Sampling using Piecewise Deterministic Markov Processes
On this website (continuously work in progress) I aim to collect references to papers on the use and analysis of Piecewise Deterministic Markov Processes (PDMPs) for use in MCMC. I will try to list all papers that I find important, will put years of first appearance on arXiv or elsewhere, and list in reverse chronological order. I will highlight papers which in my opinion reflect the current state of the art. Inevitably some of this page will reflect some of my own judgements and prejudice. If you want to bring some paper to my attention, or feel I should correct something, please write me at joris.bierkens AT tudelft.nl.
Joris Bierkens (homepage)
Mathematics of PDMPs
Here papers are listed which concern the mathematical analysis of process underlying sampling by means of PDMPs. I have chosen not to list papers concerning the analysis of PDMPs under assumptions which are not immediately useful for MCMC.
- Joris Bierkens, Gareth Roberts, Pierre-André Zitt, Ergodicity of the zigzag process (2017)
- George Deligiannidis, Alexandre Bouchard-Côté, Arnaud Doucet, Exponential Ergodicity of the Bouncy Particle Sampler (2017)
- Joris Bierkens, Andrew Duncan, Limit theorems for the Zig-Zag process (2016)
- Joris Bierkens, Gareth Roberts, A piecewise deterministic scaling limit of Lifted Metropolis-Hastings in the Curie-Weiss model (2015). In this work we discovered PDMPs as a scaling limit of a discrete MCMC algorithm (see the paper by Turitsyn et al. (2008) listed below). We obtain exponential ergodicity of the Zig-Zag process in the one-dimensional case.
- Pierre Monmarché, Piecewise deterministic simulated annealing (2014). Most of the building blocks for sampling in the one-dimensional case are here, but the focus is on using PDMPs for optimization by means of simulated annealing. So in a sense, this paper is immediately taking the next step and skipping a discussion of MCMC.
Methodology using PDMPs
Here papers are listed which describe sampling methods based on PDMPs. A concise introduction to the topic may be found in the bold paper.
- Paul Vanetti, Alexandre Bouchard-Côté, George Deligiannidis, Arnaud Doucet, Piecewise Deterministic Markov Chain Monte Carlo (2017)
- Changye Wu, Christian P. Robert, Generalized Bouncy Particle Sampler (2017)
- Joris Bierkens, Alexandre Bouchard-Côté, Arnaud Doucet, Andrew B. Duncan, Paul Fearnhead, Thibaut Lienart, Gareth Roberts, Sebastian J. Vollmer, Piecewise Deterministic Markov Processes for Scalable Monte Carlo on Restricted Domains (2017)
- Paul Fearnhead, Joris Bierkens, Murray Pollock, Gareth O Roberts, Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo (2016)
- Joris Bierkens, Paul Fearnhead, Gareth Roberts, The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data (2016)
- Alexandre Bouchard-Côté, Sebastian J. Vollmer, Arnaud Doucet, The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method (2015)
As usual many ideas concerning sampling methods originated from physics; these are a few key papers in this respect.
Machine learning literature
Key references on non-reversible MCMC sampling
The use of PDMPs for sampling originated from the attempts to design non-reversible MCMC algorithms. Here I list several key references from the physics, mathematics and statistics literature.
Last update: April 2018