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

• 成果类型: Article
• 署名作者: Ascolani, Filippo; Roberts, Gareth O.; Zanella, Giacomo
• 署名单位: Duke University; University of Warwick; Bocconi University; Bocconi University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkaf084
• 发表日期: 2026-09
• 页码: 1231-1250
• 关键词: CONVERGENCE PROPERTIES; geometric ergodicity; markov-chains; sampler; complexity; hastings; rates; computation; algorithm

摘要

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.