DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS
Publication
, Journal Article
Ascolani, F; Zanella, G
Published in: Annals of Statistics
June 1, 2024
Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performance, however, there are still relatively few quantitative results on their convergence properties, for example, much less than for gradient-based sampling methods. In this work, we analyse the behaviour of total variation mixing times of Gibbs samplers targeting hierarchical models using tools from Bayesian asymptotics. We obtain dimension-free convergence results under random data-generating assumptions for a broad class of two-level models with generic likelihood function. Specific examples with Gaussian, binomial and categorical likelihoods are discussed.
Duke Scholars
Published In
Annals of Statistics
DOI
EISSN
2168-8966
ISSN
0090-5364
Publication Date
June 1, 2024
Volume
52
Issue
3
Start / End Page
869 / 894
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1403 Econometrics
- 0104 Statistics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Ascolani, F., & Zanella, G. (2024). DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS. Annals of Statistics, 52(3), 869–894. https://doi.org/10.1214/24-AOS2367
Ascolani, F., and G. Zanella. “DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS.” Annals of Statistics 52, no. 3 (June 1, 2024): 869–94. https://doi.org/10.1214/24-AOS2367.
Ascolani F, Zanella G. DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS. Annals of Statistics. 2024 Jun 1;52(3):869–94.
Ascolani, F., and G. Zanella. “DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS.” Annals of Statistics, vol. 52, no. 3, June 2024, pp. 869–94. Scopus, doi:10.1214/24-AOS2367.
Ascolani F, Zanella G. DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS. Annals of Statistics. 2024 Jun 1;52(3):869–894.
Published In
Annals of Statistics
DOI
EISSN
2168-8966
ISSN
0090-5364
Publication Date
June 1, 2024
Volume
52
Issue
3
Start / End Page
869 / 894
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1403 Econometrics
- 0104 Statistics
- 0102 Applied Mathematics