# The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method

arXiv: https://arxiv.org/abs/1510.02451 · HTML: https://mlsanity.com/paper/1510.02451/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2015.

## Built on by (most cited first, 27 of 27)

- [Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics](https://mlsanity.com/paper/2211.00450/) (2022)
- [Convergence Analysis of Schr"odinger-F"ollmer Sampler without Convexity](https://mlsanity.com/paper/2107.04766/) (2021)
- [Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopes](https://mlsanity.com/paper/2207.04387/) (2022)
- [Stereographic Markov Chain Monte Carlo](https://mlsanity.com/paper/2205.12112/) (2022)
- [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 Methods for Sampling, Optimisation, Inference and Adaptive Agents](https://mlsanity.com/paper/2203.10592/) (2022)
- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [Ensemble-Based Annealed Importance Sampling](https://mlsanity.com/paper/2401.15645/) (2024)
- [Piecewise deterministic generative models](https://mlsanity.com/paper/2407.19448/) (2024)
- [Divide-and-Conquer Fusion](https://mlsanity.com/paper/2110.07265/) (2021)
- [Efficient computation of the volume of a polytope in high-dimensions using Piecewise Deterministic Markov Processes](https://mlsanity.com/paper/2202.09129/) (2022)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler](https://mlsanity.com/paper/2609.06905/) (2026)
- [Neural parameter calibration and uncertainty quantification for epidemic forecasting](https://mlsanity.com/paper/2312.03147/) (2023)
- [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)
- [A stepped sampling method for video detection using LSTM](https://mlsanity.com/paper/2107.08471/) (2021)
- [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)
- [Markov chain Monte Carlo without evaluating the target: an auxiliary variable approach](https://mlsanity.com/paper/2406.05242/) (2024)
- [Effect of Random Learning Rate: Theoretical Analysis of SGD Dynamics in Non-Convex Optimization via Stationary Distribution](https://mlsanity.com/paper/2406.16032/) (2024)
- [Numerical Generalized Randomized Hamiltonian Monte Carlo for piecewise smooth target densities](https://mlsanity.com/paper/2504.18210/) (2025)
- [Boosting Statistic Learning with Synthetic Data from Pretrained Large Models](https://mlsanity.com/paper/2505.04992/) (2025)
- [Bouncy particle sampler with infinite exchanging parallel tempering](https://mlsanity.com/paper/2509.02003/) (2025)
- [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)

Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the Metropolis-Hastings algorithm. We explore and propose several original extensions of an alternative approach introduced recently in Peters and de With (2012) where the target distribution of interest is explored using a continuous-time Markov process. In the Metropolis-Hastings algorithm, a trial move to a region of lower target density, equivalently "higher energy", than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines continuously around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. The resulting non-reversible Markov process provides a rejection-free MCMC sampling scheme. We propose several original techniques to simulate this continuous-time process exactly in a wide range of scenarios of interest to statisticians. When the target distribution factorizes as a product of factors involving only subsets of variables, such as the posterior distribution associated to a probabilistic graphical model, it is possible to modify the original algorithm to exploit this structure and update in parallel variables within each clique. We present several extensions by proposing methods to sample mixed discrete-continuous distributions and distributions restricted to a connected smooth domain. We also show that it is possible to move the particle using a general flow instead of straight lines. We demonstrate the efficiency of this methodology through simulations on a variety of applications and show that it can outperform Hybrid Monte Carlo schemes in interesting scenarios.