JRSSB Jan 14, 2026

Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models

Authors
Giacomo Zanella Filippo Ascolani Gareth O Roberts
Research Topics
High-Dimensional Statistics Bayesian Statistics
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Paper Information
  • Journal:
    Journal of the Royal Statistical Society Series B
  • DOI:
    10.1093/jrsssb/qkaf084
  • Published:
    January 14, 2026
  • Added to Tracker:
    Feb 10, 2026
Abstract

Abstract We study general coordinate-wise Markov chain Monte Carlo schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding (potentially not implementable) random scan Gibbs sampler through the notion of conditional conductance. This allows us to study the performances of popular Metropolis-within-Gibbs schemes for non-conjugate hierarchical models, in high-dimensional regimes where both number of datapoints and parameters increase. Given random data-generating assumptions, we establish dimension-free convergence results, which are in close accordance with numerical evidences. Application to Bayesian models for binary regression with unknown hyperparameters is also discussed. Motivated by such statistical applications, auxiliary results of independent interest on approximate conductances and perturbation of Markov operators are provided.

Author Details
Giacomo Zanella
Author
Filippo Ascolani
Author
Gareth O Roberts
Author
Research Topics & Keywords
High-Dimensional Statistics
Research Area
Bayesian Statistics
Research Area
Citation Information
APA Format
Giacomo Zanella , Filippo Ascolani & Gareth O Roberts (2026) . Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models. Journal of the Royal Statistical Society Series B , 10.1093/jrsssb/qkaf084.
BibTeX Format
@article{paper832,
  title = { Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models },
  author = { Giacomo Zanella and Filippo Ascolani and Gareth O Roberts },
  journal = { Journal of the Royal Statistical Society Series B },
  year = { 2026 },
  doi = { 10.1093/jrsssb/qkaf084 },
  url = { https://doi.org/10.1093/jrsssb/qkaf084 }
}
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