James P . HOBERT and Jorge

On Reparametrization and the Gibbs Sampler

Gibbs samplers derived under different parametrizations of the target density can have radically different rates of convergence. In this article, we specify conditions under which reparametrization leaves the convergence rate of a Gibbs chain unchanged. An example illustrates how these results can be exploited in convergence rate analyses.

Geometric Ergodicity of Gibbs Samplers for Bayesian General Linear Mixed Models with Proper Priors

When a Bayesian version of the general linear mixed model is created by adopting a conditionally conjugate prior distribution, a simple block Gibbs sampler can be employed to explore the resulting intractable posterior density. In this article it is shown that, under mild conditions that nearly always hold in practice, the block Gibbs Markov chain is geometrically ergodic.

Convergence Analysis of the Gibbs Sampler for Bayesian General Linear Mixed Models with Improper Priors by Jorge

Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple Gibbs sampler that can be employed to explore the posterior density. A popular default among the conditionally conjugate priors is an improper prior that takes a...

Negative Binomial Loglinear Mixed Models

On the Appli ability of Regenerative