https://mlsanity.com/paper/1903.00617/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [Statistical and Computational Trade-offs in Variational Inference: A Case Study in Inferential Model Selection](https://mlsanity.com/paper/2207.11208/) (2022)

## Abstract (arXiv)

Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive density and KL divergence for the linear Gaussian multi-equation regression. Our results indicate that VB approximates the posterior mean perfectly. Factors affecting the magnitude of underestimation in posterior variance and mode are revealed. Importantly, We demonstrate that VB estimates predictive densities accurately.