We consider two Bayesian hierarchical one-way random effects models and establish geometric ergodicity of the corresponding random scan Gibbs samplers. Geometric ergodicity, along with a moment condition, guarantees a central limit theorem for sample means and quantiles. In addition, it ensures the consistency of various methods for estimating the variance in the asymptotic normal distribution. Thus our results make available the tools for practitioners to be as confident in inferences based on the observations from the random scan Gibbs sampler as they would be with inferences based on random samples from the posterior.
Bibliographical noteFunding Information:
The second author research was supported by the National Science Foundation DMS-13-10096 and the National Institutes for Health NIBIB R01 EB012547 .
© 2015 Elsevier Inc.
- Geometric ergodicity
- Gibbs sampling
- Markov chain Monte Carlo
- One-way random effects