Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models

Alicia A. Johnson and Galin L. Jones

Journal of Multivariate Analysis, 2015, vol. 140, issue C, 325-342

Abstract: 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.

Keywords: Markov chain Monte Carlo; Convergence; Gibbs sampling; Geometric ergodicity; One-way random effects (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2015.06.002

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