# The Boomerang Sampler

arXiv: https://arxiv.org/abs/2006.13777 · HTML: https://mlsanity.com/paper/2006.13777/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions](https://mlsanity.com/paper/2209.02001/) (2022)
- [Geometric convergence of elliptical slice sampling](https://mlsanity.com/paper/2105.03308/) (2021)
- [Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler](https://mlsanity.com/paper/2609.06905/) (2026)
- [Stochastic Gradient Piecewise Deterministic Monte Carlo Samplers](https://mlsanity.com/paper/2406.19051/) (2024)
- [Windowed thinning and query complexity for the bouncy particle and Zigzag samplers](https://mlsanity.com/paper/2607.28413/) (2026)
- [The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo](https://mlsanity.com/paper/2111.10210/) (2021)
- [Continuously-Tempered PDMP Samplers](https://mlsanity.com/paper/2205.09559/) (2022)
- [Piecewise Deterministic Markov Processes for Bayesian Neural Networks](https://mlsanity.com/paper/2302.08724/) (2023)
- [Piecewise Deterministic Markov Processes for Bayesian Inference of PDE Coefficients](https://mlsanity.com/paper/2602.05559/) (2026)
- [Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling](https://mlsanity.com/paper/2610.16248/) (2026)

## Abstract (arXiv)

This paper introduces the Boomerang Sampler as a novel class of continuous-time non-reversible Markov chain Monte Carlo algorithms. The methodology begins by representing the target density as a density, e-U, with respect to a prescribed (usually) Gaussian measure and constructs a continuous trajectory consisting of a piecewise elliptical path. The method moves from one elliptical orbit to another according to a rate function which can be written in terms of U. We demonstrate that the method is easy to implement and demonstrate empirically that it can out-perform existing benchmark piecewise deterministic Markov processes such as the bouncy particle sampler and the Zig-Zag. In the Bayesian statistics context, these competitor algorithms are of substantial interest in the large data context due to the fact that they can adopt data subsampling techniques which are exact (ie induce no error in the stationary distribution). We demonstrate theoretically and empirically that we can also construct a control-variate subsampling boomerang sampler which is also exact, and which possesses remarkable scaling properties in the large data limit. We furthermore illustrate a factorised version on the simulation of diffusion bridges.