Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model

Journal of Multivariate Analysis

Volumn 67, Issue 2, 1998, Pages 414-430

  Hobert, James P ^a   Geyer, Charles J ^a  

^a NONE

Author keywords

Bayesian model, central limit theorem; drift condition; Markov chain; Monte Carlo; rate of convergence; variance components

Indexed keywords

EID: 0038569359     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1998.1778     Document Type: Article

References (21)

1. Chan K. S. Asymptotic behavior of the Gibbs sampler. J. Amer. Statist. Assoc. 88:1993;320-326.
2. Chan K. S., Geyer C. J. Discussion of "Markov Chains for Exploring Posterior Distributions. Ann. Statist. 22:1994;1747-1757.
3. Gelfand A. E., Smith A. F. M. Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85:1990;398-409.
4. Hobert J. P., Casella G. The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. J. Amer. Statist. Assoc. 91:1996;1461-1473.
5. Hobert J. P., Casella G. Functional compatibility, Markov chains, and Gibbs sampling with improper posteriors. J. Comput. Graph. Statist. 7:1998;42-60.
6. Kass R. E., Steffey D. Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models). J. Amer. Statist. Assoc. 84:1989;717-726.
7. Liu J. S., Wong W. H., Kong A. Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika. 81:1994;27-40.
8. Mengersen K. L., Tweedie R. L. Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24:1996;101-121.
9. Meyn S. P., Tweedie R. L. Markov Chains and Stochastic Stability. 1993;Springer-Verlag, London.
10. Nummelin E. General Irreducible Markov Chains and Non-negative Operators. 1984;Cambridge Univ. Press, London.
11. Roberts G. O., Polson N. G. On the geometric convergence of the Gibbs sampler. J. Roy. Statist. Soc. Ser. B. 56:1994;377-384.
12. Roberts G. O., Rosenthal J. S. Geometric ergodicity and hybrid Markov chains. Elect. Comm. Probab. 2:1997;13-25.
13. Roberts G. O., Rosenthal J. S. Markov chain Monte Carlo: Some practical implications of theoretical results (with discussion). Canad. J. Statist. 26:1998;5-31.
14. Roberts G. O., Sahu S. K. Updating schemes, correlation structure, blocking and parameterization for the Gibbs sampler. J. Roy. Statist. Soc. Ser. B. 59:1997;291-317.
15. Roberts G. O., Tweedie R. L. Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika. 83:1996;95-110.
16. Rosenthal J. S. Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 90:1995a;558-566.
17. Rosenthal J. S. Rates of convergence for Gibbs sampling for variance component models. Ann. Statist. 23:1995b;740-761.
18. Searle S. R., Casella G., McCulloch C. E. Variance Components. 1992;Wiley, New York.
19. Tierney L. Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22:1994;1701-1762.
20. Tierney L., Kass R. E., Kadane J. B. Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Amer. Statist. Assoc. 84:1989;710-716.
21. Wang C. S., Rutledge J. J., Gianola D. Marginal inferences about variance components in a mixed linear model using Gibbs sampling. Genet. Sel. Evol. 25:1993;41-62.