Analysis of the Polya-Gamma block Gibbs sampler for Bayesian logistic linear mixed models

2017/07/31 by Xin Wang, Wang, Xin, Vivekananda Roy +1
Computer Science · Mathematics · #60J05 (Primary) #62F15 (Secondary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1708.00100

openalex publication_date 2017/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Bayesian Analysis of Binary and Polychotomous Response Data
• Convergence analysis of the block Gibbs sampler for Bayesian probit linear mixed models with improper priors

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