Bayesian Nonparametric Modeling and Data Analysis: An Introduction

Handbook of Statistics

Volumn 25, Issue , 2005, Pages 245-278

  Hanson, Timothy E ^a   Branscum, Adam J ^a   Johnson, Wesley O ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649364226     PISSN: 01697161     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-7161(05)25009-5     Document Type: Review

References (106)

1. Antoniak C.E. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2 (1974) 1152-1174
2. Barron A., Schervish M., and Wasserman L. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 (1999) 536-561
3. Bedrick E.J., Christensen R., and Johnson W.O. A new perspective on priors for generalized linear models. J. Amer. Statist. Assoc. 91 (1996) 1450-1460
4. Bedrick E.J., Christensen R., and Johnson W.O. Bayesian accelerated failure time analysis with application to veterinary epidemiology. Statist. in Med. 19 (2000) 221-237
5. Berger J.O., and Gugliemi A. Bayesian testing of a parametric model versus nonparametric alternatives. J. Amer. Statist. Assoc. 96 (2001) 174-184
6. Berry D., and Christensen R. Empirical Bayes estimation of a binomial parameter via mixture of Dirichlet processes. Ann. Statist. 7 (1979) 558-568
7. Blackwell D. Discreteness of Ferguson selections. Ann. Statist. 1 (1973) 356-358
8. Blackwell D., and MacQueen J.B. Ferguson distributions via Polya urn schemes. Ann. Statist. 2 (1973) 353-355
9. Brinkman N.D. Ethanol fuel - a single-cylinder engine study of efficiency and exhaust emissions. SAE Transactions 90 (1981) 1410-1424
10. Brown E.R., and Ibrahim J.G. A Bayesian semiparametric joint hierarchical model for longitudinal and survival data. Biometrics 59 (2003) 221-228
11. Burridge J. Empirical Bayes analysis of survival time data. J. Roy. Statist. Soc., Ser. B 43 (1981) 65-75
12. Bush C.A., and MacEachern S.N. A semi-parametric Bayesian model for randomized block designs. Biometrika 83 (1996) 275-286
13. Choudhuri N., Ghosal S., and Roy A. Bayesian methods for function estimation. In: Dey D.K., and Rao C.R. (Eds). Bayesian Thinking: Modeling and Computation. Handbook of Statistics vol. 25 (2005), Elsevier, Amsterdam 373-414 This volume
14. Christensen R., and Johnson W.O. Modeling accelerated failure time with a Dirichlet process. Biometrika 75 (1988) 693-704
15. Clayton D.G. A Monte Carlo method for Bayesian inference in frailty models. Biometrics 47 (1991) 467-485
16. Clyde M., and George E.I. Model uncertainty. Statist. Sci. 19 (2004) 81-94
17. Congdon P. Bayesian Statistical Modeling (2001), Wiley, Chichester
18. Cox D.R. Regression models and life-tables (with discussion). J. Roy. Statist. Soc., Ser. B Methodological 34 (1972) 187-220
19. Crainiceanu, C.M., Ruppert, D., Wand, M.P. (2004). Bayesian analysis for penalized spline regression using WinBUGS. Johns Hopkins University, Dept. of Biostatistics Working Papers, Working Paper 40. http://www.bepress.com/jhubiostat/paper40
20. Diaconis P., and Freedman D. On inconsistent Bayes estimates of location. Ann. Statist. 14 (1986) 68-87
21. De Iorio M., Müller P., Rosner G.L., and MacEachern S.N. An ANOVA model for dependent random measures. J. Amer. Statist. Assoc. 99 (2004) 205-215
22. Denison D.G.T., Holmes C.C., Mallick B.K., and Smith A.F.M. Bayesian Methods for Nonlinear Classification and Regression (2002), Wiley, Chichester
23. Dey, D., Müller, P., Sinha, D. (1998). Practical Nonparametric and Semiparametric Bayesian Statistics. Springer Lecture Notes, New York
24. Do, K.-A., Müller, P., Tang, F. (2004). A Bayesian mixture model for differential gene expression. Preprint
25. Doksum K.A. Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2 (1974) 183-201
26. Doss H. Bayesian nonparametric estimation for incomplete data via successive substitution sampling. Ann. Statist. 22 (1994) 1763-1786
27. Doss H., and Huffer F.W. Monte Carlo methods for Bayesian analysis of survival data using mixtures of Dirichlet process priors. J. Comput. Graph. Statist. 12 (2004) 282-307
28. Dykstra R.L., and Laud P.W. A Bayesian nonparametric approach to reliability. Ann. Statist. 9 (1981) 356-367
29. Efromovich S. Nonparametric Curve Estimation (1999), Springer-Verlag, New York
30. Escobar M.D. Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89 (1994) 268-277
31. Escobar M.D., and West M. Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 (1995) 577-588
32. Fabius J. Asymptotic behavior of Bayes' estimates. Ann. Math. Statist. 35 (1964) 846-856
33. Ferguson T.S. A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 (1973) 209-230
34. Ferguson T.S. Prior distributions on spaces of probability measures. Ann. Statist. 2 (1974) 615-629
35. Freedman D.A. On the asymptotic behavior of Bayes' estimates in the discrete case. Ann. Math. Statist. 34 (1963) 1194-1216
36. Gehan E.A. A generalized Wilcoxin test for comparing arbitrarily single-censored samples. Biometrika 52 (1965) 203-224
37. Gelfand A.E. Approaches for semiparametric Bayesian regression. In: Ghosh S. (Ed). Asymptotics, Nonparametrics and Time Series (1999), Marcel Dekker, New York 615-638
38. Gelfand A.E., and Kottas A.A. Nonparametric Bayesian modeling for stochastic order. Ann. Inst. Statist. Math. 53 (2001) 865-876
39. Gelfand A.E., and Kottas A.A. Computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. J. Comput. Graph. Statist. 11 (2002) 289-305
40. Gelfand A.E., and Mukhopadhyay S. On nonparametric Bayesian inference for the distribution of a random sample. Canad. J. Statist. 23 (1995) 411-420
41. Gelfand A.E., and Smith A.F.M. Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 (1990) 398-409
42. Gelfand, A.E., Kottas, A.A., MacEachern, S.N. (2004). Bayesian nonparametric spatial modeling with Dirichlet process mixing. J. Amer. Statist. Assoc., submitted for publication
43. Ghosh J.K., and Ramamoorthi R. Bayesian Nonparametrics (2003), Springer-Verlag, New York
44. Ghosal S., Ghosh J.K., and Ramamoorthi R. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 17 (1999) 143-158
45. Green P.J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 (1995) 711-732
46. Haar A. Zur theorie der orthogonalen funktionensysteme. Math. Ann. 69 (1910) 331-371
47. Hanson T.E., and Johnson W.O. Modeling regression error with a mixture of Polya trees. J. Amer. Statist. Assoc. 97 (2002) 1020-1033
48. Hanson T.E., and Johnson W.O. A Bayesian semiparametric AFT model for interval censored data. J. Comput. Graph. Statist. 13 (2004) 341-361
49. Hjort N.L. Nonparametric Bayes estimators based on beta processes in models of life history data. Ann. Statist. 18 (1990) 1259-1294
50. Hoff P.D. Bayesian methods for partial stochastic orderings. Biometrika 90 (2003) 303-317
51. Holmes C.C., and Mallick B.K. Bayesian regression with multivariate linear splines. J. Roy. Statist. Soc., Ser. B 63 (2001) 3-17
52. Huzurbazar A.V. Flowgraph Models for Multistate Time-to-Event Data (2004), Wiley, New York
53. Ibrahim J.G., and Kleinman K.P. Semiparametric Bayesian methods for random effects models. Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statistics vol. 133 (1998), Springer-Verlag, New York
54. Ibrahim J.G., Chen M.-H., and MacEachern S.N. Bayesian variable selection for proportional hazards models. Canad. J. Statist. 37 (1999) 701-717
55. Ibrahim J.G., Chen M.-H., and Sinha D. Bayesian Survival Analysis (2001), Springer-Verlag, New York
56. Ishwaran H., and James L.F. Computational methods for multiplicative intensity models using weighted gamma processes: Proportional hazards, marked point processes and panel count data. J. Amer. Statist. Assoc. 99 (2004) 175-190
57. Johnson W.O., and Christensen R. Bayesian nonparametric survival analysis for grouped data. Canad. J. Statist. 14 (1986) 307-314
58. Johnson W.O., and Christensen R. Nonparametric Bayesian analysis of the accelerated failure time model. Statist. Probab. Lett. 8 (1989) 179-184
59. Kalbfleisch J.D. Non-parametric Bayesian analysis of survival time data. J. Roy. Statist. Soc., Ser. B 40 (1978) 214-221
60. Kaplan E.L., and Meier P. Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 (1958) 457-481
61. Kim Y., and Lee J. Bayesian analysis of proportional hazard models. Ann. Statist. 31 (2003) 493-511
62. Kleinman K., and Ibrahim J. A semi-parametric Bayesian approach to generalized linear mixed models. Statist. in Med. 17 (1998) 2579-2596
63. Kottas A.A., and Gelfand A.E. Bayesian semiparametric median regression modeling. J. Amer. Statist. Assoc. 95 (2001) 1458-1468
64. Kottas A.A., and Gelfand A.E. Modeling variability order: A semiparametric Bayesian approach. Methodology and Computing in Applied Probability 3 (2001) 427-442
65. Kuo L., and Mallick B. Bayesian semiparametric inference for the accelerated failure-time model. Canad. J. Statist. 25 (1997) 457-472
66. Laud P., Damien P., and Smith A.F.M. Bayesian nonparametric and covariate analysis of failure time data. In: Dey D., Müller P., and Sinha D. (Eds). Practical Nonparametric and Semiparametric Bayesian Statistics (1998), Springer, New York 213-226
67. Lavine M. Some aspects of Polya tree distributions for statistical modeling. Ann. Statist. 20 (1992) 1222-1235
68. Lavine M. More aspects of Polya tree distributions for statistical modeling. Ann. Statist. 22 (1994) 1161-1176
69. Lindley D.V., and Smith A.F.M. Bayes estimates for the linear model (with discussion). J. Roy. Statist. Soc., Ser. B 34 (1972) 1-41
70. Lo A.Y. On a class of Bayesian nonparametric estimates: I. Density estimates. Ann. Statist. 12 (1984) 351-357
71. Lo A.Y., and Weng C.S. On a class of Bayesian nonparametric estimates: II. Hazard rate estimates. Ann. Inst. Statist. Math. 41 (1989) 227-245
72. MacEachern S.N. Estimating normal means with a conjugate style Dirichlet process prior. Comm. Statist. Simulation Comput. 23 (1994) 727-741
73. MacEachern, S.N. (2000). Dependent Dirichlet processes. Technical Report, Dept. of Statistics, The Ohio State University
74. MacEachern S.N., Clyde M., and Liu J. Sequential importance sampling for nonparametric Bayes models: The next generation. Canad. J. Statist. 27 (1999) 251-267
75. MacEachern S.N., and Müller P. Estimating mixture of Dirichlet process models. J. Comput. Graph. Statist. 7 (1998) 223-238
76. Mallick B.K., Denison D.G.T., and Smith A.F.M. Bayesian survival analysis using a MARS model. Biometrics 55 (1999) 1071-1077
77. Mallick B.K., and Walker S.G. A Bayesian semiparametric transformation model incorporating frailties. J. Statist. Plann. Inference 112 (2003) 159-174
78. MathSoft, Inc. (1999). S-Plus 5 for UNIX Guide to Statistics. Data Analysis Products Division, MathSoft, Seattle
79. Mauldin R.D., Sudderth W.D., and Williams S.C. Polya trees and random distributions. Ann. Statist. 20 (1992) 1203-1221
80. Moore D.S. The Basic Practice of Statistics. first ed (1995), W.H. Freeman and Company
81. Mukhopadhyay S., and Gelfand A.E. Dirichlet process mixed generalized linear models. J. Amer. Statist. Assoc. 92 (1997) 633-639
82. Müller P., Erkanli A., and West M. Bayesian curve fitting using multivariate normal mixtures. Biometrika 83 (1996) 67-79
83. Müller P., and Quintana F.A. Nonparametric Bayesian data analysis. Statist. Sci. 19 (2004) 95-110
84. Müller P., and Vidakovic B. Bayesian Inference in Wavelet-Based Models (1999), Springer-Verlag, New York
85. Neal R.M. Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Statist. 9 (2000) 249-265
86. Nieto-Barajas L., and Walker S. Markov beta and gamma processes for modeling hazard rates. Scand. J. Statist. 29 (2002) 413-424
87. Nieto-Barajas L., and Walker S. Bayesian nonparametric survival analysis via Lévy driven Markov processes. Statistica Sinica 14 (2004) 1127-1146
88. Paddock S.M., Ruggeri F., Lavine M., and West M. Randomized Polya tree models for nonparametric Bayesian inference. Statistica Sinica 13 2 (2003) 443-460
89. Regazzini E., Guglielmi A., and Di Nunno G. Theory and numerical analysis for exact distributions of functionals of a Dirichlet process. Ann. Statist. 30 (2002) 1376-1411
90. Richardson S., and Green P. On Bayesian analysis of mixtures with an unknown number of components. J. Roy. Statist. Soc., Ser. B 59 (1997) 731-792
91. Sethuraman J. A constructive definition of the Dirichlet prior. Statistica Sinica 4 (1994) 639-650
92. Sinha D., and Dey D.K. Semiparametric Bayesian analysis of survival data. J. Amer. Statist. Assoc. 92 (1997) 1195-1212
93. Smith M., and Kohn R. Nonparametric regression using Bayesian variable selection. J. Econometrics 75 (1996) 317-343
94. Spiegelhalter, D., Thomas, A., Best, N., Lunn, D. (2003). WinBUGS 1.4 User Manual. MRC Biostatistics Unit, Cambridge. www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml
95. Susarla J., and van Ryzin J. Nonparametric Bayesian estimation of survival curves from incomplete observations. J. Amer. Statist. Assoc. 71 (1976) 897-902
96. Tierney L. Markov chains for exploring posterior distributions. Ann. Statist. 22 (1994) 1701-1762
97. Titterington D.M., Smith A.F.M., and Makov U.E. Statistical Analysis of Finite Mixture Distributions (1985), Wiley, New York
98. Turnbull B.W. Nonparametric estimation of a survivorship function with doubly censored data. J. Amer. Statist. Soc. 69 (1974) 169-173
99. Vidakovic B. Wavelet-based nonparametric Bayes methods. In: Dey D., Müller P., and Sinha D. (Eds). Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statistics vol. 133 (1998), Springer-Verlag, New York 133-155
100. Walker, S., Damien, P. (1998). Sampling methods for Bayesian nonparametric inference involving stochastic processes. In: D. Dey, P. Mueller, D. Sinha, (Eds.), Practical Nonparametric and Semiparametric Bayesian Statistics, Springer Lecture Notes, pp. 243-254
101. Walker S.G., and Mallick B.K. Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. J. Roy. Statist. Soc., Ser. B 59 (1997) 845-860
102. Walker S.G., and Mallick B.K. Semiparametric accelerated life time model. Biometrics 55 (1999) 477-483
103. Walker S.G., Damien P., Laud P., and Smith A.F.M. Bayesian nonparametric inference for random distributions and related functions (with discussion). J. Roy. Statist. Soc., Ser. B 61 (1999) 485-527
104. Wang Y., and Taylor J.M.G. Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. J. Amer. Statist. Assoc. 96 (2001) 895-905
105. West M., Müller P., and Escobar M.D. Hierarchical priors and mixture models with applications in regression and density estimation. In: Smith A.F.M., and Freeman P.R. (Eds). Aspects of Uncertainty: A Tribute D. Lindley (1994), Wiley, London 363-386
106. Wiper M.P., Ríos Insua D., and Ruggeri F. Mixtures of gamma distributions with applications. J. Comput. Graph. Statist. 10 (2001) 440-454