Nonparametric Bayesian Data Analysis
Peter Müller and Fernando A. Quintana
Source: Statist. Sci. Volume 19, Number 1
(2004), 95-110.
Abstract
We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametric Bayesian models and approaches including Dirichlet process (DP) models and variations, Pólya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models and model validation with DP and Pólya tree extensions of parametric models.
First Page:
Show
Hide
Keywords: Dirichlet process; regression; density estimation; survival analysis; Pólya tree; random probability model (RPM)
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ss/1089808275
Digital Object Identifier: doi:10.1214/088342304000000017
Zentralblatt MATH identifier: 1057.62032
Mathematical Reviews number (MathSciNet): MR2082149
References
Antoniak, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2 1152--1174.
Mathematical Reviews (MathSciNet): MR365969
JSTOR: links.jstor.org
Arjas, E. and Gasbarra, D. (1994). Nonparametric Bayesian inference from right censored survival data, using the Gibbs sampler. Statist. Sinica 4 505--524.
Mathematical Reviews (MathSciNet): MR1309427
Arjas, E. and Heikkinen, J. (1997). An algorithm for nonparametric Bayesian estimation of a Poisson intensity. Comput. Statist. 12 385--402.
Mathematical Reviews (MathSciNet): MR1477272
Barron, A., Schervish, M. J. and Wasserman, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 536--561.
Mathematical Reviews (MathSciNet): MR1714718
Digital Object Identifier: doi:10.1214/aos/1017939142
Project Euclid: euclid.aos/1018031206
Zentralblatt MATH: 0980.62039
Berger, J. and Guglielmi, A. (2001). Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives. J. Amer. Statist. Assoc. 96 174--184.
Mathematical Reviews (MathSciNet): MR1952730
Digital Object Identifier: doi:10.1198/016214501750333045
Zentralblatt MATH: 1014.62029
Bernardo, J. M. and Smith, A. F. M. (1994). Bayesian Theory. Wiley, New York.
Mathematical Reviews (MathSciNet): MR1274699
Zentralblatt MATH: 0796.62002
Blackwell, D. and MacQueen, J. B. (1973). Ferguson distributions via Pólya urn schemes. Ann. Statist. 1 353--355.
Mathematical Reviews (MathSciNet): MR362614
Bondesson, L. (1982). On simulation from infinitely divisible distributions. Adv. in Appl. Probab. 14 855--869.
Mathematical Reviews (MathSciNet): MR677560
Digital Object Identifier: doi:10.2307/1427027
Zentralblatt MATH: 0494.60013
Bush, C. A. and MacEachern, S. N. (1996). A semiparametric Bayesian model for randomised block designs. Biometrika 83 275--285.
Zentralblatt MATH: 0102.14802
Carota, C. and Parmigiani, G. (1996). On Bayes factors for nonparametric alternatives. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 507--511. Oxford Univ. Press.
Mathematical Reviews (MathSciNet): MR1425421
Carota, C. and Parmigiani, G. (2002). Semiparametric regression for count data. Biometrika 89 265--281.
Mathematical Reviews (MathSciNet): MR1913958
Zentralblatt MATH: 1017.62035
Digital Object Identifier: doi:10.1093/biomet/89.2.265
Carota, C., Parmigiani, G. and Polson, N. G. (1996). Diagnostic measures for model criticism. J. Amer. Statist. Assoc. 91 753--762.
Mathematical Reviews (MathSciNet): MR1395742
Cheng, B. and Titterington, D. M. (1994). Neural networks: A review from a statistical perspective (with discussion). Statist. Sci. 9 2--54.
Mathematical Reviews (MathSciNet): MR1278678
JSTOR: links.jstor.org
Chipman, H. A., George, E. I. and McCulloch, R. E. (1998). Bayesian CART model search (with discussion). J. Amer. Statist. Assoc. 93 935--960.
Mathematical Reviews (MathSciNet): MR1631325
Chipman, H. A., Kolaczyk, E. D. and McCulloch, R. E. (1997). Adaptive Bayesian wavelet shrinkage. J. Amer. Statist. Assoc. 92 1413--1421.
Cifarelli, D. M. and Melilli, E. (2000). Some new results for Dirichlet priors. Ann. Statist. 28 1390--1413.
Mathematical Reviews (MathSciNet): MR1805789
Digital Object Identifier: doi:10.1214/aos/1015957399
Project Euclid: euclid.aos/1015957399
Zentralblatt MATH: 1105.62303
Cifarelli, D. and Regazzini, E. (1978). Problemi statistici non parametrici in condizioni di scambialbilita parziale e impiego di medie associative. Technical report, Quaderni dell'Istituto di Matematica Finanziaria, Univ. Torino.
Clyde, M. and George, E. (2000). Flexible empirical Bayes estimation for wavelets. J. R. Stat. Soc. Ser. B Stat. Methodol. 62 681--698.
Mathematical Reviews (MathSciNet): MR1796285
Digital Object Identifier: doi:10.1111/1467-9868.00257
Zentralblatt MATH: 0957.62006
Conigliani, C., Castro, J. I. and O'Hagan, A. (2000). Bayesian assessment of goodness of fit against nonparametric alternatives. Canad. J. Statist. 28 327--342.
Mathematical Reviews (MathSciNet): MR1792053
Cox, D. R. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187--220.
Mathematical Reviews (MathSciNet): MR341758
Dalal, S. R. (1979). Dirichlet invariant processes and applications to nonparametric estimation of symmetric distribution functions. Stochastic Process. Appl. 9 99--108.
Mathematical Reviews (MathSciNet): MR544719
Digital Object Identifier: doi:10.1016/0304-4149(79)90043-7
Zentralblatt MATH: 0415.60035
Damien, P., Laud, P. and Smith, A. F. M. (1996). Implementation of Bayesian nonparametric inference based on beta processes. Scand. J. Statist. 23 27--36.
Mathematical Reviews (MathSciNet): MR1380479
Damien, P., Wakefield, J. and Walker, S. (1999). Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 331--344.
Mathematical Reviews (MathSciNet): MR1680334
Digital Object Identifier: doi:10.1111/1467-9868.00179
Zentralblatt MATH: 0913.62028
De Iorio, M., Müller, P., Rosner, G. L. and MacEachern, S. N. (2004). An ANOVA model for dependent random measures. J. Amer. Statist. Assoc. 99 205--215.
Mathematical Reviews (MathSciNet): MR2054299
Denison, D. G. T., Mallick, B. K. and Smith, A. F. M. (1998a). A Bayesian CART algorithm. Biometrika 85 363--377.
Mathematical Reviews (MathSciNet): MR1649118
Digital Object Identifier: doi:10.1093/biomet/85.2.363
Zentralblatt MATH: 1048.62502
Denison, D. G. T., Mallick, B. K. and Smith, A. F. M. (1998b). Automatic Bayesian curve fitting. J. R. Stat. Soc. Ser. B Stat. Methodol. 60 333--350.
Mathematical Reviews (MathSciNet): MR1616029
Digital Object Identifier: doi:10.1111/1467-9868.00128
Zentralblatt MATH: 0907.62031
Denison, D. G. T., Mallick, B. K. and Smith, A. F. M. (1998c). Bayesian MARS. Statist. Comput. 8 337--346.
Dey, D., Müller, P. and Sinha, D., eds. (1998). Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133. Springer, New York.
Mathematical Reviews (MathSciNet): MR1630072
Zentralblatt MATH: 0893.00018
Diaconis, P. and Freedman, D. (1986). On the consistency of Bayes estimates (with discussion). Ann. Statist. 14 1--67.
Mathematical Reviews (MathSciNet): MR829555
JSTOR: links.jstor.org
Diaconis, P. and Kemperman, J. (1996). Some new tools for Dirichlet priors. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 97--106. Oxford Univ. Press.
Mathematical Reviews (MathSciNet): MR1425401
DiMatteo, I., Genovese, C. R. and Kass, R. (2001). Bayesian curve fitting with free-knot splines. Biometrika 88 1055--1071.
Mathematical Reviews (MathSciNet): MR1872219
Zentralblatt MATH: 0986.62026
Digital Object Identifier: doi:10.1093/biomet/88.4.1055
Doksum, K. (1974). Tailfree and neutral random probabilities and their posterior distributions. Ann. Probab. 2 183--201.
Mathematical Reviews (MathSciNet): MR373081
Digital Object Identifier: doi:10.1214/aop/1176996703
Dominici, F. and Parmigiani, G. (2001). Bayesian semi-parametric analysis of developmental toxicology data. Biometrics 57 150--157.
Mathematical Reviews (MathSciNet): MR1833301
Digital Object Identifier: doi:10.1111/j.0006-341X.2001.00150.x
Doss, H. (1994). Bayesian nonparametric estimation for incomplete data via successive substitution sampling. Ann. Statist. 22 1763--1786.
Mathematical Reviews (MathSciNet): MR1329167
JSTOR: links.jstor.org
Durrett, R. (1996). Probability: Theory and Examples, 2nd ed. Duxbury, Belmont, CA.
Mathematical Reviews (MathSciNet): MR1609153
Dykstra, R. L. and Laud, P. (1981). A Bayesian nonparametric approach to reliability. Ann. Statist. 9 356--367.
Mathematical Reviews (MathSciNet): MR606619
JSTOR: links.jstor.org
Escobar, M. (1988). Estimating the means of several normal populations by estimating the distribution of the means. Ph.D. dissertation, Dept. Statistics, Yale Univ.
Escobar, M. D. and West, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577--588.
Mathematical Reviews (MathSciNet): MR1340510
Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209--230.
Mathematical Reviews (MathSciNet): MR350949
Ferguson, T. S. and Klass, M. J. (1972). A representation of independent increment processes without Gaussian components. Ann. Math. Statist. 43 1634--1643.
Mathematical Reviews (MathSciNet): MR373022
Digital Object Identifier: doi:10.1214/aoms/1177692395
Ferguson, T. S. and Phadia, E. G. (1979). Bayesian nonparametric estimation based on censored data. Ann. Statist. 7 163--186.
Mathematical Reviews (MathSciNet): MR515691
JSTOR: links.jstor.org
Ferguson, T. S., Phadia, E. G. and Tiwari, R. C. (1992). Bayesian nonparametric inference. In Current Issues in Statistical Inference: Essays in Honor of D. Basu (M. Ghosh and P. K. Pathak, eds.) 127--150. IMS, Hayward, CA.
Mathematical Reviews (MathSciNet): MR1194414
Zentralblatt MATH: 0770.62025
Florens, J.-P. and Rolin, J.-M. (2001). Simulation of posterior distributions in nonparametric censored analysis. Technical report, Univ. Sciences Sociales de Toulouse.
Friedman, J. H. (1991). Multivariate adaptive regression splines (with discussion). Ann. Statist. 19 1--141.
Mathematical Reviews (MathSciNet): MR1091842
JSTOR: links.jstor.org
Gamerman, D. (1991). Dynamic Bayesian models for survival data. Appl. Statist. 40 63--79.
Gasparini, M. (1996). Bayesian density estimation via mixture of Dirichlet processes. J. Nonparametr. Stat. 6 355--366.
Mathematical Reviews (MathSciNet): MR1386345
Gelfand, A. E. and Kottas, A. (2002). A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. J. Comput. Graph. Statist. 11 289--305.
Mathematical Reviews (MathSciNet): MR1938136
Digital Object Identifier: doi:10.1198/106186002760180518
Gelfand, A. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398--409.
Mathematical Reviews (MathSciNet): MR1141740
Ghosal, S. (2001). Convergence rates for density estimation with Bernstein polynomials. Ann. Statist. 29 1264--1280.
Mathematical Reviews (MathSciNet): MR1873330
Digital Object Identifier: doi:10.1214/aos/1013203453
Project Euclid: euclid.aos/1013203453
Zentralblatt MATH: 1043.62024
Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1999). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27 143--158.
Mathematical Reviews (MathSciNet): MR1701105
Digital Object Identifier: doi:10.1214/aos/1018031105
Project Euclid: euclid.aos/1018031105
Zentralblatt MATH: 0932.62043
Giudici, P., Mezzetti, M. and Muliere, P. (2003). Mixtures of products of Dirichlet processes for variable selection in survival analysis. J. Statist. Plann. Inference 111 101--115.
Mathematical Reviews (MathSciNet): MR1955875
Digital Object Identifier: doi:10.1016/S0378-3758(02)00291-4
Zentralblatt MATH: 1033.62099
Gray, R. J. (1994). A Bayesian analysis of institutional effects in a multicenter cancer clinical trial. Biometrics 50 244--253.
Mathematical Reviews (MathSciNet): MR1309310
Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711--732.
Mathematical Reviews (MathSciNet): MR1380810
Zentralblatt MATH: 0861.62023
Digital Object Identifier: doi:10.2307/2337340
Hanson, T. and Johnson, W. (2002). Modeling regression error with a mixture of Pólya trees. J. Amer. Statist. Assoc. 97 1020--1033.
Mathematical Reviews (MathSciNet): MR1951256
Digital Object Identifier: doi:10.1198/016214502388618843
Zentralblatt MATH: 1048.62101
Hjort, N. L. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18 1259--1294.
Mathematical Reviews (MathSciNet): MR1062708
JSTOR: links.jstor.org
Ishwaran, H. and James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96 161--173.
Mathematical Reviews (MathSciNet): MR1952729
Digital Object Identifier: doi:10.1198/016214501750332758
Zentralblatt MATH: 1014.62006
Ishwaran, H. and James, L. F. (2002). Approximate Dirichlet process computing in finite normal mixtures: Smoothing and prior information. J. Comput. Graph. Statist. 11 508--532.
Mathematical Reviews (MathSciNet): MR1938445
Digital Object Identifier: doi:10.1198/106186002411
Ishwaran, H. and James, L. F. (2003). Generalized weighted Chinese restaurant processes for species sampling mixture models. Statist. Sinica 13 1211--1235.
Ishwaran, H. and Takahara, G. (2002). Independent and identically distributed Monte Carlo algorithms for semiparametric linear mixed models. J. Amer. Statist. Assoc. 97 1154--1166.
Mathematical Reviews (MathSciNet): MR1951267
Digital Object Identifier: doi:10.1198/016214502388618951
Zentralblatt MATH: 1041.62030
Ishwaran, H. and Zarepour, M. (2000). Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models. Biometrika 87 371--390.
Mathematical Reviews (MathSciNet): MR1782485
Zentralblatt MATH: 0949.62037
Digital Object Identifier: doi:10.1093/biomet/87.2.371
Johnson, W. and Christensen, R. (1989). Nonparametric Bayesian analysis of the accelerated failure time model. Statist. Probab. Lett. 8 179--184.
Mathematical Reviews (MathSciNet): MR1017888
Kalbfleisch, J. D. (1978). Nonparametric Bayesian analysis of survival time data. J. Roy. Statist. Soc. Ser. B 40 214--221.
Mathematical Reviews (MathSciNet): MR517442
Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 457--481.
Mathematical Reviews (MathSciNet): MR93867
Kleinman, K. and Ibrahim, J. (1998). A semi-parametric Bayesian approach to the random effects model. Biometrics 54 921--938.
Korwar, R. M. and Hollander, M. (1973). Contributions to the theory of Dirichlet processes. Ann. Probab. 1 705--711.
Mathematical Reviews (MathSciNet): MR350950
Digital Object Identifier: doi:10.1214/aop/1176996898
Kottas, A. and Gelfand, A. E. (2001). Bayesian semiparametric median regression modeling. J. Amer. Statist. Assoc. 96 1458--1468.
Mathematical Reviews (MathSciNet): MR1946590
Digital Object Identifier: doi:10.1198/016214501753382363
Kuo, L. and Mallick, B. (1997). Bayesian semiparametric inference for the accelerated failure time model. Canad. J. Statist. 25 457--472.
Laud, P., Damien, P. and Smith, A. F. M. (1998). Bayesian nonparametric and covariate analysis of failure time data. In Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 213--225. Springer, New York.
Mathematical Reviews (MathSciNet): MR1630083
Zentralblatt MATH: 0918.62077
Lavine, M. (1992). Some aspects of Pólya tree distributions for statistical modelling. Ann. Statist. 20 1222--1235.
Mathematical Reviews (MathSciNet): MR1186248
JSTOR: links.jstor.org
Lavine, M. (1994). More aspects of Pólya tree distributions for statistical modelling. Ann. Statist. 22 1161--1176.
Mathematical Reviews (MathSciNet): MR1311970
JSTOR: links.jstor.org
Lavine, M. (1995). On an approximate likelihood for quantiles. Biometrika 82 220--222.
Mathematical Reviews (MathSciNet): MR1332852
Zentralblatt MATH: 0823.62002
Digital Object Identifier: doi:10.2307/2337641
Lavine, M. and Mockus, A. (1995). A nonparametric Bayes method for isotonic regression. J. Statist. Plann. Inference 46 235--248.
Lee, H. (2001). Model selection for neural network classification. J. Classification 18 227--243.
Mathematical Reviews (MathSciNet): MR1868630
Lee, J. and Berger, J. (2001). Semiparametric Bayesian analysis of selection models. J. Amer. Statist. Assoc. 96 1397--1409.
Mathematical Reviews (MathSciNet): MR1946585
Digital Object Identifier: doi:10.1198/016214501753382318
Zentralblatt MATH: 1051.62029
Lenk, P. (1988). The logistic normal distribution for Bayesian, nonparametric predictive densities. J. Amer. Statist. Assoc. 83 509--516.
Mathematical Reviews (MathSciNet): MR971380
Leonard, T. (1978). Density estimation, stochastic processes and prior information (with discussion). J. Roy. Statist. Soc. Ser. B 40 113--146.
Mathematical Reviews (MathSciNet): MR517434
Liu, J. S. (1996). Nonparametric hierarchical Bayes via sequential imputations. Ann. Statist. 24 911--930.
Mathematical Reviews (MathSciNet): MR1401830
Digital Object Identifier: doi:10.1214/aos/1032526949
Project Euclid: euclid.aos/1032526949
Zentralblatt MATH: 0880.62038
Lo, A. Y. (1984). On a class of Bayesian nonparametric estimates. I. Density estimates. Ann. Statist. 12 351--357.
Mathematical Reviews (MathSciNet): MR733519
JSTOR: links.jstor.org
MacEachern, S. (1994). Estimating normal means with a conjugate style Dirichlet process prior. Comm. Statist. Simulation Comput. 23 727--741.
Mathematical Reviews (MathSciNet): MR1293996
MacEachern, S. (1999). Dependent nonparametric processes. Proc. Bayesian Statistical Science Section 50--55. Amer. Statist. Assoc., Alexandria, VA.
MacEachern, S. N., Clyde, M. and Liu, J. S. (1999). Sequential importance sampling for nonparametric Bayes models: The next generation. Canad. J. Statist. 27 251--267.
Mathematical Reviews (MathSciNet): MR1704407
MacEachern, S. N. and Müller, P. (1998). Estimating mixture of Dirichlet process models. J. Comput. Graph. Statist. 7 223--238.
MacEachern, S. N. and Müller, P. (2000). Efficient MCMC schemes for robust model extensions using encompassing Dirichlet process mixture models. In Robust Bayesian Analysis. Lecture Notes in Statist. 152 295--316. Springer, New York.
Mathematical Reviews (MathSciNet): MR1795222
Mazzuchi, T. A., Soofi, E. S. and Soyer, R. (2000). Computation of maximum entropy Dirichlet for modeling lifetime data. Comput. Statist. Data Anal. 32 361--378.
Mathematical Reviews (MathSciNet): MR1746178
Mira, A. and Petrone, S. (1996). Bayesian hierarchical nonparametric inference for change-point problems. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 693--703. Oxford Univ. Press.
Mathematical Reviews (MathSciNet): MR1425440
Mukhopadhyay, S. and Gelfand, A. (1997). Dirichlet process mixed generalized linear models. J. Amer. Statist. Assoc. 92 633--639.
Mathematical Reviews (MathSciNet): MR1467854
Muliere, P. and Petrone, S. (1993). A Bayesian predictive approach to sequential search for an optimal dose: Parametric and nonparametric models. J. Italian Statistical Society 2 349--364.
Muliere, P. and Secchi, P. (1995). A note on a proper Bayesian bootstrap. Technical Report 18, Dipt. Economia Politica e Metodi Quantitativi, Univ. Studi di Pavia.
Muliere, P. and Tardella, L. (1998). Approximating distributions of random functionals of Ferguson--Dirichlet priors. Canad. J. Statist. 26 283--297.
Mathematical Reviews (MathSciNet): MR1648431
Müller, P., Erkanli, A. and West, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika 83 67--79.
Mathematical Reviews (MathSciNet): MR1399156
Zentralblatt MATH: 0865.62029
Digital Object Identifier: doi:10.1093/biomet/83.1.67
Müller, P. and Ríos-Insua, D. (1998). Issues in Bayesian analysis of neural network models. Neural Computation 10 749--770.
Müller, P. and Rosner, G. (1997). A Bayesian population model with hierarchical mixture priors applied to blood count data. J. Amer. Statist. Assoc. 92 1279--1292.
Müller, P. and Vidakovic, B. (1998). Bayesian inference with wavelets: Density estimation. J. Comput. Graph. Statist. 7 456--468.
Müller, P. and Vidakovic, B. (1999). MCMC methods in wavelet shrinkage: Non-equally spaced regression, density and spectral density estimation. In Bayesian Inference in Wavelet-Based Models. Lecture Notes in Statist. 141 187--202. Springer, New York.
Mathematical Reviews (MathSciNet): MR1699833
Neal, R. M. (1996). Bayesian Learning for Neural Networks. Springer, New York.
Zentralblatt MATH: 0888.62021
Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Statist. 9 249--265.
Mathematical Reviews (MathSciNet): MR1823804
Newton, M. A., Czado, C. and Chappell, R. (1996). Bayesian inference for semiparametric binary regression. J. Amer. Statist. Assoc. 91 142--153.
Mathematical Reviews (MathSciNet): MR1394068
Newton, M. A. and Zhang, Y. (1999). A recursive algorithm for nonparametric analysis with missing data. Biometrika 86 15--26.
Mathematical Reviews (MathSciNet): MR1688068
Zentralblatt MATH: 0917.62045
Digital Object Identifier: doi:10.1093/biomet/86.1.15
Nieto-Barajas, L. and Walker, S. G. (2001). A semiparametric Bayesian analysis of survival data based on Markov gamma processes. Technical report, Dept. Mathematical Sciences, Univ. Bath.
Nieto-Barajas, L. and Walker, S. G. (2002a). Bayesian nonparametric survival analysis via Lévy driven Markov processes. Technical report, Dept. Mathematical Sciences, Univ. Bath.
Nieto-Barajas, L. and Walker, S. G. (2002b). Markov beta and gamma processes for modelling hazard rates. Scand. J. Statist. 29 413--424.
Mathematical Reviews (MathSciNet): MR1925567
Digital Object Identifier: doi:10.1111/1467-9469.00298
Zentralblatt MATH: 1036.62105
Paddock, S., Ruggeri, F., Lavine, M. and West, M. (2003). Randomised Pólya tree models for nonparametric Bayesian inference. Statist. Sinica 13 443--460.
Mathematical Reviews (MathSciNet): MR1977736
Zentralblatt MATH: 1015.62051
Peterson, A. V. (1977). Expressing the Kaplan--Meier estimator as a function of empirical subsurvival functions. J. Amer. Statist. Assoc. 72 854--858.
Mathematical Reviews (MathSciNet): MR471165
Petrone, S. (1999a). Bayesian density estimation using Bernstein polynomials. Canad. J. Statist. 27 105--126.
Mathematical Reviews (MathSciNet): MR1703623
Petrone, S. (1999b). Random Bernstein polynomials. Scand. J. Statist. 26 373--393.
Mathematical Reviews (MathSciNet): MR1712051
Digital Object Identifier: doi:10.1111/1467-9469.00155
Zentralblatt MATH: 0939.62046
Petrone, S. and Wasserman, L. (2002). Consistency of Bernstein polynomial posteriors. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 79--100.
Mathematical Reviews (MathSciNet): MR1881846
Digital Object Identifier: doi:10.1111/1467-9868.00326
Zentralblatt MATH: 1015.62033
Pitman, J. (1996). Some developments of the Blackwell--MacQueen urn scheme. In Statistics, Probability and Game Theory. Papers in Honor of David Blackwell (T. S. Ferguson, L. S. Shapley and J. B. MacQueen, eds.) 245--267. IMS, Hayward, CA.
Mathematical Reviews (MathSciNet): MR1481784
Pitman, J. and Yor, M. (1997). The two-parameter Poisson--Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25 855--900.
Mathematical Reviews (MathSciNet): MR1434129
Digital Object Identifier: doi:10.1214/aop/1024404422
Project Euclid: euclid.aop/1024404422
Zentralblatt MATH: 0880.60076
Qiou, Z., Ravishanker, N. and Dey, D. K. (1999). Multivariate survival analysis with positive stable frailties. Biometrics 55 637--644.
Quintana, F. A. (1998). Nonparametric Bayesian analysis for assessing homogeneity in $k\times l$ contingency tables with fixed right margin totals. J. Amer. Statist. Assoc. 93 1140--1149.
Mathematical Reviews (MathSciNet): MR1649208
Digital Object Identifier: doi:10.2307/2669616
Zentralblatt MATH: 1064.62532
Quintana, F. A. and Newton, M. A. (2000). Computational aspects of nonparametric Bayesian analysis with applications to the modeling of multiple binary sequences. J. Comput. Graph. Statist. 9 711--737.
Mathematical Reviews (MathSciNet): MR1821814
Regazzini, E. (1999). Old and recent results on the relationship between predictive inference and statistical modeling either in nonparametric or parametric form. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 571--588. Oxford Univ. Press.
Ríos-Insua, D. and Müller, P. (1998). Feedforward neural networks for nonparametric regression. In Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 181--193. Springer, New York.
Mathematical Reviews (MathSciNet): MR1630081
Rolin, J.-M. (1992). Some useful properties of the Dirichlet process. Technical Report 9207, Center for Operations Research and Econometrics, Univ. Catholique de Louvain.
Salinas-Torres, V. H., de Bragança Pereira, C. A. and Tiwari, R. (1997). Convergence of Dirichlet measures arising in context of Bayesian analysis of competing risks models. J. Multivariate Anal. 62 24--35.
Mathematical Reviews (MathSciNet): MR1467871
Digital Object Identifier: doi:10.1006/jmva.1997.1679
Zentralblatt MATH: 0874.62051
Salinas-Torres, V. H., de Bragança Pereira, C. A. and Tiwari, R. (2002). Bayesian nonparametric estimation in a series system or a competing-risks model. J. Nonparametr. Stat. 14 449--458.
Mathematical Reviews (MathSciNet): MR1919049
Digital Object Identifier: doi:10.1080/10485250213114
Zentralblatt MATH: 1009.62090
Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4 639--650.
Mathematical Reviews (MathSciNet): MR1309433
Shively, T. S., Kohn, R. and Wood, S. (1999). Variable selection and function estimation in additive nonparametric regression using a data-based prior (with discussion). J. Amer. Statist. Assoc. 94 777--806.
Mathematical Reviews (MathSciNet): MR1723272
Sinha, D. (1993). Semiparametric Bayesian analysis of multiple event time data. J. Amer. Statist. Assoc. 88 979--983.
Sinha, D. and Dey, D. K. (1997). Semiparametric Bayesian analysis of survival data. J. Amer. Statist. Assoc. 92 1195--1212.
Mathematical Reviews (MathSciNet): MR1482151
Sinha, D. and Dey, D. K. (1998). Survival analysis using semiparametric Bayesian methods. In Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 195--211. Springer, New York.
Mathematical Reviews (MathSciNet): MR1630082
Zentralblatt MATH: 0918.62087
Smith, M. and Kohn, R. (1996). Nonparametric regression using Bayesian variable selection. J. Econometrics 75 317--343.
Smith, M. and Kohn, R. (1997). A Bayesian approach to nonparametric bivariate regression. J. Amer. Statist. Assoc. 92 1522--1535.
Mathematical Reviews (MathSciNet): MR1615262
Smith, M. and Kohn, R. (1998). Nonparametric estimation of irregular functions with independent or autocorrelated errors. In Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 157--179. Springer, New York.
Mathematical Reviews (MathSciNet): MR1630080
Zentralblatt MATH: 0918.62037
Stern, H. S. (1996). Neural networks in applied statistics (with discussion). Technometrics 38 205--220.
Mathematical Reviews (MathSciNet): MR1411878
Susarla, V. and Van Ryzin, J. (1976). Nonparametric Bayesian estimation of survival curves from incomplete observations. J. Amer. Statist. Assoc. 71 897--902.
Mathematical Reviews (MathSciNet): MR436445
Vannucci, M. and Corradi, F. (1999). Covariance structure of wavelet coefficients: Theory and models in a Bayesian perspective. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 971--986.
Mathematical Reviews (MathSciNet): MR1722251
Digital Object Identifier: doi:10.1111/1467-9868.00214
Zentralblatt MATH: 0940.62023
Vidakovic, B. (1998). Nonlinear wavelet shrinkage with Bayes rules and Bayes factors. J. Amer. Statist. Assoc. 93 173--179.
Mathematical Reviews (MathSciNet): MR1614620
Digital Object Identifier: doi:10.2307/2669614
Zentralblatt MATH: 0953.62037
Walker, S. G. (1995). Generating random variates from D-distributions via substitution sampling. Statist. Comput. 5 311--315.
Walker, S. G. and Damien, P. (1998). Sampling methods for Bayesian nonparametric inference involving stochastic processes. In Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 243--254. Springer, New York.
Mathematical Reviews (MathSciNet): MR1630085
Zentralblatt MATH: 0947.62064
Walker, S. G. and Damien, P. (2000). Representation of Lévy processes without Gaussian components. Biometrika 87 477--483.
Mathematical Reviews (MathSciNet): MR1782492
Digital Object Identifier: doi:10.1093/biomet/87.2.477
Walker, S. G., Damien, P., Laud, P. and Smith, A. F. M. (1999). Bayesian nonparametric inference for random distributions and related functions (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 61 485--527.
Mathematical Reviews (MathSciNet): MR1707858
Digital Object Identifier: doi:10.1111/1467-9868.00190
Zentralblatt MATH: 0983.62027
Walker, S. G. and Mallick, B. K. (1997). Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. J. Roy. Statist. Soc. Ser. B 59 845--860.
Mathematical Reviews (MathSciNet): MR1483219
Digital Object Identifier: doi:10.1111/1467-9868.00101
Walker, S. G. and Mallick, B. (1999). A Bayesian semiparametric accelerated failure time model. Biometrics 55 477--483.
Mathematical Reviews (MathSciNet): MR1705102
Digital Object Identifier: doi:10.1111/j.0006-341X.1999.00477.x
Zentralblatt MATH: 1059.62531
Wang, Y. and Taylor, J. M. (2001). Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. J. Amer. Statist. Assoc. 96 895--905.
Mathematical Reviews (MathSciNet): MR1946362
Digital Object Identifier: doi:10.1198/016214501753208591
Zentralblatt MATH: 1047.62115
West, M., Müller, P. and Escobar, M. (1994). Hierarchical priors and mixture models with applications in regression and density estimation. In Aspects of Uncertainty: A Tribute to D. V. Lindley (P. R. Freeman and A. F. M. Smith, eds.) 363--386. Wiley, New York.
Mathematical Reviews (MathSciNet): MR1309702
Zentralblatt MATH: 0842.62001
Wild, C. J. and Kalbfleisch, J. D. (1981). A note on a paper by Ferguson and Phadia. Ann. Statist. 9 1061--1065.
Mathematical Reviews (MathSciNet): MR628761
JSTOR: links.jstor.org
Wolpert, R. L. and Ickstadt, K. (1998a). Poisson/gamma random field models for spatial statistics. Biometrika 85 251--267.
Mathematical Reviews (MathSciNet): MR1649114
Digital Object Identifier: doi:10.1093/biomet/85.2.251
Zentralblatt MATH: 0951.62082
Wolpert, R. L. and Ickstadt, K. (1998b). Simulation of Lévy random fields. In Practical Nonparametric and Semiparametric Bayesian Statistics. Lecture Notes in Statist. 133 227--242. Springer, New York.
Mathematical Reviews (MathSciNet): MR1630084
Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with $g$-prior distributions. In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti (P. K. Goel and A. Zellner, eds.) 233--243. North-Holland, Amsterdam.
Mathematical Reviews (MathSciNet): MR881437
Zentralblatt MATH: 0655.62071
