A Scalable Blocked Gibbs Sampling Algorithm For Gaussian And Poisson Regression Models

TL;DR

This paper presents a scalable blocked Gibbs sampling algorithm tailored for Gaussian and Poisson regression models within a subset of GLMMs, enhancing Bayesian inference for large datasets.

Contribution

It introduces a scalable blocked Gibbs sampler for certain GLMMs, jointly updating variance parameters and random effects, with potential extensions to flexible priors.

Findings

The sampler is scalable for large problems.

It effectively updates variance and effects jointly.

Extensions to flexible priors are discussed.

Abstract

Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these techniques for large problems. We do not develop new sampling methods but instead describe a blocked Gibbs sampler which is sufficiently scalable to accomodate many interesting problems. The sampler we describe applies to a restricted subset of the Generalized Linear Mixed-effects Models (GLMM's); this subset includes Poisson and Gaussian regression models. The blocked Gibbs sampling steps jointly update a prior variance parameter along with all of the random effects underneath it. We also discuss extensions such as flexible prior distributions.