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April 2022 On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms
Jianfeng Lu, Lihan Wang
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Ann. Appl. Probab. 32(2): 1333-1361 (April 2022). DOI: 10.1214/21-AAP1710

Abstract

We establish L2-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincaré-type inequality in time-augmented state space and a standard L2 energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing results.

Funding Statement

This work is supported in part by National Science Foundation via grants CCF-1910571 and DMS-2012286.

Citation

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Jianfeng Lu. Lihan Wang. "On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms." Ann. Appl. Probab. 32 (2) 1333 - 1361, April 2022. https://doi.org/10.1214/21-AAP1710

Information

Received: 1 August 2020; Revised: 1 March 2021; Published: April 2022
First available in Project Euclid: 28 April 2022

Digital Object Identifier: 10.1214/21-AAP1710

Subjects:
Primary: 60J22 , 60J25 , 65C40

Keywords: convergence rate , hypocoercivity , Piecewise deterministic Markov process , Poincaré-type inequality

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.32 • No. 2 • April 2022
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