Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models

Biometrika

Volumn 87, Issue 2, 2000, Pages 371-390

  Ishwaran, Hemant ^a   Zarepour, Mahmoud ^b  

^a LERNER RESEARCH INSTITUTE   (United States)

^b UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Almost sure truncation; Generalised Dirichlet distribution; Mixture of Dirichlet processes; Nonparametric hierarchical model; Normal mean mixture; Random probability measure; Weak convergence in distribution

Indexed keywords

EID: 0001677650     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/87.2.371     Document Type: Article

References (27)

1. ANTONIAK, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2, 1152-74.
2. BLACKWELL, D. & MACQUEEN, J. B. (1973). Ferguson distributions via Polya urn schemes. Ann. Statist. 1, 353-5.
3. CONNOR, R. J. & MOSIMANN, J. E. (1969). Concepts of independence for proportions with a generalization of the Dirichlet distribution. J. Am. Statist. Assoc. 64, 194-206.
4. DANIELS, M. J. (1998). Computing posterior distributions for covariance matrices. In Computing Science and Statistics, 30, Proceedings of the 30th Symposium on the Interface, Ed. S. Weisberg, pp. 192-6. Minneapolis, MN: Computing Science and Statistics.
5. ESCOBAR, M. D. (1994). Estimating normal means with a Dirichlet process prior. J. Am. Statist. Assoc. 89, 268-77.
6. ESCOBAR, M. D. & WEST, M. (1995). Bayesian density estimation and inference using mixtures. J. Am. Statist. Assoc. 90, 577-88.
7. ESCOBAR, M. D. & WEST, M. (1998). Computing nonparametric hierarchical models. In Practical Nonparametric and Semiparametric Bayesian Statistics, Ed. D. Dey, P. Müller and D. Sinha, pp. 1-22. New York: Springer.
8. FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209-30.
9. GUSTAFSON, P. (1997). Large hierarchical Bayesian analysis of multivariate survival data. Biometrics 53, 230-42.
10. HJORT, N. L. (1996). Bayesian approaches to non- and semiparametric density estimation. In Bayesian Statistics 5, Ed. J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, pp. 223-53. Oxford: Oxford University Press.
11. ISHWARAN, H. (1999). Applications of hybrid Monte Carlo to Bayesian generalized linear models: quasi-complete separation and neural networks. J. Comp. Graph. Statist. 8, 779-99.
12. KORWAR, R. & HOLLANDER, M. (1973). Contributions to the theory of Dirichlet processes. Ann. Prob, 1, 705-11.
13. MACEACHERN, S. N. (1994). Estimating normal means with a conjugate style Dirichlet process prior. Commun. Statist. B 23, 727-41.
14. MACEACHERN, S. N. (1998). Computational methods for mixture of Dirichlet process models. In Practical Nonparametric and Semiparametric Bayesian Statistics, Ed. D. Dey, P. Müller and D. Sinha, pp. 23-43. New York: Springer.
15. MACEACHERN, S. N. & MÜLLER, P. (1998). Estimating mixture of Dirichlet process models. J. Comp. Graph. Statist. 7, 223-38.
16. MULIERE, P. & SECCHI, P. (1996). Bayesian nonparametric predictive inference and bootstrap techniques. Ann. Inst. Statist. Math. 48, 663-73.
17. MULIERE, P. & TARDELLA, L. (1998). Approximating distributions of random functionals of Ferguson-Dirichlet priors. Can. J. Statist. 26, 283-97.
18. MULIERE, P. & WALKER, S. (1998). Extending the family of Bayesian bootstraps and exchangeable urn schemes. J. R. Statist. Soc. B 60, 175-82.
19. MÜLLER, P., ERKANLI, A. & WEST, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika 83, 67-79.
20. NEAL, R. M. (1996). Bayesian Learning for Neural Networks. New York: Springer-Verlag.
21. PITMAN, J. & YOR, M. (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Prob. 25, 855-900.
22. ROEDER, K. (1990). Density estimation with confidence sets exemplified by superclusters and voids in the galaxies. J. Am. Statist. Assoc. 85, 617-24.
23. SETHURAMAN, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4, 639-50.
24. WALKER, S. & DAMIEN, P. (1998). Sampling methods for Bayesian nonparametric inference involving stochastic processes. In Practical Nonparametric and Semiparametric Bayesian Statistics, Ed. D. Dey, P. Müller and D. Sinha, pp. 243-54. New York: Springer.
25. WALKER, S. & MULIERE, P. (1997). Beta-Stacy processes and a generalization of the Pólya-urn scheme. Ann. Statist. 25, 1762-80.
26. WALKER, S. & WAKEFIELD, J. (1998). Population models with a nonparametric random coefficient distribution. Sankhyā B 60, 196-214.
27. WEST, M., MÜLLER, P. & ESCOBAR, M. D. (1994). Hierarchical priors and mixture models, with applications in regression and density estimation. In Aspects of Uncertainty: A Tribute to D. V. Lindley, Ed. A. F. M. Smith and P. R. Freeman, pp. 363-86. London: John Wiley.