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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

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.

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Published In

Annals of Applied Probability

DOI

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

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Chicago
ICMJE
MLA
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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

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