Bayesian nonparametric functional data analysis through density estimation

Biometrika

Volumn 96, Issue 1, 2009, Pages 149-162

  Rodríguez, Abel ^a   Dunson, David B ^b   Gelfand, Alan E ^b  

^a University of California Santa Cruz   (United States)

^b DUKE UNIVERSITY   (United States)

Author keywords

Dependent Dirichlet process; Functional clustering; Nonparametric Bayes inference; Nonparametric regression; Random probability measure

Indexed keywords

EID: 60449108968     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asn054     Document Type: Article

References (29)

1. ALBERT, J. & CHIB, S. (1993). Bayesian analysis of binary and polychotomous response data. J. Am. Statist. Assoc. 88, 669-79.
2. ANTONIAK, C. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2, 1152-74.
3. BASU, S. & CHIB, S. (2003). Marginal likelihood and Bayes factors for Dirichiet process mixture models. J. Am. Statist. Assoc. 98, 224-35.
4. BEHSETA, S., KASS, R. E. & WALLSTROM, G. L. (2005). Hierarchical models for assessing variability among functions. Biometrika 92, 419-34.
5. BUSH, C. A. & MACEACHERN, S. N. (1996). A semiparametric Bayesian model for randomised block designs. Biometrika 83, 275-85.
6. 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.
7. DUNSON, D. (2006). Bayesian dynamic modeling of latent trait distributions. Biostatistics 7, 551-68.
8. DUNSON, D. B., PILLAI, N. & PARK, J.-H. (2007). Bayesian density regression. J. R. Statist. Soc. B 69, 163-83.
9. ESCOBAR, M. D. (1994). Estimating normal means with a Dirichlet process prior. J. Am. Statist. Assoc. 89, 268-77.
10. ESCOBAR, M. D. & WEST, M. (1995). Bayesian density estimation and inference using mixtures. J. Am. Statist. Assoc. 90, 577-88.
11. FAN, J. Q. & YIM, T. H. (2004). A crossvalidation method for estimating conditional densities. Biometrika 91, 819-34.
12. FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209-30.
13. GELFAND, A. E., KOTTAS, A. & MACEACHERN, S. N. (2005). Bayesian nonparametric spatial modeling with Dirichlet process mixing. J. Am. Statist. Assoc. 100, 1021-35.
14. GHOSAL, S., GHOSH, J. & RAMAMOORTHI, R. V. (1999). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143-58.
15. GREEN, P. & RICHARDSON, S. (2001). Modelling heterogeneity with and without the Dirichlet process. Scand. J. Statist. 28, 355-75.
16. GRIFFIN, J. E. & STEEL, M. F. J. (2006). Order-based dependent Dirichlet processes. J. Am. Statist. Assoc. 101, 179-94.
17. ISHWARAN, H. & JAMES, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Am. Statist. Assoc. 96, 161-73.
18. JAIN, S. & NEAL, R. M. (2004). A split-merge Markov chain Monte Carlo procedure for the Dirichlet process mixture model. J. Comp. Graph. Statist. 13, 158-82.
19. MACEACHERN, S. N. (1999). Dependent nonparametric processes. In Proc. Sect. Bayesian Statist. Sci., pp. 50-5. Alexandria, VA: American Statistical Association.
20. MORRIS, J. S. & CARROLL, R. J. (2006). Wavelet-based functional mixed models. J. R. Statist. Soc. B 68, 179-99.
21. MÜLLER, P., ERKANLI, A. & WEST, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika 83, 67-79.
22. MÜLLER, P., QUINTANA, F. & ROSNER, G. (2004). Hierarchical meta-analysis over related non-parametric Bayesian models. J. R. Statist. Soc. B 66, 735-49.
23. PENNELL, M. L. & DUNSON, D. B. (2006). Bayesian semiparametric dynamic frailty models for multiple event time data. Biometrics 62, 1044-52.
24. RAY, S. & MALLICK, B. K. (2006). Functional clustering by Bayesian wavelet methods. J. R. Statist. Soc. B 68, 305-32.
25. RICE, J. A. & SILVERMAN, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Statist. Soc. B 53, 233-43.
26. RODRIGUEZ, A., DUNSON, D. B. & GELFAND, A. E. (2008). The nested Dirichlet process (with discussion). J. Am. Statist. Assoc. 103, 1131-44.
27. SETHURAMAN, J. (1994). A constructive definition of Dirichlet priors. Statist. Sínica 4, 639-50.
28. TEH, Y. W., JORDAN, M. I., BEAL, M. J. & BLEI, D. M. (2006). Sharing clusters among related groups: hierarchical Dirichlet processes. J. Am. Statist. Assoc. 101, 1566-81.
29. WU, H. & ZHANG, J. T. (2002). Local polynomial mixed-effects models for longitudinal data. J. Am. Statist. Assoc. 97, 883-97.