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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

Abstract

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.

Citation

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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. https://doi.org/10.1214/19-AAP1552

Information

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

Subjects:
Primary: 60J22, 65C40

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 5 • October 2020
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