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October 2020 Geometric ergodicity of the Bouncy Particle Sampler
Alain Durmus, Arnaud Guillin, Pierre Monmarché
Ann. Appl. Probab. 30(5): 2069-2098 (October 2020). DOI: 10.1214/19-AAP1552


The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic piecewise deterministic Markov process for which the target measure is invariant. This paper deals with theoretical properties of BPS. First, we establish geometric ergodicity of the associated semi-group under weaker conditions than in (Ann. Statist. 47 (2019) 1268–1287) both on the target distribution and the velocity probability distribution. This result is based on a new coupling of the process which gives a quantitative minorization condition and yields more insights on the convergence. In addition, we study on a toy model the dependency of the convergence rates on the dimension of the state space. Finally, we apply our results to the analysis of simulated annealing algorithms based on BPS.


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Alain Durmus. Arnaud Guillin. Pierre Monmarché. "Geometric ergodicity of the Bouncy Particle Sampler." Ann. Appl. Probab. 30 (5) 2069 - 2098, October 2020.


Received: 1 July 2018; Revised: 1 November 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149523
Digital Object Identifier: 10.1214/19-AAP1552

Primary: 60J22 , 65C40

Keywords: Bouncy particle sampler , coupling , geometric ergodicity , MCMC , simulated annealing

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.30 • No. 5 • October 2020
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