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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
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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