DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS

• 成果类型: Article
• 署名作者: Ascolani, Filippo; Zanella, Giacomo
• 署名单位: Duke University; Bocconi University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2367
• 发表日期: 2024
• 页码: 869-894
• 关键词: COMPUTATIONAL-COMPLEXITY; markov-chains; CONVERGENCE; mcmc; rates; algorithm; Finite

摘要

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.