Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 61, Issue 2, 1999, Pages 331-344

  Damien, Paul ^a   Wakefield, Jon ^b   Walker, Stephen ^c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b IMPERIAL COLLEGE SCHOOL OF MEDICINE   (United Kingdom)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Gibbs sampler; Hierarchical model; Latent variable; Non conjugate model

Indexed keywords

EID: 0033481108     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00179     Document Type: Article

References (23)

1. Albert, J. H. and Chib, S. (1993) Bayesian analysis of binary and polychotomous response data. J. Am. Statist. Ass., 88, 669-679.
2. Bennett, J. E., Racine-Poon, A. and Wakefield, J. C. (1996) MCMC for nonlinear hierarchical models. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter), pp. 339-357. London: Chapman and Hall.
3. Besag, J. and Green, P. J. (1993) Spatial statistics and Bayesian computation. J. R. Statist. Soc. B, 55, 25-37.
4. Carlin, B. P. and Poison, N. G. (1992) Monte Carlo Bayesian methods for discrete regression models and categorical time series. In Bayesian Statistics 4 (eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), pp. 577-586. Oxford: Oxford University Press.
5. Chib, S. and Greenberg, E. (1995) Understanding the Metropolis-Hastings algorithm. Am. Statistn, 49, 327-335.
6. Dellaportas, P. and Smith, A. F. M. (1993) Bayesian inference for generalized linear and proportional hazards models via Gibbs sampling. Appl. Statist., 42, 443-459.
7. Devroye, L. (1986) Non-uniform Random Variate Generation. New York: Springer.
8. Edwards, R. G. and Sokal, A. D. (1988) Generalisation of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithms. Phys. Rev. D, 38, 2009-2012.
9. Gilks, W. R., Best, N. G. and Tan, K. K. C. (1995) Adaptive rejection Metropolis sampling within Gibbs sampling. Appl. Statist., 44, 455-472.
10. Gilks, W. R., Neal, R. M., Best, N. G. and Tan, K. K. C. (1997) Corrigendum: Adaptive rejection Metropolis sampling. Appl. Statist., 46, 541-542.
11. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling. Appl. Statist., 41, 337-348.
12. Hastings, W. K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.
13. Higdon, D. (1998) Auxiliary variable methods for Markov chain Monte Carlo with applications. J. Am. Statist. Ass., 93, 585-595.
14. Lindstrom, M. J. and Bates, D. M. (1990) Nonlinear mixed-effects models for repeated-measures data. Biometrics, 46, 673-687.
15. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953) Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087-1091.
16. 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), pp. 297-321. Oxford: Oxford University Press.
17. Robert, C. P. (1995) Simulation of truncated normal variables. Statist. Comput., 5, 121-125.
18. Roberts, G. O., Gelman, A. and Gilks, W. R. (1997) Weak convergence and optimal scalings of random walk Metropolis algorithms. Ann. Appl. Probab., 7, 110-120.
19. Smith, A. F. M. and Roberts, G. O. (1993) Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J. R. Statist. Soc. B, 55, 3-23.
20. Tanner, M. A. and Wong, W. H. (1987) The calculation of posterior distributions by data augmentation (with discussion). J. Am. Statist. Ass., 82, 528-550.
21. Tierney, L. (1994) Markov chains for exploring posterior distributions. Ann. Statist., 22, 1701-1762.
22. Wakefield, J. C., Gelfand, A. E. and Smith, A. F. M. (1991) Efficient generation of random variates via the ratio-of-uniform method. Statist. Comput., 1, 129-133.
23. Wakefield, J. C., Smith, A. F. M., Racine-Poon, A. and Gelfand, A. E. (1994) Bayesian analysis of linear and non-linear population models by using the Gibbs sampler. Appl. Statist., 43, 201-221.