Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performances, however, there are still relatively few quantitative results on their convergence properties, e.g. 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.

翻译：吉布斯采样器是近似贝叶斯层次模型后验分布的流行算法。尽管其应用广泛且经验表现良好，但其收敛性的定量结果仍相对较少（例如远少于基于梯度的采样方法）。本研究利用贝叶斯渐近理论工具，分析了针对层次模型的吉布斯采样器的总变差混合时间行为。在随机数据生成假设下，我们针对一类具有一般似然函数的两层模型获得了无维收敛结果。具体讨论了高斯、二项式和类别似然函数的实例。