# Dimension-free mixing times of Gibbs samplers for Bayesian hierarchical models

arXiv: https://arxiv.org/abs/2304.06993 · HTML: https://mlsanity.com/paper/2304.06993/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 69 references that are in the map.
- First posted on arXiv 14 Apr 2023.

## Builds on (most cited first, 3 of 3)

- [Scalable Bayesian computation for crossed and nested hierarchical models](https://mlsanity.com/paper/2103.10875/) (2021)
- [MCMC-Based Inference in the Era of Big Data: A Fundamental Analysis of the Convergence Complexity of High-Dimensional Chains](https://mlsanity.com/paper/1508.00947/) (2015)
- [Tuning Stochastic Gradient Algorithms for Statistical Inference via Large-Sample Asymptotics](https://mlsanity.com/paper/2207.12395/) (2022)

## Built on by (most cited first, 4 of 4)

- [Entropy contraction of the Gibbs sampler under log-concavity](https://mlsanity.com/paper/2410.00858/) (2024)
- [Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models](https://mlsanity.com/paper/2403.09416/) (2024)
- [Dimension-free Relaxation Times of Informed MCMC Samplers on Discrete Spaces](https://mlsanity.com/paper/2404.03867/) (2024)
- [From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Models](https://mlsanity.com/paper/2605.27352/) (2026)

## Abstract (arXiv)

Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performances, however, there are still relatively few quantitative results on their convergence properties, e.g. much less than for gradient-based sampling methods. In this work we analyse the behaviour of total variation mixing times of Gibbs samplers targeting hierarchical models using tools from Bayesian asymptotics. We obtain dimension-free convergence results under random data-generating assumptions, for a broad class of two-level models with generic likelihood function. Specific examples with Gaussian, binomial and categorical likelihoods are discussed.