310 References Broderick, T., Jordan, M. L., & Pitman, J. (2013). Cluster and feature modeling from combinatorial stochastic processes. Statistical Sc

Transcription

1 References Aalen, O. O. (1978). Nonparametric inference for a family of counting processes. Annals of Statistics, 6, Ammann, L. P. (1984). Bayesian nonparametric inference for quantal response data. Annals of Statistics, 12, Ammann, L. P. (1985). Conditional Laplace transforms for Bayesian nonparametric inference in reliability theory. Stochastic Processes and Their Applications, 20, Antoniak, C. (1974). Mixtures of Dirichlet processes with applications Bayesian nonparametric problems. Annals of Statistics, 2, Barlow, R. E., Barthalomew, D. J., Bremner, J. M., & Brunk, H. D. (1972). Statistical inference under order restrictions. New York: Wiley. Basu, D., &Tiwari, R. C. (1982). A note on the Dirichlet process. In G. Kallianpur, R. Krishnaiah, & J. K. Ghosh (Eds.) Statistics and probability: Essays in honor of C. R. Rao (pp ). Berry, D. A., & Christensen, R. (1979). Empirical Bayes estimation of a binomial parameter via mixtures of Dirichlet process. Annals of Statistics, 7, Bhattacharya, P. K. (1981). Posterior distribution of a Dirichlet process from quantal response data. Annals of Statistics, 1, Billingsley, P. (1968). Convergence of probability measures. New York: Wiley. Binder, D. A. (1982). Nonparametric Bayesian models for samples from finite populations. Journal of the Royal Statistical Society B, 44, Blackwell, D. (1973). Discreteness of Ferguson selections. Annals of Statistics, 1, Blackwell, D., & MacQueen, J. B. (1973). Ferguson distributions via Polya urn schemes. Annals of Statistics, 9, Blei, D. M., & Frazier, P. I. (2011). Distant dependent Chinese restaurant processes. Journal of Machine Learning Research, 12, Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet allocation. Journal of Machine Learning Research, 3, Blum, J., & Susarla, V. (1977). On the posterior distribution of a Dirichlet process given randomly right censored observations. Stochastic Processes and Their Applications, 5, Bondesson, L. (1982). On simulation from infinitely divisible distributions. Advances in Applied Probability, 14, Breth, M. (1978). Bayesian confidence bands for a distribution function. Annals of Statistics, 6, Breth, M. (1979). Nonparametric Bayesian interval estimation. Biometrika, 66, Broderick, T., Jordan, M. L., & Pitman, J. (2012). Beta processes, Stick-breaking and power laws. Bayesian Analysis, 7, Springer International Publishing Switzerland 2016 E.G. Phadia, Prior Processes and Their Applications, Springer Series in Statistics, DOI /

2 310 References Broderick, T., Jordan, M. L., & Pitman, J. (2013). Cluster and feature modeling from combinatorial stochastic processes. Statistical Science, 28(3), Bulla, P., Muliere, P., & Walker, S. (2007). Bayesian nonparametric estimation of a bivariate survival function. Statistica Sinica, 17, Bulla, P., Muliere, P., & Walker, S. (2009). A Bayesian nonparametric estimator of a multivariate survival function. Journal of Statistical Planning and Inference, 139, Burridge, M. (1981). Empirical Bayes analysis of survival data. Journal of the Royal Statistical Society B, 43, Campbell, G., & Hollander, M. (1978). Rank order estimation with the Dirichlet prior. Annals of Statistics, 6(1), Caron, F., Davy, M., & Doucet, A. (2007). Generalized Polya urn for time-varying Dirichlet process mixtures. In Proceedings of the Conference on Uncertainty in Artificial Intelligence (Vol. 23). Christensen, R., Hanson, T., & Jara, A. (2008). Parametric nonparametric statistics: An introduction to mixtures of finite Polya trees. Annals of Statistics, 62, Chung, Y., & Dunson, D. B. (2011). The local Dirichlet process. Annals of the Institute of Statistical Mathematics, 63, Cifarelli, D. M., & Regazzini, E. (1979). Considerazioni generali sull impostazione bayesiana di problemi non parametrici, Rivista di matematica per le Scienze Economicje e Socialli, 2,PartI 39 52, Part II Clayton, M. K. (1985). A Bayesian nonparametric sequential test for the mean of a population. Annals of Statistics, Clayton, M. K. (1991). A Monte Carlo method for Bayesian inference in frailty models. Biometrika, 47, Clayton, M. K., Berry, D. (1985). Bayesian nonparametric bandits. Annals of Statistics, 13, Connor, R. J., & Mosimann, J. E. (1969). Concept of independence for proportions with a generalization of the Dirichlet distribution. Journal of the American Statistical Association, 64, Dabrowska, D. M. (1988). Kaplan-Meier estimate on the plane. Annals of Statistics, 15, Dalal, S. R. (1979a). Dirichlet invariant processes and applications to nonparametric estimation of symmetric distribution functions. Stochastic Processes and Their Applications, 9, Dalal, S. R. (1979b). Nonparametric and Robust Bayes estimation of location. In Optimizing methods in statistics (pp ). New York: Academic. Dalal, S. R., & Hall, G. J. (1980). On approximating parametric Bayes models by nonparametric Bayes models. Annals of Statistics, 8, Dalal, S. R., & Phadia, E. G. (1983). Nonparametric Bayes inference for concordance in Bivariate distributions. Communications in Statistics - Theory & Methods, 12(8), Damien, P., Laud, P. W., & Smith, A. F. M. (1995). Random variate generation form infinitely divisible distributions with applications to Bayesian inference. Journal of the Royal Statistical Society B, 57, Damien, P., Laud, P. W., & Smith, A. F. M. (1996). Implementation of Bayesian non-parametric inference based on beta processes. Scandinavian Journal of Statistics, 23, Damien, P., & Walker, S. (2002). A Bayesian nonparametric comparison of two treatments. Scandinavian Journal of Statistics, 29, DeIorio, M., Müller, P., Rosner, G.L., & MacEachern, S. N. (2004). An anova model for dependent random measures. Journal of the American Statistical Association, 99, Dey, J., Erickson, R. V., & Ramamoorthi, R. V. (2003). Some aspects of neutral to right priors. International Statistical Review, 71(2), Dey, D., Müller, P., & Sinha, D. (Eds.). (1998). Practical nonparametric and semiparametric Bayesian statistics. Lecture notes in statistics. New York: Springer. Diaconis, P., & Freedman, D. A. (1986). On inconsistent of Bayes estimates of location. Annals of Statistics, 14,

3 References 311 Doksum, K. A. (1972). Decision theory for some nonparametric models. Proceedings of the Sixth Berkeley symposium on Mathematical Statistics and Probability, Vol. I: Theory of Statistics (pp ). Doksum, K. A. (1974). Tailfree and neutral random probabilities and their posterior distributions.annals of Probability, 2, Doss, H. (1984). Bayesian estimation in the symmetric location problem. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 68, Doss, H. (1985a). Bayesian nonparametric estimation of the median: Part I: computation of the estimates. Annals of Statistics, 13, Doss, H. (1985b). Bayesian nonparametric estimation of the median: Part II: Asymptotic properties of the estimates. Annals of Statistics, 13, Doss, H. (1994). Bayesian nonparametric estimation for incomplete data via successive substitution sampling. Annals of Statistics, 22, Dråghici, L., & Ramamoorthi, R. V. (2000). A note on the absolute continuity and singularity of Polya tree priors and posteriors. Scandinavian Journal of Statistics, 27, Duan, J. A., Guindani, M., & Gelfand, A. E. (2007). Generalized spatial Dirichlet process model. Biometrika, 94, Dubins, L. E., & Freedman, D. A. (1966). Random distribution functions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 2, pp ). Dunson, D. B. (2006). Bayesian dynamic modeling of latent trait distributions. Biostatistics, 7(4), Dunson, D. B., & Park, J. H. (2008). Kernel Stick-breaking processes. Biometrika, 95, Dykstra, R. L., & Laud, P. (1981). A Bayesian nonparametric approach to reliability. Annals of Statistics, 9, Engen, S. (1975). A note on the geometric series as a species frequency model. Biometrika, 62, Engen, S. (1978). Stochastic Abundance Models with emphasis on biological communities and species diversity. London: Chapman and Hall. Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theoretical Population Biology, 3, Escobar, M. D. (1994). Estimating normal means with a Dirichlet process prior. Journal of the American Statistical Association, 89, Escobar, M. D., & West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, Efron, B. (1967). The two sample problem with censored data. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 4, pp ). Fabius, J. (1964). Asymptotic behavior of Bayes estimates. Annals of Mathematical Statistics, 35, Fabius, J. (1973). Neutrality and Dirichlet distributions. In Transactions of the 6th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes (pp ). Favaro, S., & Teh, Y. W. (2013). MCMC for normalized random measure mixture models. Statistical Science, 28, Feller, W. (1966). An introduction to probability theory and its applications (Vol. II). New York: Wiley. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1, Ferguson, T. S. (1974). Prior distributions on spaces of probability measures. Annals of Statistics, 2, Ferguson, T. S. (1982). Sequential estimation with Dirichlet process priors. In S. Gupta & J. Berger (Eds.). Statistical decision theory and related topics III (Vol. 1, pp ). Ferguson, T. S. (1983). Bayesian density estimation by mixtures of normal distributions. In H. Rizvi & J. S. Rustagi (Eds.). Recent advances in statistics (pp ). New York: Academic.

4 312 References Ferguson, T. S., & Klass, M. J. (1972). A representation of independent increment processes without Gaussian components. Annals of Mathematical Statistics, 43, Ferguson, T. S., & Phadia, E. G. (1 979). Bayesian nonparametric estimation based on censored data. Annals of Statistics, 7, Ferguson, T. S., Phadia, E. G., & Tiwari, R. C. (1992 ). Bayesian nonparametric inference. In M. Ghosh & P. K. Pathak (Eds.). Current issues in statistical inference: Essays in honor of D. Basu. IMS lecture notes-monograph series (Vol. 17, pp ). Foti, N. J., Futoma, J. D., Rockmore, D. N., & Williamson, S. (2012). A unifying representation for a class of dependent random measures. arxiv: v1[stat.ml] Freedman, D. A. (1963). On the asymptotic behavior of Bayes estimates in the discrete case. Annals of Mathematical Statistics, 34, Gardiner, J. C., & Susarla, V. (1981). A nonparametric estimator of the survival function under progressive censoring. In J. Crowley & R. A. Johnson (Eds.). Survival analysis. IMS lecture notes-monograph series (Vol. 2, pp ). Gardiner, J. C., & Susarla, V. (1983). Weak convergence of a Bayesian nonparametric estimator of the survival function under progressive censoring. Statistics and Decision, 1, Gehan, E. A. (1965). A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika, 52, Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, Gelfand, A. E., Kottas, A., & MacEachern, S. N. (2005). Bayesian nonparametric spatial modeling with Dirichlet process mixing. Journal of the American Statistical Association, 100, Ghosh, J. K., & Ramamoorthi, R. V. (2003). Bayesian nonparametric.springer series in statistics. New York: Springer. Ghosh, J. K., Hjort, N. L., Messan, C., & Ramamoorthi, R. V. (2006). Bayesian bivariate survival estimation. Journal of Statistical Planning and Inference, 136, Ghosh, M. (1985). Nonparametric empirical Bayes estimation of certain functionals. Communications in Statistics - Theory & Methods, 14(9), Ghosh, M., Lahiri, P., & Tiwari, R. C. (1989). Nonparametric empirical Bayes estimation of the distribution and the mean. Communications in Statistics - Theory & Methods, 18(1), Ghorai, J. K. (1981). Empirical Bayes estimation of a distribution function with a gamma process prior. Communications in Statistics - Theory & Methods, A10(12), Ghorai, J. K. (1989). Nonparametric Bayesian estimation of a survival function under the proportional hazard model. Communications in Statistics - Theory & Methods, A18(5), Ghorai, J. K., & Susarla, V. (1982). Empirical Bayes estimation of probability density function with Dirichlet process prior. In W. Grossmann, et al. (Eds.). Probability and statistical inference (pp ). Dordrecht: D. Reidel Publishing Company. Gnedin, A., & Pitman, J. (2007). Poisson representation of a Ewens fragmentation process. Combinatorics, Probability and Computing, 16, Griffin, J. E., & Steel, M. F. J. (2006). Order-based dependent Dirichlet processes. Journal of the American Statistical Association, 101, Griffiths, R. C. (1980). Allele frequencies in multidimensional Wright-Fisher models with a general symmetric mutation structure. Theoretical Population Biology, 17(1), Griffiths, T. L., & Ghahramani, Z. (2006). Infinite latent feature models and the Indian buffet process. In Advances in neural information processing systems (Vol. 18). Cambridge, MA: MIT. Ghahramani, Z.,Griffiths, T.L., &Sollich,P. (2007). Bayesian nonparametric latent feature models (with discussion and rejoinder). In J. M. Bernado, et al. (Eds.). Bayesian statistics (Vol. 8). Oxford, UK: Oxford University Press. Griffiths, T. L., & Ghahramani, Z. (2011). The Indian buffet process: An introduction and review. Journal of Machine Learning Research, 12,

5 References 313 Gross, A. J., & Clark, V. A. (1975). Survival distributions. Reliability applications in biomedical sciences. New York: Wiley. Hall, G. J., Jr. (1976). Sequential search with random overlook probabilities. Annals of Statistics, 4, Hall, G. J., Jr. (1977). Strongly optimal policies in sequential search with random overlook probabilities. Annals of Statistics, 5, Hannah, L. A., Blei, D. M., & Powell, W. B. (2011). Dirichlet process mixtures of general linear models. Journal of Machine Learning Research, 12, Hannum, R. C., & Hollander, M. (1983). Robustness of Ferguson s Bayes estimator of a distribution function. Annals of Statistics, 11, , Hannum, R. C., Hollander, M., & Langberg, N. A. (1981). Distributional results for random functionals of a Dirichlet process. Annals of Probability, 9, Hansen, B., & Pitman, J. (2000). Prediction rules for exchangeable sequences related to species sampling. Statistics & Probability Letters, 46, Hanson, T. E. (2006). Inference for mixtures of finite Polya tree models. Journal of the American Statistical Association, 101, Hanson, T. E. (2007). Polya trees and their use in reliability and survival analysis. In Encyclopedia of statistcs in quality and reliability (pp ). New York: Wiley. Hanson, T. E., Branscum, A., & Gardner, I. (2008). Multivariate mixtures of Polya trees for modelling ROC data. Statistical Modelling, 8, Hanson, T. E., & Johnson, W. O. (2002). Modeling regression error with a mixture of Polya trees. Journal of the American Statistical Association, 97, Hjort, N. L. (1985). Bayesian Nonparametric Bootstrap Confidence Intervals. NSF-andLCS- Technical Report, Department of Statistics, Stanford University. Hjort, N. L. (1990). Nonparametric Bayes estimators based on Beta processes in models for life history data. Annals of Statistics, 18(3), Hjort, N. L., Homes, C., Müller, P., & Walker, S. G. (2010). Bayesian nonparametrics. Cambridge series in statistical and probabilistic mathematics. Cambridge: Cambridge University Press. Hollander, M., & Korwar, R. M. (1976). Nonparametric empirical Bayes estimation of the probability that X Y. Communications in Statistics - Theory & Methods, A5(14), Hollander, M., & Korwar, R. M. (1982). Nonparametric Bayesian estimation of the horizontal distance between two populations. In Nonparametric statistical inference (Vol. 1). New York: North Holland. Ishwaran, H., & James, L. F. (2001). Gibbs sampling methods for Stick-breaking priors. Journal of the American Statistical Association, 96, Ishwaran, H., & James, L. F. (2003). Generalized weighted Chinese restaurant processes for species sampling mixture models. Statistica Sinica, 13, Ishwaran, H., & Zarepour, M. (2000). Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models. Biometrika, 87, Ishwaran, H., & Zarepour, M. (2003). Exact and approximate sum representations for the Dirichlet process. Canadian Journal of Statistics, 30, Ishwaran, H., & Zarepour, M. (2003). Random probability measures via Polya sequences: Revisiting the Blackwell-MacQueen Urn scheme. airxiv:math/ v1. Ibrahim, J. L., Chen, M., & Sinha, D. (2001). Bayesian survival analysis. New York: Springer. Jain, S., & Neal, R. (2004). A split-merge Markov chain monte Carlo procedure for the Dirichlet process mixture model. Journal of Computational and Graphical Statistics, 13, James, L. F. (2006). Poisson calculus for spatial neutral to the right processes. Annals of Statistics, 34, Johnson, N. L., & Kotz, S. (1970). Distributionsinstatistics-continuous multivariatedistributions. New York: Wiley. Johnson, N. L., Kotz, S., & Balkrishnan, N. (1997). Multivariate Ewens distribution. In Discrete multivariate distributions (Chap. 41, pp ). New York: Wiley. Johnson, R. A., Susarla, V., & Van Ryzin, J. (1979). Bayesian non-parametric estimation for agedependent branching processes. Stochastic Processes and Their Applications, 9,

6 314 References Jordan, M. I. (2010). Hierarchical models, nested models and completely random measures. In M.- H.Chen,D.Dey,P.Mueller,D.Sun,&K.Ye(Eds.),Frontiers of statistical decision making and Bayesian analysis: In honor of James O. Berger. New York: Springer. Kalbfleisch, J. D. (1978). Nonparametric Bayesian analysis of survival data. Journal of the Royal Statistical Society B, 40, Kalbfleisch, J. D., & Prentice, R. L. (1980). The statistical analysis of failure time data. New York: Wiley. Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, Kim, Y. (1999). Nonparametric Bayesian estimators for counting processes. Annals of Statistics, 27, Kingman, J. F. C. (1967). Completely random measures. Pacific Journal of Mathematics, 21, Kingman, J. F. C. (1975). Random discrete distributions. Journal of the Royal Statistical Society B, 75, Kingman, J. F. C. (1993). Poisson processes. Oxford: Clarendon Press. Korwar, R. M. & Hollander, M. (1973). Contributions to the theory of Dirichlet processes. Annals of Probability, 1, Korwar, R. M., & Hollander, M. (1976). Empirical Bayes estimation of a distribution function. Annals of Statistics, 4, Kraft, C. H. (1964). A class of distribution function processes which have derivatives. Journal of Applied Probability, 1, Kraft, C. H., & van Eeden, C. (1964). Bayesian bioassay. Annals of Mathematical Statistics, 35, Kuo, L. (1986a). A note on Bayes empirical Bayes estimation by means of Dirichlet processes. Statistics & Probability Letters, 4, Kuo, L. (1986b). Computations of mixtures of Dirichlet processes. SIAM Journal on Scientific Computing, 7, Kuo, L. (1988). Linear Bayes estimators of the potency curve in bioassay. Biometrika, 75, Lavine, M. (1992). Some aspects of Polya tree distributions for statistical modelling. Annals of Statistics, 20, Lavine, M. (1994). More aspects of Polya trees for statistical modelling. Annals of Statistics, 22, Lijoi, A., & Prünster, I. (2010). Models beyond the Dirichlet process. In N. L. Hjort, et al. (Eds.). Bayesian nonparametrics. Cambridge series in statistical and probabilistic mathematics (pp ). Lin, D., Grimson, E., & Fisher, J. (2010). Construction of dependent Dirichlet processes based on Poisson processes. In Neural Information Processing Systems. Lo, A. Y. (1981). Bayesian nonparametric statistical inference for shock models and wear processes. Scandinavian Journal of Statistics, 8, Lo, A. Y. (1982). Bayesian nonparametric statistical inference for Poisson point processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 59, Lo, A. Y. (1983). Weak convergence for Dirichlet processes. Sankhya, 45, Lo, A. Y. (1984). On a class of Bayesian nonparametric estimates; I. Density estimates. Annals of Statistics, 12, Lo, A. Y. (1986). Bayesian statistical inference for sampling a finite population. Annals of Statistics, 14, Lo, A. Y. (1987). A large sample study of the Bayesian bootstrap. Annals of Statistics, 15(1), Lo, A. Y. (1988). A Bayesian bootstrap for a finite population. Annals of Statistics, 16, Lo, A. Y. (1991). A characterization of the Dirichlet process.statistics & Probability Letters, 12, Lo, A. Y. (1993a). A Bayesian bootstrap for censored data. Annals of Statistics, 21, Lo, A. Y. (1993b). A Bayesian method for weighted sampling. Annals of Statistics, 21,

7 References 315 MacEachern, S. N. (1998). Computational methods for mixture of Dirichlet process models. In D. Dey, P. Müller, & D. Sinha (Eds.). Practical nonparametric and semiparametric Bayesian statistics (pp ). MacEachern, S. N. (1999). Dependent nonparametric processes. In ASA Proceedings of the Section on Bayesian Statistical science. Alexandria: American Statistical Association. MacEachern, S. N., & Müller, P. (1998). Estimating mixtures of Dirichlet process models. Journal of Computational and Graphical Statistics, 7, Mauldin, R. D., Sudderth, W. D., & Williams, S. C. (1992). Polya trees and random distributions. Annals of Statistics, 20, McCloskey, J. W. (1965). A Model for the Distribution of Individuals by Species in an Environment, unpublished Ph.D. thesis, Michigan State University. Muliere, P., & Petrone, S. (1993). A Bayesian predictive approach to sequential search for an optimal dose: parametric and nonparametric models. Journal of the Italian Statistical Society, 2, Muliere, P., & Tardella, L. (1998). Approximating distributions of random functionals of Ferguson- Dirichlet priors. Canadian Journal of Statistics, 26, Muliere, P., & Walker, S. (1997). A Bayesian non-parametric approach to survival analysis using Polya trees. Scandinavian Journal of Statistics, 24, Müller, P., & Quintana, F. A. (2004). Nonparametric Bayesian data analysis. Statistical Science, 19, Müller, P., Quintana, F. A., Jara, A., & Hanson, T. (2015). Bayesian nonparametric data analysis. New York: Springer. Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9, Neal, R. M. (2003). Slice sampling. Annals of Statistics, 31, Neath, A. A., & Bodden, K. (1997). Bayesian nonparametric confidence bounds for a distribution function. Journal of Statistical Computation and Simulation, 59, Neath, A. A. (2003). Polya tree distributions for statistical modeling of censored data. Journal of Applied Mathematics and Decision Sciences, 7(3), Neath, A. A., & Samaniego, F. J. (1996). On Bayesian estimation of the multiple decrement function in the competing risks problem. Statistics & Probability Letters, 31, Neath, A. A., & Samaniego, F. J. (1997). On Bayesian estimation of the multiple decrement function in the competing risks problem, II. Statistics & Probability Letters, 35, Nieto-Barajas, L. E., Prunster, I., & Walker, S. G. (2004). Normalized random measures driven by increasing additive processes. Annals of Statistics, 32, Nieto-Barajas, L. E., Müller, P., Ji, Y., Lu, Y., & Mills, G. B. (2012). A time-series DDP for functional proteomics profiles. Biometrics, 68, Ongaro, A., & Cattaneo, C. (2004). Discrete random probability measures: A general framework for nonparametric Bayesian inference. Statistics & Probability Letters, 67, Paddock, S., Ruggeri, F., Lavine, M., & West, M. (2003). Randomised Polya tree models for nonparametric Bayesian inference. Statistica Sinica, 13, Padgett, W. J., & Wei, L. J. (1981). A Bayesian nonparametric estimator of survival probability assuming increasing failure rate. Communications in Statistics - Theory & Methods, A10(1), Paisley, J., Blei, D. M., & Jordan, M. I. (2012). Stick-breaking beta processes and the Poisson process. In Proceedings of the 15th International Conference on Artificial Intelligence and Statistics, La Palma, Canary Islands. Paisley, J., Zaas, A., Woods, C. W., Ginsburg, G. S., & Carin, L. (2010). A stick-breaking construction of the beta process. In Proceedings of the 27th International Conference on Machine Learning, Haifa. Papaspiliopoulos, O., & Roberts, G. O. (2008). Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models. Biometrika, 95, Patil, G. P., & Taillie, C. (1977). Diversity as a concept and its implications for random communities. Bulletin International Statistical Institute, 47,

8 316 References Peterson, A. V. (1977). Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions. Journal of the American Statistical Association, 72, Perman, M., Pitman, J., & Yor, M. (1992). Size-biased sampling of Poisson point processes and excursions. Probability Theory and Related Fields, 92, Petrone, S. (1999). Random Bernstein polynomials. Scandinavian Journal of Statistics, 26, Petrone, S., Guindani, M., & Gelfand, A. E. (2009). Hybrid Dirichlet mixture models for functional data. Journal of the Royal Statistical Society B, 71, Phadia, E. G. (1971). Minimax Estimation of a Cumulative Distribution Function. Technical Report 71-1, Division of Statistics, The Ohio State University. Phadia, E. G. (1973). Minimax estimation of a cumulative distribution function. Annals of Statistics, 1, Phadia, E. G. (1974). Best invariant confidence bands for a continuous cumulative distribution function. Australian Journal of Statistics, 16(3), Phadia, E. G. (1980). A note on empirical Bayes estimation of a distribution function based on censored data. Annals of Statistics, 8(1), Phadia, E. G. (2007). On bivariate tailfree processes. In Proceedings of the 56th Session of the International Statistical Institute, Lisbon (2007) (electronic version) Phadia, E. G., & Susarla, V. (1983). Nonparametric Bayesian estimation of a survival curve with dependent censoring mechanism. Annals of the Institute of Statistical mathematics, 35, Phadia, E. G., & Susarla, V. (1979). An empirical Bayes approach to two-sample problems with censored data. Communications in Statistics - Theory & Methods, A8(13), Pitman, J. (1995). Exchangeable and partially exchangeable random partitions. Probability Theory and Related Fields, 102, Pitman, J. (1996a). Some developments of the Blackwell-MacQueen urn scheme. In T. S. Ferguson, L. S. Shapley & J. B. MacQueen (Eds.). Statistics, Probability and Game Theory. Papers in Honor or David Blackwell (pp ). Hayward, CA: IMS. Pitman, J. (1996b). Random discrete distributions invariant under size-biased permutation. Advances in Applied Probability, 28, Pitman, J., & Yor, M. (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Annals of Probability, 25, Pruitt, R. C. (1992). An inconsistent Bayes estimate in bivariate survival curve analysis. Statistics and Probability Letters, 15(3), Ramsey, F. L. (1972). A Bayesian approach to bioassay. Biometrics, 28, Randles, R. H., & Wolf, D. A. (1979). Introduction to the Theory of Nonparametric Statistics. New York: Wiley. Rao, V., & Teh, Y. W. (2009). Spatial normalized gamma processes. In Neural Information Processing Systems, Regazzini, E., Lijoi, A., & Prunster, I. (2003). Distributional results for means of normalized random measures with independent increments. Annals of Statistics, 31, Reich, B. J., & Fuentes, M. (2007). A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields. Annals of Applied Statistics, 1, Ren, L., Dunson, D., & Carin, L. (2008). Dynamic hierarchical Dirichlet process. In Proceedings of the International Conference on Machine Learning, Helsinki. Ren, L., Wang, Y., Dunson, D., & Carin, L. (2011). The kernel Beta process. In Neural Information Processing Systems, Rodriguez, A., & Dunson, D. B. (2011). Nonparametric Bayesian models through probit stickbreaking processes. Bayesian Analysis, 6(1), Rodriguez, A., Dunson, D. B., & Gelfand, A. E (2008). The nested Dirichlet process. Journal of the American Statistical Association, 103, Rodriguez, A., Dunson, D. B., & Gelfand, A. E. (2010). Latent stick-breaking processes. Journal of the American Statistical Association, 105,

9 References 317 Salinas-Torres, V. H., Pereira, C. A. B., & Tiwari, R. C. (2002). Bayesian nonparametric estimation in a series system or a competing-risks model. Nonparametric Statistics, 14, Samaniego, F. J., & Whitaker, L. R. (1988). On estimating population characteristics from recordbreaking observations. II. Nonparametric results. Naval Research Logistics, 35, Savitsky, T. D., & Paddock, S. M. (2013). Bayesian nonparametric hierarchical modeling for multiple membership data in grouped attendance interventions. Annals of Applied Statistics, 7, Sethuraman, J. (1994). A constructive definition of thedirichlet process prior. Statistica Sinica, 2, Sethuraman, J., & Tiwari, R. C. (1982). Convergence of Dirichlet measures and the interpretation of their parameter. In S. Gupta & J. Berger (Eds.). Statistical decision theory and related topics III (Vol. 1, pp ). Shahbaba, B., & Neal, R. M. (2009). Non-linear models using Dirichlet process mixtures. Journal of Machine Learning Research, 10, Sinha, D. (1997). Time-discrete beta-process model for interval-censored survival data. Canadian Journal of Statistics, 25, Sinha, D. (1998). Posterior likelihood methods for multivariate survival data. Biometrics, 54, Steck, G. P. (1971). Rectangle probabilities for uniform order statistics and the probability that the empirical distribution function lies between two distributions. Annals of Mathematical Statistics, 42, Susarla, V, & Phadia, E. G. (1976). Empirical Bayes testing of a distribution function with Dirichlet process priors. Communications in Statistics - Theory & Methods, A5(5), Susarla, V., & Van Ryzin, J. (1976). Nonparametric Bayesian estimation of survival curves from incomplete observations. Journal of the American Statistical Association, 71, Susarla, V., & Van Ryzin, J. (1978a). Empirical Bayes estimation of a distribution (survival) function from right-censored observations. Annals of Statistics, 6, Susarla, V., & Van Ryzin, J. (1978b). Large sample theory for a Bayesian nonparametric survival curve estimator based on censored samples. Annals of Statistics, 6, Susarla, V., & Van Ryzin, J. (1978c). Addendum to large sample theory for a Bayesian nonparametric survival curve estimator based on censored samples. Annals of Statistics, 8, 693. Teh, Y. W., & Gorur, D. (2009). Indian buffet processes with power-law behavior. In Advances in neural information processing systems (Vol. 22). Teh, Y. W., Gorur, D., & Ghahramani, Z. (2007). Sick-breaking construction for the Indian buffet process. In M. Meila & X. Shen (Eds.). Proceedings of the International Conference on Artificial Intelligence and Statistics (Vol. 11, pp ). Brookline, MA: Microtone. Teh, Y. W., & Jordan, M. I. (2010). Hierarchical Bayesian nonparametric models with applications. In N. L. Hjort, et al. (Eds.). Bayesian nonparametrics. Cambridge series in statistical and probabilistic mathematics. Teh, Y. W., Jordan, M. I, Beal, M. J., & Blei, D. M. (2004). Hierarchical Dirichlet processes. In Advances in neural information processing systems, Vol. 17. Cambridge, MA: MIT Press. Teh, Y. W., Jordan, M. I, Beal, M. J., & Blei, D. M. (2006). Hierarchical Dirichlet processes. Journal of the American Statistical Association, 101, Thibaux, R. (2008). Nonparametric Bayesian Models for Machine Learning. Ph.D. dissertation, Department of Statistics, University of California, Berkeley. Thibaux, R., & Jordan, M. I. (2007). Hierarchical beta processes and the Indian buffet process. In M. Meila and X. Shen (Eds.). Proceedings of the International Conference on Artificial Intelligence and Statistics (Vol. 11, pp ). Brookline, MA: Microtone. Titsias, M. K. (2008). The infinite Gamma-Poisson feature model. Advances in Neural Information Processing Systems, 20, Tiwari, R. C. (1981). A Mathematical Study of the Dirichlet Process. Ph.D. dissertation, Department of Statistics, Florida State University. Tiwari, R. C. (1988). Convergence of the Dirichlet Invariant measures and the limits of Bayes estimates. Communications in Statistics - Theory & Methods, 17(2),

10 318 References Tiwari, R. C., Jammalamadaka, S. R., & Zalkikar, J. N. (1988). Bayes and empirical Bayes estimation of survival function under progressive censoring. Communications in Statistics - Theory & Methods, A17(10), Tiwari, R. C., & Lahiri, P. (1989). On Robust Bayes and empirical Bayes estimation of means and variances from stratified samples. Communications in Statistics: Theory and Methods, 18(3), Tiwari, R. C., & Zalkikar, J. N. (1985). Empirical Bayes estimation of functionals of unknown probability measures. Communications in Statistics - Theory & Methods, 14, Tiwari, R. C., & Zalkikar, J. N. (1991a). Empirical Bayes estimate of certain estimable parameters of degree two. Calcutta Statistical Association Bulletin, 34, Tiwari, R. C., & Zalkikar, J. N. (1991b). Bayesian inference of survival curve from record-breaking observations: Estimation and asymptotic results. Naval Research Logistics, 38, Tiwari, R. C., & Zalkikar, J. N. (1993). Nonparametric Bayesian estimation of survival function under random left truncation. Journal of Statistical Planning and Inference, 35, Tsai, W. Y. (1986). Estimation of survival curves from dependent censorship models via a generalized self-consistent property with nonparametric Bayesian estimation application. Annals of Statistics, 14, Wade, S., Dunson, D. B., Petrone, S., & Trippa, L. (2014). Improving prediction from Dirichlet process mixtures via enrichment. Journal of Machine Learning Research, 15, Walker, S. G. (2007). Sampling the Dirichlet mixture model with slices. Communications in Statistics - Simulation and Computation, 36, Walker, S. G., & Damien, P. (1998). A full Bayesian nonparametric analysis involving a neutral to the right process. Scandinavian Journal of Statistics, 25, Walker, S. G., Damien, P., Laud, P., & Smith, A. F. M. (1999). Bayesian nonparametric inference for random distributions and related functions. Journal of the Royal Statistical Society B, 61, Walker, S. G., & Mallick, B. K. (1997). A note on the scale parameter of the Dirichlet Process. Canadian Journal of Statistics, 25, Walker, S. G., & Mallick, B. K. (1997). Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. Journal of the Royal Statistical Society B, 59, Walker, S. G., & Mallick, B. K. (1999). Semiparametric accelerated life time models. Biometrics, 55, Walker, S. G., & Muliere, P. (1997a). Beta-Stacy processes and a generalization of the Polya-urn scheme. Annals of Statistics, 25(4), Walker, S. G., & Muliere, P. (1997b). A characterization of Polya tree distributions. Statistics & Probability Letters, 31, Walker, S. G., & Muliere, P. (1999). A characterization of a neutral to the right prior via an extension of Johnson s sufficientness postulate. Annals of Statistics, 27(2), Walker, S. G., & Muliere, P. (2003). A bivariate Dirichlet process. Statistics & Probability Letters, 64, 1 7. West, M. (1992). Modelling with mixtures (with discussion). In J. M. Bernardo, J. 0. Berger, A. P. Dawid, & A. F. M. Smith (Eds.). Bayesian statistics (Vol. 4, pp ). Oxford: Oxford University Press. West, M., Müller, P., & Escobar, M. D. (1994). Hierarchical priors and mixture models, with applications in regression and density estimation. In A. F. M. Smith & P. R. Freeman (Eds.). Aspects of uncertainty: A tribute to D.V. Lindley (pp ). New York: Wiley. Wild, C. J., & Kalbfleisch, J. D. (1981). A note on a paper by Ferguson and Phadia. Annals of Statistics, 9, Wolpart, R. L., & Ickstadt, K. (1998). Poisson/gamma random field models for spatial statistics. Biometrika, 85, Yamato, H. (1975). A Bayesian estimation of a measure of the difference between two continuous distributions. Reports of the Faculty of Science Kagoshima University (Mathematics, Physics and Chemistry), 8,

11 References 319 Yamato, H. (1977a). Relations between limiting Bayes estimates and the U-statistics for estimable parameters of degree 2 and 3. Communications in Statistics - Theory & Methods, A6, Yamato, H. (1977b). Relations between limitingbayes estimates and the U-statistics for estimable parameters. Journal of the Japan Statistical Society, 7, Yamato, H. (1984). Characteristic functions of means of distributions chosen from a Dirichlet process. Annals of Probability, 12, Yamato, H. (1986). Bayes Estimates of estimable parameters with a Dirichlet Invariant process. Communications in Statistics - Theory & Methods, 15(8), Yamato, H. (1987). Nonparametric Bayes estimates of estimable parameters with a Dirichlet invariant process and invariant U-statistics. Communications in Statistics - Theory & Methods, 16(2), Yang, M., Hanson, T., & Christensen, R. (2008). Nonparametric Bayesian estimation of a bivariate density with interval censored data. Computational Statistics & Data Analysis, 52(12), Zabel, S. L. (1982). W. E. Johnson s sufficientness postulate. Annals of Statistics, 10, Zacks, S. (1971). The theory of statistical inference. New York: Wiley. Zalkikar, J. N., Tiwari, R. C., & Jammalamadaka, S. R. (1986). Bayes and empirical Bayes estimation of the probability that Z > X C Y. Communications in Statistics Theory & Methods, 15(10), Zalkikar, J. N., Tiwari, R. C., & Jammalamadaka, S. R. (1986). Bayes and empirical Bayes estimation of the probability that Z > X C Y. Communications in Statistics - Theory & Methods, 15(10), Zehnwirth, B. (1981). A note on the asymptotic optimality of the empirical Bayes distribution function. Annals of Statistics, 9, Zehnwirth, B. (1985). Nonparametric Linear Bayes estimation of survival curves from incomplete observations. Communications in Statistics - Theory & Methods, 14(8),

12 Author Index A Ammann, L.P., 161, 242 Antoniak, C., 2, 3, 9, 22, 24, 32 35, 38, 45, 46, 49 51, 115, 117, , 224, 241, 244, 247 B Balkrishnan, N., 27 Barlow, R.E., 243 Barthalomew, D. J., 243 Basu, D., 3, 20, 28, 29 Beal, M.J., 93, 107, 174 Berry, D.A., 229, 240 Bhattacharya, P. K., 242 Binder, D.A., 234 Blackwell, D., 5, 7, 15, 20, 28, 34, 38, 41, 54, 86, 117, 120, 122, 124, 125, 210 Blei, D.M., 50, 192 Blum, J., 50, 272, 275 Bodden, K., 230, 232 Breth, M., 230, 231 Bulla, P., 216, 217 Burridge, M., 306 C Cattaneo, C., 13, 41, 83, 89 Chen, M., 224 Christensen, R., 216, 240 Chung, Y., 14, 76, 91, 93, 104, 108 Cifarelli, D.M., 33, 91 Clark, V.A., 269 Clayton, M.K., 229, 239, 306 Connor, R. J., 4, 140 D Dabrowska, D.M., 216 Dalal, S.R., 3, 9, 43 46, 216, 223, 237, 249, 251, 255, 256, 259, 266 Damien, P., 33, 132, 142, 143, , 159, 162, 166, 172, 191, 303 Dey, D., 17, 53, 143, 144, 155, 188, 224 Doksum, K.A., 4, 5, 7, 10, 36, 127, 129, , 144, 146, 147, 155, 158, 160, 161, 164, 205, 207, 261, 274, 281 Doss, H., 8, 45, 224, Dråghici, L., 212 Dubins, L.E., 2, 39, 210 Dunson, D.B., 7, 9, 14, 41, 66, 72, 73, 76, 84, 91, 93, 99, 104, 106, 108, 181 Dykstra, R. L., 4, 11, 132, 144, , 164, 189, 287 E Efron, B., 281, 302 Engen, S., 25, 84, 90, 114, 116 Escobar, M.D., 51, 52, 54, 55, 59, 99, 240, 247, 248 Ewens, W.J, 35, 115, 117, 203 F Fabius, J., 3, 5, 205 Feller, W., 129 Ferguson, T.S., 2, 3, 5 8, 10, 13, 14, 17, 19 25, 28 30, 32, 35, 37, 41, 43, 45, 47, 51, 52, 111, 114, 120, 128, 130, , 139, 141, 142, 146, Springer International Publishing Switzerland 2016 E.G. Phadia, Prior Processes and Their Applications, Springer Series in Statistics, DOI /

13 322 Author Index , 157, 159, 160, , 170, 172, 173, 187, 189, 191, 192, 206, , 213, 216, 217, 219, 223, , , 237, 241, , 252, 260, 264, 272, 274, 276, 278, , 286, 293, Freedman, D.A., 3, 5, 51, 205, 210 G Gardiner, J.C., 275 Gehan, E.A., 302 Gelfand, A.E., 14, 41, 83, 92, 93, 99, 100, 103 Ghahramani, Z., 15, 39, 83, 175, 193, Ghorai, J.K., 246, 277, 278, 284, 285 Ghosh, J.K., 216 Ghosh, M., 28, 33, 165, 216, , 233, 234, 259 Gorur, D., 174, 200 Griffiths, T.L., 15, 25, 39, 83, 84, 193, 196, 197, 199 Gross, A.J., 269 H Hall, G.J. Jr., 46, 229 Hannum, R.C., 33, 223 Hanson, T., 215, 216, 244 Hjort, N.L., 2, 4, 10, 11, 78, 127, 133, 139, 143, 148, 152, 156, 164, 165, 167, 168, 170, 171, 173, 177, 184, 190, 210, 232, 285, 295, 297, 307 Hollander, M., 34, 223, 226, 227, 231, 233, 234, 248, 258, 260, 263, 291 Homes, C., 2 I Ibrahim, J.L., 17, 173, 224 Ickstadt, K, 132, 152 Ishwaran, H., 7, 13, 24, 27, 41, 54, 57, 59, 61, 71, 74, 82, 83, 85 88, 93, 97, 99, 103, 104, 106, 107, 116, 118, 120, 124, 214 J James, L.F., 7, 13, 24, 33, 41, 54, 57, 71, 74, 77, 82, 83, 85, 93, 97, 99, 103, 104, 106, 107, 116, 118, 156, 171, 173, 214 Jammalamadaka, S.R., 238 Johnson, N.L., 293 Johnson, R.A., 25, 84, 215, 244, 293, 300 Jordan, M.I., 4, 14, 72, 76, 94, 107, 116, 128, 134, 164, 174, 177, 178 K Kalbfleisch, J.D., 4, 10, 11, 91, 127, 139, 144, , 162, 164, 166, 184, 280, Kaplan, E.L., 191, 269, 271, 274, 276 Kim, Y., 173, 300 Kingman, J.F.C., 2, 7, 12, 21, 22, 24, 84, 86, 87, 93, 107, , 128, , 177 Korwar, R.M., 34, 226, 227, 231, 233, 234, 258, 260, 263, 291 Kotz, S., 293 Kraft, C.H., 3, 210, 241 Kuo, L., 240, 242, 243, 246, 247 L Langberg, N.A., 33 Laud, P.W., 4, 11, 32, 132, 144, 152, , 189, 287 Lavine, M, 5, 12, 13, 208, 209, , 217, 219, 240, 243, 246 Lijoi, A., 7, 38 Lo, A.Y., 4, 36, 51, 70, 77, 93, 99, 106, 163, 210, 217, 239, 240, 244, 246, 247, 274, 282, 299, 300 M MacEachern, S.N., 7, 14, 41, 54, 56 59, 66, 83, 91, 95, 100, 156, 171 MacQueen, J.B., 5, 7, 15, 20, 28, 38, 41, 54, 86, 117, 120 Mallick, B.K., 215, 244 Mauldin, R.D., 5, 6, 13, 208, 210, 214, 217 McCloskey, J.W., 25, 84, 110, Meier, P., 42, 191, 216, 269, 271, 274, 276 Messan, C., 216 Mosimann, J.E., 4, 140 Muliere, P., 4, 7, 10, 12, 78, 88, 91, 127, 133, 139, 144, 148, 154, 171, , 189, 190, 210, 212, 214, 216, 217, 285, 286 Müller, P., 9, 17, 57, 58, 62, 72 N Neath, A.A., 230, 232, 287, 293, 294

14 Author Index 323 O Ongaro, A., 6, 13, 41, 83, 89 P Padgett, W.J., 287 Park, J.H., 7, 9, 14, 41, 84, 93, 99, 106 Patil, G.P., 27, 87, 89, 90, 113, 114 Pereira, C.A.B., 77, 216, 281, 294, 295 Perman, M., 113, 115, 118, 179 Peterson, A.V., 294 Petrone, S., 78, 91, 103 Phadia, E.G., 10, 16, 128, 132, 143, 146, 149, 151, 152, 157, 159, 160, 162, 164, 170, 172, 173, 191, 192, 213, , 229, 231, 241, 242, 249, 251, 255, 258, 259, 264, 266, 273, 274, 278, 281, 283, 284, 291, 292, 302, Pitman, J., 6, 8, 13, 16, 24, 25, 35, 39, 41, 42, 76, 84, 86, 93, 111, , , 179, 200 Prentice, R. L., 280 Prünster, I., 7, 38, 128, 134, 137 R Ramamoorthi, R.V., 28, 33, 155, 165, 212 Ramsey, F.L., 241, 278 Randles, R.H., 258 Regazzini, E., 7, 23, 24, 33, 83, 91 S Salinas-Torres, V.H., 77, 216, 281, 294, 295 Samaniego, F.J., 276, 293, 294 Sethuraman, J., 6, 22, 24, 32, 81, 175, 223, 254, 258 Sinha, D., 173, 224, 306 Smith. A.F.M., 162 Sollich, P., 175, 200 Steck, G. P., 231 Sudderth, W. D., 5, 6, 13, 208, 210, 214, 217 Susarla, V., 12, 50, 190, 216, 246, 258, 264, , 284, , 302 T Taillie, C., 27, 87, 89, 90, 113, 114 Teh, Y.W., 4, 15, 17, 64 67, 69, 73, 75, 76, 83, 93, 107, 116, 137, 174, 175, 179, 196, 199, 200 Thibaux, R., 4, 14, 55, 76, 94, 107, 128, 134, 157, 164, 174, 177, 179, 193 Tiwari, R.C., 3, 6, 20, 22, 24, 28, 31, 32, 43, 44, 223, 234, 238, , 258, 259, Tsai, W.Y., 216, 279, 280 V van Eeden, C., 3 van Ryzin. J., 12, 190, , 276, 284, 290 W Walker, S.G., 4, 5, 7, 10, 12, 13, 33, 54, 62, 78, 99, 127, 133, 139, , 148, 151, 153, 154, 184, 191, 210, 212, , 244, 285, 286, 303 Wei, L.J., 287 West, M., 51, 52, 54 56, 58, 59, 99, 240, 247, 248 Whitaker, L.R., 276 Wild, C.J., 10, 157, 303, 304, 306, 307 Williams, S.C., 6, 13, 208, 210, 214, 217 Wolf, D.A., 258 Wolpart, R.L., 132, 152 Y Yamato, H., 31, 32, 44, 233, , 261 Yang, M., 217 Yor, M., 8, 13, 35, 41, 86, 93, 111, 115, 116, 118, 200 Z Zacks, S., 253 Zalkikar, J.N., 238, , 258, 259, 276, 277, 290 Zarepour, M., 13, 27, 54, 59, 61, 71, 82, 86 88, 120, 124 Zehnwirth, B., 226, 227, 288

15 Subject Index A Asymptotic optimality, 224, 228, 246, 259, 292 B Bayes empirical Bayes, Bayes estimator of concordant coefficient, 42, , 255, 259, 266 covariance, 42, 242, , 255, 257, 273 cumulative hazard function, 11 density function, 42, 52, , , 287 distribution function, 1, 2, 8, 42, 44, 51, 63, 160, , 216, , , 236, 239, 247, 249, 263, 264, 270, 277, 291, 300 estimable functions, 254 hazard rate, 11, , 287, location parameter, 42, 44, mean, 8, 190, , 241, 255, 261 median, modal, 241, q-th quantile, 42, 230, 231, survival function, symmetric distribution function, 44, 237 variance, Bayes risk, , 233, 234, 259, 264, 267, 303 Binary matrix, 198, 199 Bioassay problem, 3, 9, 42, 45, C Competing risk models, Confidence bands, 8, 222, , 239 Conjugacy, 7 8, 10, 12, 13, 38, 42, 44, 48, 54, 58, 60, 89, 146, 159, 162, 163, 166, 170, 178, 189, 190, 193, 205, 208, 250 Cox model, 11, 91, 157, 173, 307 D Distribution Bernoulli, 1, 14, 76, 89, 93 94, 107, 128, 159, 164, , 193, 200, 201 beta distribution, 1, 7, 11, 12, 24, 26, 41, 62, 76, 83, 86, 96, 113, 127, 139, 145, 146, , 169, 174, 175, 181, 184, 209, 212, 213, 217, 219, 229, 241, 272 bivariate, 52, 216, 222, , 265 Dirichlet, 2 4, 13, 19 79, 86, 87, 90, 104, 112, 113, 116, 140, 145, 154, 163, 194, 207, 217, 219, 231, 243, 261, 278, 298 gamma distribution, 4, 23, 24, 127, , 163, 166, 300, 306 GEM, 25, 84, 110, 113, 114 log-beta distribution, 7, 10, 12, 127, 130, 133, 144, , mixing, 28, 29, 38, 46 51, 75, 95, 102, 214, 224, 240, 244 multinomial, 55, 71, 77 Poisson distribution, 2, 7, 12, 22, 24, 27, 93, 98, 107, 108, , 128, , , 159, 163, , , 198, , 287, 299, 300 symmetric, 4, 43, 44, 112, 223, 237, 238 Springer International Publishing Switzerland 2016 E.G. Phadia, Prior Processes and Their Applications, Springer Series in Statistics, DOI /

16 326 Subject Index E Engen s model, 114 Estimable functions, 254 Estimation based on covariates, Bayes empirical Bayes, concordance coefficient, covariance, empirical Bayes, , , , linear Bayes, location parameter, maximum likelihood, 8, 227, 229, 236, 279, 301 mean, median, minimax, 42, 222, 229, 235 mode, quantiles, sequential, shock model, variance, Ewen s formula, 117 F Function cummulative hazard, 4, 11, 14, 78, 127, 139, 143, , , 285, , 306, 307 cumulative distribution, 20, 102, 159, , , 241, 252, 266 density, 4, 42, 51, 52, 106, 158, 159, 206, 208, 210, 211, 239, , 287 distribution, , random distribution, 1, 2, 7, 24, 45, 79, 94, 100, 103, 106, 122, 138, 139, 141, 142, , , 154, 224, 225, 231, 282, 305 survival, 11, 12, 144, 151, 156, 157, 161, 173, 216, 217, 241, 249, Functionals of p; G Group of transformations, 3, 43, 237 H Hazard rate, 9, 11, 144, 155, , , 170, 287, Hierarchical models, 4, 30, 64, 76, 91, 119 Hypothesis testing, 8, 42, 221, , K Kernel, 4, 7, 15, 41, 46, 51, 53, 56, 77, 93, 95, 99, 101, 110, 128, 136, , 210, 244, 246, 253, 256 kernel-based, 14, 17, 83, 84, L Loss function integrated squared error, 241 squared error, 221, 229, 233, 234, 238, 249, 250, 260, 261, 273, 276, 279, 283, 288, , 301, 307 weighted, 249 M Markov Chain, 11, 53, 54, 93, 108, 165, 166, 173, Measure Lévy, 4, 7, 10, 14, 24, 64, 109, 110, 128, , 136, 137, , , 156, 157, 165, 167, 168, , 174, , 182, 183, 185, 189, 191, 300 probability, 1 3, 5 7, 12, 14, 16, 19 24, 30, 33, 41 43, 52, 66, 70, 78, 79, 82, 84, 89, 99, , 112, , 140, 142, 166, 177, 196, 198, 205, 209, 210, 215, 216, 223, 232, 244, 246, 249, 258, 264 random, 2, 4, 7, 12, 21, 22, 24, 59, 64, 72, 76, 82, 87, 93, 107, 108, 118, 128, , 174, 215 P Permutation rank ordered, 111, 114, 116 size-biased, 27, 90, 111, 113, 114, 116 Polya generalized urn scheme, 3, 6, 7, 41, 75, 86, 107, 117, 119, 217 sequence, 28, 40, 120, 121 tree, 5, 6, 12, 13, 17, 41, 171, , 219, 240, 243, 244, 246, urn scheme, 5, 13, 15, 38, 39, 118, 120, 124, 193 Predictive distribution, 5, 6, 8, 12, 28, 35, 41, 52, 54, 55, 115, 201, 211, 213, 216, 247, 286 rule, 28, 86, 117, 120, 121, 124