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

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  • Wang, Xin
  • Roy, Vivekananda

Abstract

In this article, we construct a two-block Gibbs sampler using Polson et al.’s (2013) data augmentation technique for Bayesian logistic linear mixed models under proper priors. Furthermore, we prove the uniform ergodicity of this Gibbs sampler.

Suggested Citation

  • Wang, Xin & Roy, Vivekananda, 2018. "Analysis of the Pólya-Gamma block Gibbs sampler for Bayesian logistic linear mixed models," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 251-256.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:251-256
    DOI: 10.1016/j.spl.2018.02.003
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    References listed on IDEAS

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    1. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623, September.
    2. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    3. Gareth O. Roberts & Jeffrey S. Rosenthal, 2001. "Markov Chains and De‐initializing Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 489-504, September.
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