Fitting Bayesian multiple random effects models

Statistics and Computing

Volumn 6, Issue 4, 1996, Pages 337-346

  Vines, S K ^a   Gilks, W R ^b   Wild, P ^c  

^a OPEN UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c INSTITUT NATIONAL DE RECHERCHE ET DE SÉCURITÉ   (France)

Author keywords

Bayesian inference; Convergence; Gibbs sampling; Longitudinal data; Markov chain Monte Carlo; Parametric transformation; Random effect; Rubella antibody

Indexed keywords

EID: 21444459350     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00143554     Document Type: Article

References (27)

1. Besag, J. and Green, P. J. (1993) Spatial statistics and Bayesian computation, Journal of the Royal Statistical Society B, 55, 25-37.
2. Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9-25.
3. Casella, G. and George, E. I. (1992) Explaining the Gibbs sampler, The American Statistician, 46, 167-74.
4. Coursaget, P., Yvonnet, P., Gilks, W. R., Wang, C. C., Day, N. E., Chiron, J-P. and Diop-Mar, I. (1991) Scheduling of revaccinations against Hepatitis B virus, The Lancet, 337, 1180-83.
5. Dellaportas, P. and Smith, A. F. M. (1993) Bayesian inference for generalised linear and proportional hazards models via Gibbs sampling, Applied Statistics, 42, 443-59.
6. 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.
7. Gelfand, A. E., Sahu, S. K. and Carlin, B. P. (1994) Efficient parametrizations for normal linear mixed models, Technical Report 94-01, Department of Statistics, University of Connecticut.
8. Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-41.
9. Gilks, W. R. (1992) Derivative-free adaptive rejection sampling for Gibbs sampling. In J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (eds) Bayesian Statistics 4 pp. 641-49, Oxford: University Press.
10. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling, Applied Statistics, 41, 337-48.
11. Gilks, W. R., Clayton, D. G., Spiegelhalter, D. J., Best, N. G., McNeil, A. J., Sharples, L. D. and Kirby, A. J. (1993a) Modelling complexity: applications of Gibbs sampling in medicine, Journal of the Royal Statistical Society B, 55, 39-52.
12. Gilks, W. R., Wang, C. C., Coursaget, P. and Yvonnet, B. (1993b) Random effects models for longitudinal data using Gibbs sampling, Biometrics, 49, 441-53.
13. Gilks, W. R., Thomas, A. and Spiegelhalter, D. J. (1994) A language and program for complex Bayesian modelling. The Statistician, 43, 169-77.
14. Goldstein, H. (1986) Multilevel mixed linear model analysis using iterative generalized least squares, Biometrika, 73, 43-56.
15. Goldstein, H. (1991) Nonlinear multilevel models, with an application to discrete response data, Biometrika, 78, 45-51.
16. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chain and their applications. Biometrika, 57, 97-109.
17. Hills, S. E. and Smith, A. F. M. (1992) Parameterisation issues in Bayesian inference. In J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (eds) Bayesian Statistics 4 pp. 227-46, Oxford: University Press.
18. Laird, N. M. and Ware, J. H. (1982) Random-effects models for longitudinal data, Biometrics, 38, 963-74.
19. Liang, K. Y. and Zeger, S. L. (1986) Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22.
20. Lindley, D. V. and Smith, A. F. M. (1972) Bayes estimates for the linear model, Journal of the Royal Statistical Society B, 34, 1-19.
21. Morrison, D. F. (1967) Multivariate Statistical Methods, pp. 86-8, McGraw-Hill.
22. Raftery, A. E. and Lewis, S. M. (1992a) How many iterations in the Gibbs Sampler? In J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (eds) Bayesian Statistics 4 pp. 763-73, Oxford: University Press.
23. Raftery, A. E. and Lewis, S. M. (1992b) One long run with diagnostics: implementation strategies for Markov chain Monte Carlo. Comment to Gelman, A. and Rubin, D. B. (1992) Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457-72.
24. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods, Journal of the Royal Statistical Society B, 55, 3-23.
25. Spiegelhalter, D., Thomas, A., Best, N. and Gilks, W. (1995) BUGS: Bayesian inference using Gibbs sampling, Version 0.50. MRC Biostatistics Unit, Cambridge.
26. Thomas, A., Spiegelhalter, D. J. and Gilks, W. R. (1992) BUGS: a Program to perform Bayesian inference using Gibbs sampling. In J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (eds) Bayesian Statistics 4 pp. 837-42, Oxford: University Press.
27. Wakefield, J. C., Smith, A. F. M., Racine-Poon, A. and Gelfand, A. E. (1994) Bayesian analysis of linear and non-linear population models using the Gibbs sampler, Applied Statistics, 43, 201-21.