Geometric ergodicity of the Bouncy Particle Sampler

By Alain Oliviero Durmus, Arnaud Guillin, Pierre Monmarch'e. The Annals of Applied Probability, 2018

56 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/53118fc216ba2b5ef95e9dc3bb9289fa3ddbeef0

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Citations in the corpus

Piecewise deterministic Markov processes and their invariant measures (2018, background): “Ergodicity of the BPS is studied in [12], to which we will refer for details on this matter in the following.”