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Journal Articles The Annals of Applied Probability Year : 2020

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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Dates and versions

hal-01839335 , version 1 (14-07-2018)

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Alain Durmus, Arnaud Guillin, Pierre Monmarché. GEOMETRIC ERGODICITY OF THE BOUNCY PARTICLE SAMPLER. The Annals of Applied Probability, 2020, 30 (5), pp.2069-2098. ⟨10.1214/19-AAP1552⟩. ⟨hal-01839335⟩
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