# The Barker proposal: combining robustness and efficiency in gradient-based MCMC

arXiv: https://arxiv.org/abs/1908.11812 · HTML: https://mlsanity.com/paper/1908.11812/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2019.

## Built on by (most cited first, 20 of 20)

- [Discrete Langevin Sampler via Wasserstein Gradient Flow](https://mlsanity.com/paper/2206.14897/) (2022)
- [Optimal Scaling for Locally Balanced Proposals in Discrete Spaces](https://mlsanity.com/paper/2209.08183/) (2022)
- [Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions](https://mlsanity.com/paper/2110.00610/) (2021)
- [Optimal design of the Barker proposal and other locally-balanced Metropolis-Hastings algorithms](https://mlsanity.com/paper/2201.01123/) (2022)
- [Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2405.13574/) (2024)
- [Improving multiple-try Metropolis with local balancing](https://mlsanity.com/paper/2211.11613/) (2022)
- [Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy](https://mlsanity.com/paper/2304.14762/) (2023)
- [Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models](https://mlsanity.com/paper/2403.09416/) (2024)
- [Generalizing Score-based generative models for Heavy-tailed Distributions](https://mlsanity.com/paper/2603.00772/) (2026)
- [Robust Approximate Sampling via Stochastic Gradient Barker Dynamics](https://mlsanity.com/paper/2405.08999/) (2024)
- [Harnessing the Power of Reinforcement Learning for Adaptive MCMC](https://mlsanity.com/paper/2507.00671/) (2025)
- [A Targeted Accuracy Diagnostic for Variational Approximations](https://mlsanity.com/paper/2302.12419/) (2023)
- [Importance is Important: Generalized Markov Chain Importance Sampling Methods](https://mlsanity.com/paper/2304.06251/) (2023)
- [Stochastic Gradient Piecewise Deterministic Monte Carlo Samplers](https://mlsanity.com/paper/2406.19051/) (2024)
- [A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targets](https://mlsanity.com/paper/2603.18640/) (2026)
- [Markov chain Monte Carlo without evaluating the target: an auxiliary variable approach](https://mlsanity.com/paper/2406.05242/) (2024)
- [ATLAS: Adapting Trajectory Lengths and Step-Size for Hamiltonian Monte Carlo](https://mlsanity.com/paper/2410.21587/) (2024)
- [High-dimensional Adaptive MCMC with Reduced Computational Complexity](https://mlsanity.com/paper/2604.09286/) (2026)
- [Quenched Ensemble Sampling](https://mlsanity.com/paper/2609.15894/) (2026)
- [On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal](https://mlsanity.com/paper/2610.01448/) (2026)

## Abstract (arXiv)

There is a tension between robustness and efficiency when designing Markov chain Monte Carlo (MCMC) sampling algorithms. Here we focus on robustness with respect to tuning parameters, showing that more sophisticated algorithms tend to be more sensitive to the choice of step-size parameter and less robust to heterogeneity of the distribution of interest. We characterise this phenomenon by studying the behaviour of spectral gaps as an increasingly poor step-size is chosen for the algorithm. Motivated by these considerations, we propose a novel and simple gradient-based MCMC algorithm, inspired by the classical Barker accept-reject rule, with improved robustness properties. Extensive theoretical results, dealing with robustness to tuning, geometric ergodicity and scaling with dimension, suggest that the novel scheme combines the robustness of simple schemes with the efficiency of gradient-based ones. We show numerically that this type of robustness is particularly beneficial in the context of adaptive MCMC, giving examples where our proposed scheme significantly outperforms state-of-the-art alternatives.