Hypocoercivity of Piecewise Deterministic Markov Process-Monte Carlo

Christophe Andrieu (1) , Alain Durmus (2) , Nikolas Nüsken (3) , Julien Roussel (4, 5)

1 School of Mathematics [Bristol]
2 CB - CB - Centre Borelli - UMR 9010
3 Institut für Mathematik [Potsdam]
4 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
5 MATHERIALS - MATHematics for MatERIALS

In this paper we derive spectral gap estimates for several Piecewise Deterministic Markov Processes, namely the Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler. The hypocoercivity technique we use, presented in (Dolbeault et al., 2015), produces estimates with explicit dependence on the parameters of the dynamics. Moreover the general framework we consider allows to compare quantitatively the bounds found for the different methods.

Domaines: Calcul [stat.CO]; Analyse numérique [math.NA]

Christophe Andrieu, Alain Durmus, Nikolas Nüsken, Julien Roussel. Hypocoercivity of Piecewise Deterministic Markov Process-Monte Carlo. The Annals of Applied Probability, 2021, ⟨10.1214/20-AAP1653⟩. ⟨hal-01941467⟩