# Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo

arXiv: https://arxiv.org/abs/1611.07873 · HTML: https://mlsanity.com/paper/1611.07873/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2016.

## Built on by (most cited first, 18 of 18)

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- [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)
- [Tuning diagonal scale matrices for HMC](https://mlsanity.com/paper/2403.07495/) (2024)
- [Piecewise deterministic generative models](https://mlsanity.com/paper/2407.19448/) (2024)
- [Efficient computation of the volume of a polytope in high-dimensions using Piecewise Deterministic Markov Processes](https://mlsanity.com/paper/2202.09129/) (2022)
- [Log-density gradient covariance and automatic metric tensors for Riemann manifold Monte Carlo methods](https://mlsanity.com/paper/2211.01746/) (2022)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Centered plug-in estimation of Wasserstein distances](https://mlsanity.com/paper/2203.11627/) (2022)
- [Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGs](https://mlsanity.com/paper/2310.05655/) (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)
- [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)
- [Numerical Generalized Randomized Hamiltonian Monte Carlo for piecewise smooth target densities](https://mlsanity.com/paper/2504.18210/) (2025)
- [A fast non-reversible sampler for Bayesian mixture models](https://mlsanity.com/paper/2510.03226/) (2025)
- [Piecewise Deterministic Markov Processes for Bayesian Inference of PDE Coefficients](https://mlsanity.com/paper/2602.05559/) (2026)

## Abstract (arXiv)

Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has led to some fundamentally new Monte Carlo algorithms which can be used to sample from, say, a posterior distribution. Interestingly, continuous-time algorithms seem particularly well suited to Bayesian analysis in big-data settings as they need only access a small sub-set of data points at each iteration, and yet are still guaranteed to target the true posterior distribution. Whilst continuous-time MCMC and SMC methods have been developed independently we show here that they are related by the fact that both involve simulating a piecewise deterministic Markov process. Furthermore we show that the methods developed to date are just specific cases of a potentially much wider class of continuous-time Monte Carlo algorithms. We give an informal introduction to piecewise deterministic Markov processes, covering the aspects relevant to these new Monte Carlo algorithms, with a view to making the development of new continuous-time Monte Carlo more accessible. We focus on how and why sub-sampling ideas can be used with these algorithms, and aim to give insight into how these new algorithms can be implemented, and what are some of the issues that affect their efficiency.