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ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS

Publication ,  Journal Article
Lu, J; Wang, L
Published in: Annals of Applied Probability
April 1, 2022
Published version (DOI)

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.

Duke Scholars

Jianfeng Lu
Author Jianfeng Lu Mathematics

Published In

Annals of Applied Probability

DOI

10.1214/21-AAP1710

ISSN

1050-5164

Publication Date

April 1, 2022

Volume

32

Issue

2

Start / End Page

1333 / 1361

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Lu, J., & Wang, L. (2022). ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS. Annals of Applied Probability, 32(2), 1333–1361. https://doi.org/10.1214/21-AAP1710
Lu, J., and L. Wang. “ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS.” Annals of Applied Probability 32, no. 2 (April 1, 2022): 1333–61. https://doi.org/10.1214/21-AAP1710.
Lu J, Wang L. ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS. Annals of Applied Probability. 2022 Apr 1;32(2):1333–61.
Lu, J., and L. Wang. “ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS.” Annals of Applied Probability, vol. 32, no. 2, Apr. 2022, pp. 1333–61. Scopus, doi:10.1214/21-AAP1710.
Lu J, Wang L. ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS. Annals of Applied Probability. 2022 Apr 1;32(2):1333–1361.

Published In

Annals of Applied Probability

DOI

10.1214/21-AAP1710

ISSN

1050-5164

Publication Date

April 1, 2022

Volume

32

Issue

2

Start / End Page

1333 / 1361

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics