# GPU-accelerated Gibbs sampling: a case study of the Horseshoe Probit model

arXiv: https://arxiv.org/abs/1608.04329 · HTML: https://mlsanity.com/paper/1608.04329/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2016.

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

- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [Sparse Bayesian Lasso via a Variable-Coefficient ℓ1 Penalty](https://mlsanity.com/paper/2211.05089/) (2022)
- [Accelerating Markov Random Field Inference with Uncertainty Quantification](https://mlsanity.com/paper/2108.00570/) (2021)
- [Sampling on Metric Graphs](https://mlsanity.com/paper/2512.02175/) (2025)

## Abstract (arXiv)

Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to parallel computing environments, as their inherently sequential nature incurs a large synchronization cost. In the case study illustrated by this paper, we show how to do Gibbs sampling in a fully data-parallel manner on a graphics processing unit, for a large class of exchangeable models that admit latent variable representations. Our approach takes a systems perspective, with emphasis placed on efficient use of compute hardware. We demonstrate our method on a Horseshoe Probit regression model and find that our implementation scales effectively to thousands of predictors and millions of data points simultaneously.