Bayesian density regression

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

Volumn 69, Issue 2, 2007, Pages 163-183

  Dunson, David B ^a,b   Pillai, Natesh ^b   Park, Ju Hyun ^c  

^a NATIONAL INSTITUTE OF ENVIRONMENTAL HEALTH SCIENCES   (United States)

^b DUKE UNIVERSITY   (United States)

^c UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Conditional density function; Dirichlet process; Generalized P lya urn; Local smoothing; Mixture model; Nonparametric Bayes method

Indexed keywords

EID: 33847417083     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2007.00582.x     Document Type: Article

References (34)

1. Antoniak, C. E. (1974) Mixtures of Dirichlet processes with application to nonparametric problems. Ann. Statist., 2, 1152-1174.
2. Blackwell, D. and MacQueen, J. B. (1973) Ferguson distributions via Pólya urn schemes. Ann. Statist., 1, 353-355.
3. Cifarelli, D. and Regazzini, E. (1978) Problemi statistici non parametrici in condizioni di scambialbilita parziale e impiego di medie associative. Technical Report. Quaderni Istituto Matematica Finanziaria, Turin.
4. De Iorio, M., Müller, P., Rosner, G. L. and MacEachern, S. N. (2004) An Anova model for dependent random measures. J. Am. Statist. Ass., 99, 205-215.
5. Duan, J. A., Guidani, M. and Gelfand, A. E. (2005) Generalized spatial Dirichlet process models. Discussion Paper 2005-23. Institute of Statistics and Decision Sciences, Duke University, Durham.
6. Dunson, D. B. (2006) Bayesian dynamic modeling of latent trait distributions. Biostatistics, 7, 551-568.
7. Dunson,D. B. and Stanford, J. B. (2005) Bayesian inferences on predictors of conception probabilities. Biometrics, 61, 126-133.
8. Escobar, M. D. and West, M. (1998) Computing nonparametric hierarchical models. In Practical Nonparametric and Semiparametric Bayesian Statistcs (eds D. Dey, P. Müller and D. Sinha), pp. 1-22. New York: Springer.
9. Ferguson, T. S. (1973) A Bayesian analysis of some nonparametric problems. Ann. Statist., 1, 209-230.
10. Ferguson, T. S. (1974) Prior distributions on spaces of probability measures. Ann. Statist., 2, 615-629.
11. Gelfand, A. E., Kottas, A. and MacEachern, S. N. (2005) Bayesian nonparametric spatial modeling with Dirichlet process mixing. J. Am. Statist. Ass., 100, 1021-1035.
12. Giudici, P., Mezzetti, M. and Muliere, P. (2003) Mixtures of Dirichlet process priors for variable selection in survival analysis. J. Statist. Planng Inf., 111, 101-115.
13. Griffin, J. E. and Steel, M. F. J. (2004) Semiparametric Bayesian inference for stochastic frontier models. J. Econometr., 123, 121-152.
14. Griffin, J. E. and Steel, M. F. J. (2006) Order-based dependent Dirichlet processes. J. Am. Statist. Ass., 101, 179-194.
15. Holmes, C. C. and Held, L. (2006) Bayesian auxiliary variable models for binary and multinomial regression. Bayes. Anal., 1, 145-168.
16. Ishwaran, H. and James, L. F. (2001) Gibbs sampling methods for stick-breaking priors. J. Am. Statist. Ass., 96, 161-173.
17. Ishwaran, H. and James, L. F. (2003) Generalized weighted Chinese restaurant processes for species sampling mixture models. Statist. Sin., 13, 1211-1235.
18. Jordan, M. I. and Jacobs, R. A. (1994) Hierarchical mixtures of experts and the EM algorithm. Neur. Computn, 6, 181-214.
19. MacEachern, S. N. (1994) Estimating normal means with a conjugate style Dirichlet process prior. Communs Statist. Simuln Computn, 23, 727-741.
20. MacEachern, S. N. (1999) Dependent nonparametric processes. In Proc. Bayes. Statist. Sci. Sect. Am. Statist. Ass., 50-55.
21. MacEachern, S. N. (2000) Dependent Dirichlet processes. Manuscript. Department of Statistics, Ohio State University, Columbus. Unpublished.
22. MacEachern, S.N. (2001) Decision theoretic aspects of dependent nonparametric processes. In Bayesian Methods with Applications to Science, Policy and Official Statistics (ed. E. George), pp. 551-560. Creta: International Society for Bayesian Analysis.
23. MacEachern, S. N. and Müller, P. (1998) Estimating mixture of Dirichlet process models. J. Computnl Graph. Statist., 7, 223-238.
24. Mira, A. and Petrone, S. (1996) Bayesian hierarchical nonparametric inference for change-point problems. In Bayesian Statistics 5 (eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith). Oxford: Oxford University Press.
25. Muliere, P. and Petrone, S. (1993) A Bayesian predictive approach to sequential search for an optimal dose: parametric and nonparametric models. J. Ital. Statist. Soc., 2, 349-364.
26. Müller, P., Erkanli, A. and West, M. (1996) Bayesian curve fitting using multivariate normal mixtures. Biometrika, 83, 67-79.
27. Müller, P. and Quintana, F. A. (2004) Nonparametric Bayesian data analysis. Statist. Sci., 19, 95-110.
28. Müller, P., Quintana, F. and Rosner, G. (2004) A method for combining inference across related nonparametric Bayesian models. J. R. Statist. Soc. B, 66, 735-749.
29. Serre, D. (2002) Matrices: Theory and Application. New York: Springer.
30. Sethuraman, J. (1994) A constructive definition of the Dirichlet process prior. Statist. Sin., 2, 639-650.
31. Viele, K. and Tong, B. (2002) Modeling with mixtures of linear regressions. Statist. Comput., 12, 315-330.
32. West, M. (1992) Hyperparameter estimation in Dirichlet process mixture model. Discussion Paper 92-03. Institute of Statistics and Decision Sciences, Duke University, Durham.
33. West, M., Müller, P. and Escobar, M. D. (1994) Hierarchical priors and mixture models, with applications in regression and density estimation. In A Tribute to D. V. Lindley (eds A. F. M. Smith and P. R. Freeman). Chichester: Wiley.
34. Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, pp. 233-243. Amsterdam: North-Holland.