Dimension-free mixing times of Gibbs samplers for Bayesian hierarchical models
研究了贝叶斯分层模型中吉布斯采样器的总变差混合时间，在随机数据生成假设下得到了无维收敛结果，适用于一类广泛的两层模型。
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.