Approximate predetermined convergence properties of the gibbs sampler

Journal of Computational and Graphical Statistics

Volumn 10, Issue 2, 2001, Pages 216-229

  Roberts, Gareth O ^a   Sahu, Sujit K ^b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Em algorithm; Gaussian distribution; Generalized linear models; Hierarchical centering; Laplace approximation; Markov chain Monte Carlo

Indexed keywords

EID: 0035609585     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1198/10618600152627915     Document Type: Article

References (25)

1. Bernardo, J. M., and Smith, A. F. M. (1994), Bayesian Theory, Chichester: Wiley.
2. Breslow, N. E., and Clayton, D. G. (1993), “ApproximateInference in GeneralizedLinearMixedModels,” Journal of the American Statistical Association, 88, 9-25.
3. Crowder, M. J. (1978), “Beta-binomial ANOVA for Proportions,” Applied Statistics, 27, 34-37.
4. Dellaportas, P., and Smith, A. F. M. (1993), “Bayesian Inference for Generalised Linear andProportionalHazards Models via Gibbs Sampling,” Applied Statistics, 42, 443-459.
5. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977) “MaximumLikelihoodFrom Incomplete Data via the EM Algorithm” (with discussion), Journal of the Royal Statistical Society, Ser. B, 39, 1-38.
6. Garren, S., and Smith, R. L. (2000), “Estimating the Second Largest Eigenvalue of a Markov Transition Matrix,” Bernoulli, 6, 215-242.
7. Gaver, D. P., and O’Muircheartaigh, I. G. (1987), “RobustEmpirical Bayes Analysis ofEventRates,” Technomet rics., 29, 1-15.
8. Gelfand, A. E., Sahu, S. K., and Carlin, B. P. (1996), “Efficient Parametrizations for Generalised Linear Mixed Models” (with discussion), in Bayesian Statistics 5, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford: Oxford University Press, pp. 165-180.
9. Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical association, 85, 398-409.
10. Green, P. J., and Han, X-L. (1992), “Metropolis Methods, Gaussian Proposals, and Antithetic Variables,” in StochasticModels, Statistical Methods and Algorithms in Image Analysis, Lecture Notes on Statistics, 74, Berlin: Springer-Verlag, pp. 142-164.
11. Hills, S. E., and Smith, A. F. M. (1993), “Diagnostic Plots for Improved Parametrization in Bayesian Inference,” Biometrika, 80, 61-74.
12. Jacka, S. D., and Roberts, G. O. (1997), “On Strong Forms ofWeak Convergence,” StochasticProcesses and Their Applications, 67, 41-53.
13. Knuiman, M. W., and Speed, T. P. (1988), “Incorporating Prior Information into the Analysis of Contingency Tables,” Biometrics, 44, 1061-1071.
14. Meng, X-L., and van Dyk, D. (1997), “The EM Algorithm-An Old Folk-Song Sung to a Fast New Tune” (with discussion), Journal of the Royal Statistical Society, Ser. B, 59, 511-567.
15. Polson, N. G. (1996), “Convergence of Markov Chain Monte Carlo Algorithms,” in Bayesian Statistics 5, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith. Oxford: Oxford University Press, pp. 297-321.
16. Roberts, G. O., Rosenthal, J. S., andSchwartz, P. O. (1998), “ConvergencePropertiesofPerturbedMarkovChains,” Journalof Applied Probability, 35, 1-11.
17. Roberts, G. O., and Sahu, S. K. (1997), “Updating Schemes, CorrelationStructure, Blocking and Parameterisation for the Gibbs Sampler,” Journal of the Royal Statistical Society, Ser. B, 59, 291-317.
18. Roberts, G. O., and Smith, A. F. M. (1994), “Simple Conditions for the Convergence of the Gibbs Sampler and Metropolis-Hastings Algorithms,” Stochastic Processes and TheirApplications, 49, 207-216.
19. Roberts, G. O., and Tweedie, R. L. (1999), “Bounds on Regeneration Times and Convergence Rates for Markov Chains,” Stochastic Processes and Their Applications, 80, 211-229.
20. Rosenthal, J. S. (1995), “MinorizationConditions and Convergence Rates for Markov Chain Monte Carlo,” Journal of the American Statistical Association, 90, 558-566.
21. Sahu, S. K. (2000), Discussion ofDurbin and Koopman, Journal of the Royal Statistical Society, Ser. B, 62, 35-36.
22. Sahu, S. K., and Roberts, G. O. (1999) “On Convergence of the EM Algorithm and the Gibbs Sampler,” Statistics in Computing, 9, 55-64.
23. Spiegelhalter, D. J., Thomas, A., and Best, N. G. (1996), “Computation on Bayesian Graphical Models,” in Bayesian Statistics 5, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford: Oxford University Press, pp. 407-426.
24. Thall, P. F., and Vail, S. C. (1990), “Some Covariance Models for Longitudinal and Count Data with Overdisper sion,” Biometrics, 46, 657-671.
25. Tierney, L. (1994), “Markov Chains for Exploring Posterior Distributions” (with discussion), The Annals of Statistics, 22, 1701-1762