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Peer-reviewedCC BY 4.0Statistics and Computing

Piecewise deterministic sampling for constrained distributions

  • Joël Tatang Demano1,2
  • Paul Dobson2
  • Konstantinos Zygalakis3
  1. 1Maxwell Institute for Mathematical Sciences, Bayes Centre, 47 Potterrow EH8 9BT, Edinburgh, Scotland
  2. 2Department of Mathematics and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS Scotland
  3. 3School of Mathematics, University of Edinburgh, Edinburgh, EH9 3FD Scotland
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Abstract

In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions π π supported on a convex set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}ℳ\end{document}M. This class of PDMPs adapts the concept of a mirror map from convex optimisation to address sampling problems. The corresponding algorithms provide unbiased samples that respect the constraints and, moreover, allow for exact subsampling. We demonstrate the advantages of these algorithms against a range of constrained sampling problems where the proposed algorithms outperform state of the art stochastic differential equation-based methods.

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Cite

BibTeXRIS
BibTeX
@article{demano2026piecewise,
  title = {{Piecewise deterministic sampling for constrained distributions}},
  author = {Joël Tatang Demano and Paul Dobson and Konstantinos Zygalakis},
  journal = {Statistics and Computing},
  year = {2026},
  month = sep,
  doi = {10.1007/s11222-026-10976-9},
  url = {https://doi.org/10.1007/s11222-026-10976-9},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Piecewise deterministic sampling for constrained distributions
AU  - Joël Tatang Demano
AU  - Paul Dobson
AU  - Konstantinos Zygalakis
PY  - 2026
DA  - 2026/09/23
JO  - Statistics and Computing
DO  - 10.1007/s11222-026-10976-9
UR  - https://doi.org/10.1007/s11222-026-10976-9
AB  - In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions π π supported on a convex set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}ℳ\end{document}M. This class of PDMPs adapts the concept of a mirror map from convex optimisation to address sampling problems. The corresponding algorithms provide unbiased samples that respect the constraints and, moreover, allow for exact subsampling. We demonstrate the advantages of these algorithms against a range of constrained sampling problems where the proposed algorithms outperform state of the art stochastic differential equation-based methods.
SN  - 0960-3174
ER  -