A class of mixtures of dependent tail-free processes

Biometrika

Volumn 98, Issue 3, 2011, Pages 553-566

  Jara, A ^a   Hanson, T E ^b  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Bayesian nonparametrics; Median regression; Partial exchangeability; Polya tree; Related probability distribution

Indexed keywords

EID: 80052295157     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asq082     Document Type: Article

References (39)

1. CHRISTENSEN, R. (2002). Plane Answers to Complex Questions: The Theory of Linear Models, 3rd ed. New York: Springer.
2. CHUNG, Y. & DUNSON, D. B. (2009). Nonparametric Bayes conditional distribution modeling with variable selection. J. Am. Statist. Assoc. 104, 1646-60.
3. DE IORIO, M., JOHNSON, W. O., MÜLLER, P. & ROSNER, G. L. (2009). Bayesian nonparametric non-proportional hazards survival modelling. Biometrics 65, 762-71.
4. DE IORIO, M., MÜLLER, P., ROSNER, G. L. & MACEACHERN, S. N. (2004). An ANOVA model for dependent random measures. J. Am. Statist. Assoc. 99, 205-15. (Pubitemid 38545207)
5. DUBINS, L. E. & FREEDMAN, D. A. (1967). Random distribution functions. In Proc. Fifth Berkeley Symp. Math. Statist. Prob., Statistical Laboratory, University of California, Berkeley, USA, between June 21 and July 18, 1965, and between December 27, 1965, and January 7, 1966, Vol 2, pp. 183-214.
6. DUNSON, D. B., PILLAI, N. & PARK, J. H. (2007). Bayesian density regression. J. R. Statist. Soc. B 69, 163-183.
7. ESCOBAR, M. D. & WEST, M. (1995). Bayesian density estimation and inference using mixtures. J. Am. Statist. Assoc. 90, 577-88.
8. FABIUS, J. (1964). Asymptotic behavior of Bayes' estimates. Ann. Math. Statist. 35, 846-56.
9. FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209-30.
10. FERGUSON, T. S. (1974). Prior distribution on the spaces of probability measures. Ann. Statist. 2, 615-29.
11. FREEDMAN, D. (1963). On the asymptotic distribution of Bayes' estimates in the discrete case. Ann. Math. Statist. 34, 1386-403.
12. GAMERMAN, D. (1997). Sampling from the posterior distribution in generalized linear mixed models. Statist. Comput. 7, 57-68.
13. GEISSER, S. & EDDY, W. (1979). A predictive approach to model selection. J. Am. Statist. Assoc. 74, 153-60.
14. GELFAND, A. E. & KOTTAS, A. (2002). A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. J. Comput. Graph. Statist. 11, 289-304.
15. MACEACHERN, S. N., GELFAND, A. E., KOTTAS, A. (2005). Bayesian nonparametric spatial modeling with Dirichlet process mixing. J. Am. Statist. Assoc. 100, 1021-35. (Pubitemid 41276346)
16. GELMAN, A., JAKULIN, A., PITTAU, M. G. & SU, Y. S. (2008). A default prior distribution for logistic and other regression models. Ann. Appl. Statist. 2, 1360-83.
17. GHOSH, J. K. & RAMAMOORTHI, R. V. (2003). Bayesian Nonparametrics. New York, USA: Springer.
18. GRIFFIN, J. E. & STEEL, M. F. J. (2006). Order-based dependent Dirichlet processes. J. Am. Statist. Assoc. 101, 179-94. (Pubitemid 43500034)
19. GRIFFIN, J. E. & STEEL, M. F. J. (2010). Bayesian nonparametric modelling with the Dirichlet process regression smoother. Statist. Sinica 20, 1507-27.
20. HANSON, T. (2006). Inference for mixtures of finite Polya tree models. J. Am. Statist. Assoc. 101, 1548-65.
21. HOLMES, C. C. & HELD, L. (2006). Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Anal. 1, 145-68.
22. ISAACS, D., ALTMAN, D. G., TIDMARSH, C. E., VALMAN, H. B. & WEBSTER, A. D. B. (1983). Serum immunoglobulin concentrations in preschool children measured by laser nephelometry: reference ranges for IgG, IgA, IgM. J. Clin. Pathol. 36, 1193-1196. (Pubitemid 14229111)
23. JARA, A. (2007). Applied Bayesian non-and semi-parametric inference using DPpackage. Rnews 7, 17-26.
24. JARA, A., LESAFFRE, E., DE IORIO, M. & QUINTANA, F. A. (2010). Bayesian semiparametric inference for multivariate doubly-interval-censored data. Ann. Appl. Statist. 4, 2126-49.
25. JOHNSON, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika 36, 149-76.
26. KAPITULA, L. R. & BEDRICK, E. J. (2005). Diagnostics for the exponential normal growth curve model. Statist. Med. 24, 95-108. (Pubitemid 40074067)
27. KRAFT, C. M. (1964). A class of distribution function processes which have derivatives. J. Appl. Probabil. 1, 385-88.
28. KUO, L. & MALLICK, B. (1998). Variable selection for regression models. Sankya B 60, 65-81.
29. MACEACHERN, S. N. (1999). Dependent nonparametric processes. In ASA Proc. Section on Bayesian Statist. Sci. Alexandria, VA. American Statistical Association.
30. METIVIER, M. (1971). Sur la construction de mesures aléatoires presque sûrement absolument continues par rapport à une mesure donnée. Z. Wahrs. verw. Geb. 20, 332-4.
31. MULIERE, P. & TARDELLA, L. (1998). Approximating distributions of random functionals of Ferguson-Dirichlet priors. Can. J. Statist. 26, 283-97. (Pubitemid 128187208)
32. MÜLLER, P., ERKANLI, A. & WEST, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika 83, 67-79.
33. ROYSTON, P. & WRIGHT, E. M. (1998). A method for estimation age-specific reference intervals ('normal ranges') based on fractional polynomials and exponential transformation. J. R. Statist. Soc. A 161, 79-101. (Pubitemid 128371556)
34. SETHURAMAN, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 2, 639-50.
35. SMITH, M. S. & KOHN, R. (1996). Nonparametric regression using Bayesian variable selection. J. Economet. 75, 317-44.
36. TOKDAR, S. T., ZHU, Y. M. & GHOSH, J. K. (2010). Bayesian density regression with logistic Gaussian process and subspace projection. Bayesian Anal. 5, 1-26.
37. VILLANI, M., KOHN, R. & GIORDANI, P. (2009). Regression density estimation using smooth adaptive Gaussian mixtures. J. Economet. 153, 155-173.
38. WANG, Y. & TAYLOR, J. M. G. (2001). Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. J. Am. Statist. Assoc. 96, 895-905.
39. ZELLNER, A. (1983). Applications of Bayesian analysis in econometrics. Statistician 32, 23-34.