  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.
