Title: Analysis of the Polya-Gamma block Gibbs sampler for Bayesian logistic linear mixed models,
Abstract: In this article, we construct a two-block Gibbs sampler using Polson et al.
(2013) data augmentation technique with Polya-Gamma latent variables for
Bayesian logistic linear mixed models under proper priors. Furthermore, we
prove the uniform ergodicity of this Gibbs sampler, which guarantees the
existence of the central limit theorems for MCMC based estimators.