On explicit $L^2$-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms
Publication
, Journal Article
Lu, J; Wang, L
Published in: Ann. Appl. Probab. 32(2): 1333-1361 (April 2022)
July 29, 2020
We establish $L^2$-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 Poincar\'{e}-type inequality in time-augmented state space and a standard $L^2$ energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing results.
Duke Scholars
Published In
Ann. Appl. Probab. 32(2): 1333-1361 (April 2022)
Publication Date
July 29, 2020
Citation
APA
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Lu, J., & Wang, L. (2020). On explicit $L^2$-convergence rate estimate for piecewise deterministic
Markov processes in MCMC algorithms. Ann. Appl. Probab. 32(2): 1333-1361 (April 2022).
Lu, Jianfeng, and Lihan Wang. “On explicit $L^2$-convergence rate estimate for piecewise deterministic
Markov processes in MCMC algorithms.” Ann. Appl. Probab. 32(2): 1333-1361 (April 2022), July 29, 2020.
Lu J, Wang L. On explicit $L^2$-convergence rate estimate for piecewise deterministic
Markov processes in MCMC algorithms. Ann Appl Probab 32(2): 1333-1361 (April 2022). 2020 Jul 29;
Lu, Jianfeng, and Lihan Wang. “On explicit $L^2$-convergence rate estimate for piecewise deterministic
Markov processes in MCMC algorithms.” Ann. Appl. Probab. 32(2): 1333-1361 (April 2022), July 2020.
Lu J, Wang L. On explicit $L^2$-convergence rate estimate for piecewise deterministic
Markov processes in MCMC algorithms. Ann Appl Probab 32(2): 1333-1361 (April 2022). 2020 Jul 29;
Published In
Ann. Appl. Probab. 32(2): 1333-1361 (April 2022)
Publication Date
July 29, 2020