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GEOMETRIC ERGODICITY OF THE BOUNCY PARTICLE SAMPLER

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 [10] 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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https://hal.archives-ouvertes.fr/hal-01839335
Contributor : Pierre Monmarché <>
Submitted on : Saturday, July 14, 2018 - 3:51:26 PM
Last modification on : Thursday, December 10, 2020 - 4:52:38 PM
Long-term archiving on: : Tuesday, October 16, 2018 - 1:19:31 AM

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  • HAL Id : hal-01839335, version 1

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Alain Durmus, Arnaud Guillin, Pierre Monmarché. GEOMETRIC ERGODICITY OF THE BOUNCY PARTICLE SAMPLER. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2020, 30 (5), pp.2069-2098. ⟨hal-01839335⟩

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