We study general coordinate-wise MCMC 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) 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. Applications to Bayesian models for binary regression with unknown hyperparameters and discretely observed diffusions are also discussed. Motivated by such statistical applications, auxiliary results of independent interest on approximate conductances and perturbation of Markov operators are provided.

翻译：我们研究通用的逐坐标MCMC方案（例如Metropolis-within-Gibbs采样器），这些方案常用于拟合非共轭贝叶斯分层模型。通过条件电导的概念，我们将此类方案的收敛特性与相应的（可能无法实施的）Gibbs采样器的收敛特性建立联系。这使我们能够研究在数据点数量和参数同时增加的高维情形下，流行Metropolis-within-Gibbs方案在非共轭分层模型中的表现。基于随机数据生成假设，我们建立了与数值实验结果高度吻合的无维数收敛性结论。还讨论了其在未知超参数二元回归模型与离散观测扩散过程等贝叶斯模型中的应用。受此类统计应用启发，本文还提供了关于近似电导与马尔可夫算子摄动的独立辅助性结果。