Block Gibbs samplers for logistic mixed models: Convergence properties and a comparison with full Gibbs samplers

Rao, Yalin; Roy, Vivekananda

doi:10.1214/21-ejs1930

Cited by 3 publications

(6 citation statements)

References 28 publications

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“…Recently, DA algorithms have been developed and studied for Bayesian GLMMs (Wang and Roy, 2018b;Polson et al, 2013;Wang and Roy, 2018a;Rao and Roy, 2021). In this section, we propose DA algorithms for simulating from (7) corresponding to the probit and logistic mixed models.…”

Section: Data Augmentation For Glmmsmentioning

confidence: 99%

“…But, we do not pursue the use of improper priors here. Interested readers may look at Wang and Roy (2018b) and Rao and Roy (2021). On the other hand, if improper priors are used, then the posterior density ( 29) is not guaranteed to be proper.…”

Section: Mcmc For Bayesian Glmmsmentioning

confidence: 99%

“…4: Draw β (n) ∼ (40) with w = w (n) and u = u (n) . Rao and Roy (2021) also construct an efficient two-block Gibbs sampler with the two blocks being η and (w, λ). From (39), the conditional density of η given λ, w, y is given by…”

Section: Data Augmentation For Bayesian Logistic Mixed Modelsmentioning

confidence: 99%

“…A comparison of the full Gibbs sampler (Algorithm 11) and the block Gibbs sampler (Algorithm 11) in the context of some numerical examples as the dimensions of the design matrices vary can be found in Rao and Roy (2021).…”

Section: Algorithm 12mentioning

confidence: 99%

“…For example, effective data augmentation (DA) strategies have been proposed for specific GLMMs (see e.g. Wang and Roy, 2018b;Polson et al, 2013;Wang and Roy, 2018a;Rao and Roy, 2021). Also novel MH algorithms based on Langevin diffusions and Hamiltonian dynamics such as the Metropolis adjusted Langevin algorithms (MALA) (Roberts and Tweedie, 1996) and the Hamiltonian Monte Carlo (HMC) algorithms (Neal, 2011) have now emerged as the popular methods for MCMC sampling due to their ability to make distant moves with high acceptance probability and favorable scalability with respect to increasing state space dimensions.…”

Section: Introductionmentioning

confidence: 99%

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MCMC for GLMMs

Roy¹

2022

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Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not possible for GLMMs. Since the likelihood is not available in a closed-form, the associated posterior densities in Bayesian GLMMs are also intractable. Generally, Markov chain Monte Carlo (MCMC) algorithms are used for conditional simulation in GLMMs and exploring these posterior densities. In this article, we present different state of the art MCMC algorithms for fitting GLMMs. These MCMC algorithms include efficient data augmentation strategies, as well as diffusions based and Hamiltonian dynamics based methods. The Langevin and Hamiltonian Monte Carlo methods presented here are applicable to any GLMMs, and are illustrated using three most popular GLMMs, namely, the logistic and probit GLMMs for binomial data and the Poisson-log GLMM for count data. We also present efficient data augmentation algorithms for probit and logistic GLMMs.

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Section: Data Augmentation For Glmmsmentioning

confidence: 99%

Section: Mcmc For Bayesian Glmmsmentioning

confidence: 99%

Section: Data Augmentation For Bayesian Logistic Mixed Modelsmentioning

confidence: 99%

Section: Algorithm 12mentioning

confidence: 99%