Stability of the Gibbs sampler for Bayesian hierarchical models

The Annals of Statistics · 2008 · Volume 36 · Issue 1

Abstract

We characterize the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence can be uniform, geometric or subgeometric depending on the relative tail behavior of the error distributions, and on the parametrization chosen. Our theory is applied to characterize the convergence of the Gibbs sampler on latent Gaussian process models. We indicate how the theoretical framework we introduce will be useful in analyzing more complex models.

Keywords

60J27, 65C05, Bayesian robustness, capacitance, collapsed Gibbs sampler, geometric ergodicity, parametrization, state-space models

Enable JavaScript for citation tools and additional paper interactions.