Randomized Polya tree models for nonparametric Bayesian inference

Statistica Sinica

Volumn 13, Issue 2, 2003, Pages 443-460

  Paddock, Susan M ^a   Ruggeri, Fabrizio ^b   Lavine, Michael ^c   West, Mike ^c  

^a RAND CORPORATION   (United States)

^b CNR   (Italy)

^c DUKE UNIVERSITY   (United States)

Author keywords

Bayesian nonparametrics; Bayesian trees; Partitioning; Polya tree prior; Randomized Polya tree

Indexed keywords

EID: 0038721287     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Best, N., Cowles, M. and Vines, K. (1995). CODA: Convergence diagnosis and output analysis software for Gibbs sampling output. MRC Biostatistics Unit, Institute of Public Health, Cambridge University, Cambridge.
2. Chambers, J. M. (1992). Data for models. In Statistical models in S (Edited by J. Chambers and T. Hastie), 45-94. Wadsworth and Brooks, Belmont, CA.
3. Coifman, R. R. and Donoho, D. L. (1995). Translation-invariant de-noising. In Wavelets and Statistics, Lecture Notes in Statistics 103 (Edited by A. Antoniadis and G. Oppenheim), 125-150. Springer-Verlag, New York.
4. Clogg, C. C., Rubin, D. B., Schenker, N., Schultz, B. and Weidman, L. (1991). Multiple imputation of industry and occupation codes in census public-use samples using Bayesian logistic regression. J. Amer. Statist. Assoc. 86, 68-78.
5. Dubins, L. and Freedman, D. (1967). Random distribution functions. In Proceedings of the Fifth Berkeley Symposium on Mathematics, Statistics and Probability (Edited by L. LeCam and J. Neyman), 183-214. University of California Press, Berkeley/Los Angeles.
6. Ferguson, T. S. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2, 615-629.
7. Gelfand, A. E. and Smith, A. F. M. (1990). Sampling- based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398-409.
8. Gilks, W. R., Richardson, S. and Spiegelhalter, D. J. E. (1996). Markov Chain Monte Carlo in Practice. Chapman and Hall, London.
9. Hanson, T. and Johnson, W. (2002). Modeling regression error with a mixture of Polya trees. J. Amer. Statist. Assoc. 97, 1020-1033.
10. Hartigan, J. (1996). Bayesian histograms (with Discussion). In Bayesian Statistics 5. Proceedings of the Fifth Valencia International Meeting on Bayesian Statistics (Edited by J. M. Bernardo, J. O. Berger, A. P. David and A. F. M. Smith), 211-222. Oxford University Press, Oxford.
11. Kolaczyk, E. D. (1999). Bayesian multiscale models for Poisson processes. J. Amer. Statist. Assoc. 94, 920-933.
12. Lavine, M. (1992). Some aspects of Polya tree distributions for statistical modelling. Ann. Statist. 20, 1222-1235.
13. Lavine, M. (1994). More aspects of Polya tree distributions for statistical modelling. Ann. Statist. 22, 1161-1176.
14. Mauldin, R. and Williams, S. (1990). Reinforced random walks and random distributions. Proc. Amer. Math. Soc. 110, 251-258.
15. Mauldin, R. D., Sudderth, W. D., and Williams, S. C. (1992). Polya trees and random distributions. Ann. Statist. 20, 1203-1221.
16. Müller, P., Erkanli, A. and West, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika 83, 67-79.
17. Paddock, S. M. (1999). Randomized Polya trees: Bayesian nonparametrics for multivariate data analysis. Ph.D. thesis, Duke University, Durham, NC.
18. Paddock, S. M. (2002). Bayesian nonparametric multiple imputation of partially observed data with ignorable nonresponse. Biometrika 89, 529-538.
19. S-Plus (1999). S-Plus 2000 Professional Release 2. MathSoft, Inc.
20. Smith, B. (1999). Bayesian output analysis program (BOA), version 0,4.2 for UNIX S-Plus. Department of Biostatistics, School of Public Health, University of Iowa, Iowa City.
21. Tierney, L. (1994). Markov chains for exploring posterior distributions (with Discussion). Ann. Statist. 22, 1701-1728.