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.

arXiv comment10pages

References in corpus (4)

• General state space Markov chains and MCMC algorithms
• Batch means and spectral variance estimators in Markov chain Monte Carlo
• Convergence properties of Gibbs samplers for Bayesian probit regression with proper priors
• Convergence analysis of the block Gibbs sampler for Bayesian probit linear mixed models with improper priors