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.
Duke Scholars
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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
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
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