A Scalable Blocked Gibbs Sampling Algorithm For Gaussian And Poisson Regression Models
Venue
arxiv (2016) (to appear)
Publication Year
2016
Authors
Nicholas A Johnson, Frank O. Kuehnel, Ali Nasiri Amini
BibTeX
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.
