Inference for mixtures of finite polya tree models

Journal of the American Statistical Association

Volumn 101, Issue 476, 2006, Pages 1548-1565

  Hanson, Timothy E ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Bayesian nonparametric; Binomial regression; Dirichlet process; Generalized linear mixed model; Link function

Indexed keywords

EID: 33846106535     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214506000000384     Document Type: Article

References (61)

1. Albert, J., and Chib, S. (1993), "Bayesian Analysis of Binary and Polychotomous Regression," Journal of the American Statistical Association, 88, 669-679.
2. Antoniak, C. E. (1974), "Mixtures of Dirichlel Processes With Applications to Bayesian Nonparametric Problems," The Annals of Statistics, 2, 1152-1174.
3. Basu, S., and Chib, S. (2003), "Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models," Journal of the American Statistical Association, 98, 224-235.
4. Basu, S., and Mukhopadhyay, S. (2000), "Bayesian Analysis of Binary Regression Using Symmetric and Asymmetric Links," Sankhyã, Ser. B, 62, 372-387.
5. Bedrick, E. J., Christensen, R., and Johnson, W. O. (2000), "Bayesian Accelerated Failure Time Analysis With Application to Veterinary Epidemiology," Statistics in Medicine, 19, 221-237.
6. Berger, J. O., and Guglielmi, A. (2001), "Bayesian Testing of a Parametric Model versus Nonparametric Alternatives," Journal of the American Statistical Association, 96, 174-184.
7. Besag, J., Green, P., Higdon, D., and Mengersen, K. (1995), "Bayesian Computation and Stochastic Systems," Statistical Science, 10, 3-66.
8. Blaekwell, D., and MacQueen, J. B. (1973), "Ferguson Distributions via Polya Urn Schemes," The Annals of Statistics. 2, 353-355.
9. Brown, E. R., and Ibrahim, J. G. (2003), "A Bayesian Semipararnetric Joint Hierarchical Model for Longitudinal and Survival Data," Biometrics, 59, 221-228.
10. Chambers, J. M., Cleveland, S., Kleiner, B., and Tukey, A. P. (1983), Graphical Methods for Data Analysis, Boston: Duxbury.
11. Chen, M.-H., Ibrahim, J. G., and Shao, Q.-M. (2004), "Propriety of the Posterior Distribution and Existence of the MLE for Regression Models With Covariates Missing at Random." Journal of the American Statistical Association, 99, 421-438.
12. Chen, M.-H., and Shao, Q.-M. (2001), "Propriety of Posterior Distribution for Dichotomous Quantile Response Models With General Link Functions," Proceedings of the American Mathematical Society, 129, 293-302.
13. Chib, S. (1995), "Marginal Likelihood From the Gibbs Output," Journal of the American Statistical Association. 90, 1313-1321.
14. Chib, S., and Jeliazkov, I. (2001). "Marginal Likelihood From Metropolis-Hastings Output," Journal of the American Statistical Association, 96, 270-281.
15. Cox, D. R. (1972), "Regression Models and Life-Tables" (with discussion), Journal of the Royal Statistical Society, Ser. B, 34, 187-220.
16. Cox, D. R., and Snell, E. J. (1968). "A General Definition of Residuals" (with discussion), Journal of the Royal Statistical Society, Ser. B, 30, 248-275.
17. Dickey, J. (1971), "The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters," The Annals of Statistics, 42, 204-223.
18. Draper, D. (1999), Discussion on "Bayesian Nonparametric Inference for Random Distributions and Related Functions," by S. G. Walker, P. Damien, P. W. Laud, and A. F. M. Smith, Journal of the Royal Statistical Society. Ser. B, 61, 510-513.
19. Escobar, M. D., and West, M. (1995), "Bayesian Density Estimation and Inference Usine Mixtures," Journal of the American Statistical Association, 90, 577-588.
20. Ferguson, T. S. (1973), "A Bayesian Analysis of Some Nonparametric Problems," The Annals of Statistics, 1, 209-230.
21. Geisser, S., and Eddy, W. (1979), "A Predictive Approach to Model Selection," Journal of the American Statistical Association, 74, 153-160.
22. Gelfand, A. E., and Dey, D. K. (1994), "Bayesian Model Choice: Asymptotics and Exact Calculations," Journal of the Royal Statistical Society, Ser. B, 56, 501-514.
23. Gelfand, A. E., and Smith, A. F. M. (1990), "Sampling Based Approaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.
24. Green, P., and Richardson, S. (2001), "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, 28, 355-375.
25. Han, C., and Carlin, B. P. (2001), "Markov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review," Journal of the American Statistical Association, 96, 1122-1132.
26. Hanson, T. (2006), "Inference for Mixtures of Finite Polya Tree Models," technical report, University of Minnesota School of Public Health, Division of Biostatistics.
27. Hanson, T., and Johnson, W. O. (2002), "Modeling Regression Error With a Mixture of Polya Trees," Journal of the American Statistical Association, 97, 1020-1033.
28. Ibrahim, J. G., Chen, M.-H., and Sinha, D. (2001). Bayesian Survival Analysis, New York: Springer-Verlag.
29. Ishwaran, H., and James, L. F. (2001), "Gibbs Sampling Methods for Stick-Breaking Priors," Journal of the American Statistical Association, 96, 161-173.
30. Ishwaran, H., and Zarepour, M. (2000), "Markov Chain Monte Carlo in Approximate Dirichlet and Beta Two-Parameter Process Hierarchical Models," Biometrika, 87, 371-390.
31. Johnson, W. O., and Christensen, R. (1989), "Nonparametric Bayesian Analysis of the Accelerated Failure Time Model." Statistics and Probability Letters, 8, 179-184.
32. Kadane, J. B., and Lazar, N. A. (2004), "Methods and Criteria for Model Selection," Journal of the American Statistical Association, 99, 279-290.
33. Kass, R. E., and Raftery, A. E. (1995), "Bayes Factors." Journal of the American Statistical Association, 90, 773-795.
34. Kottas, A., and Gelfand, A. E. (2001), "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, 95, 1458-1468.
35. Kraft, C. H. (1964), "A Class of Distribution Function Processes Which Have Derivatives," Journal of Applied Probability, 1, 385-388.
36. Lavine, M. (1992), "Some Aspects of Polya Tree Distributions for Statistical Modeling," The Annals of Statistics, 20, 1222-1235.
37. _ (1994), "More Aspects of Polya Tree Distributions for Statistical Modeling," The Annals of Statistics, 22, 1161-1176.
38. MacEachern, S. N. (2001). "Decision Theoretic Aspects of Dependent Nonparametric Processes," in Proceedings of Bayesian Methods With Applications to Science. Policy, and Official Statistics (ISBA 2000), pp. 351-360.
39. Maksymiuk, A. W., Jett, J. R., Earle, J. D., Su, J. Q., Diegert. F. A., Mailliard, J. A., Kardinal, C. G., Krook, J. E., Veeder, M. H., Wiesenfeld, M., Tschetter, L. K., and Levitt, R. (1994), "Sequencing and Schedule Effects of Cisplatin Plus Etoposide in Small Cell Lung Cancer Results of a North Central Cancer Treatment Group Randomized Clinical Trial," Journal of Clinical Oncology, 12, 70-76.
40. Mallick, B. K., and Gelfand, A. E. (1994), "Generalized Linear Models With Unknown Link Functions," Biometrika, 81, 237-245.
41. Mallick, B. K., and Walker, S. G. (2003), "A Bayesian Semiparametric Transformation Model Incorporating Frailties," Journal of Statistical Planning and Inference, 112, 159-174.
42. Mauldin, R. D., Sudderth, W. D., and Williams, S. C. (1992), "Polya Trees and Random Distributions," The Annals of Statistics, 20, 1203-1221.
43. McCullagh, P., and Neider, J. A. (1989), Generalized Linear Models (2nd ed.), London: Chapman & Hall.
44. McMillan, G. P. (2001), "Ache Residential Grouping and Social Foraging," unpublished doctoral dissertation, University of New Mexico, Dept. of Anthropology.
45. Müller, P., Erkanli, A., and West, M. (1996), "Bayesian Curve Fitting Using Multivariate Normal Mixtures," Biometrika, 83, 67-79.
46. Müller, P., and Quintana, F. A. (2004), "Nonparametric Bayesian Data Analysis," Statistical Science, 19, 95-110.
47. Neal, R. M. (2003), "Slice Sampling" (with discussion), The Annals of Statistics, 31, 705-767.
48. Nelson, W. (1972), "Theory and Applications of Hazard Plotting for Censored Failure Data," Technometrics, 14, 945-965.
49. Newton, M. A., Czado, C., and Chappell, R. (1996), "Bayesian Inference for Semiparametric Binary Regression," Journal of the American Statistical Association, 91, 142-153.
50. Paddock, S. M., Ruggeri, F., Lavine, M., and West, M. (2003), "Randomized Polya Tree Models for Nonparametric Bayesian Inference," Statistica Sinica, 13, 443-460.
51. Richardson, S., and Green, P. (1997), "On Bayesian Analysis of Mixtures With an Unknown Number of Components," Journal of the Royal Statistical Society, Ser. B, 59, 731-792.
52. Roeder, K., and Wasserman, L. (1997), "Practical Bayesian Density Estimation Using Mixtures of Normals," Journal of the American Statistical Association, 92, 894-902.
53. Sethuraman, J. (1994), "A Constructive Definition of the Dirichlet Prior," Statistica Sinica, 4, 639-650.
54. Spiegelhalter, D., Thomas, A., Best, N., and Lunn, D. (2003), WinBUGS 1.4 User Manual, Cambridge, U.K.: MRC Biostatistics Unit, available at http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml.
55. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions," The Annals of Statistics, 22, 1701-1762.
56. Verdinelli, I., and Wasserman, L. (1995), "Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio," Journal of the American Statistical Association, 90, 614-618.
57. Walker, S. G., Damien, P., Laud, P. W., and Smith, A. F. M. (1999), "Bayesian Nonparametric Inference for Random Distributions and Related Functions," Journal of the Royal Statistical Society, Ser. B, 61, 509.
58. Walker, S. G., and Mallick, B. K. (1997), "Hierarchical Generalized Linear Models and Frailty Models With Bayesian Nonparametric Mixing," Journal of the Royal Statistical Society, Ser. B, 59, 845-860.
59. _ (1999), "Semiparametric Accelerated Life Time Model," Biometrics, 55, 477-483.
60. Yang, S. (1999), "Censored Median Regression Using Weighted Empirical Survival and Hazard Functions," Journal of the American Statistical Association, 94, 137-145.
61. Ying, Z., Jung, S. H., and Wei, L. J. (1995), "Survival Analysis With Median Regression Models," Journal of the American Statistical Association, 90, 178-184.