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References

from Appendices

Published online by Cambridge University Press:  22 July 2017

Subhashis Ghosal  and
Aad van der Vaart
Subhashis Ghosal
Affiliation:
North Carolina State University
Aad van der Vaart
Affiliation:
Universiteit Leiden
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Fundamentals of Nonparametric Bayesian Inference , pp. 623 - 637
Publisher: Cambridge University Press
Print publication year: 2017

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References

Albert, J., and S., Chib (1993). Bayesian analysis of binary and polychotomous response data. J. Amer. Statist. Assoc. 88(422), 669–679.CrossRefGoogle Scholar
Aldous, D. (1985). Exchangeability and related topics. In École d'été de probabilités de Saint-Flour, XIII— 1983, Volume 1117 of Lecture Notes in Math., pp. 1–198. Berlin: Springer.CrossRef
Amewou-Atisso,, M., S., Ghosal, J., Ghosh, and R., Ramamoorthi (2003). Posterior consistency for semiparametric regression problems. Bernoulli 9(2), 291–312.CrossRefGoogle Scholar
Andersen, P., O., Borgan, R., Gill, and N., Keiding (1993). Statistical Models Based on Counting Processes. Springer Series in Statistics. New York: Springer-Verlag.
Antoniak, C. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2, 1174–.CrossRefGoogle Scholar
Arratia, R., L., Goldstein, and L., Gordon (1990). Poisson approximation and the Chen–Stein method. Statist. Sci. 5(4), 403–434. With comments and a rejoinder by the authors.CrossRefGoogle Scholar
Barrios, E., A., Lijoi, L., Nieto-Barajas, and I., Pruenster (2013). Modeling with normalized random measure mixture models. Stat. Sci. 277, 334–.CrossRefGoogle Scholar
Barron, A. (1986). Discussion of “on the consistency of Bayes estimates” by P. Diaconis and D. Freedman. Ann. Statist. 14(1), 26–30.CrossRefGoogle Scholar
Barron, A. (1999). Information-theoretic characterization of Bayes performance and the choice of priors in parametric and nonparametric problems. In Bayesian Statistics, 6 (Alcoceber, 1998), pp. 27–52. New York: Oxford Univ. Press.
Barron, A., M., Schervish, and L., Wasserman (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27(2), 536–561.Google Scholar
Bauer, H. (2001). Measure and Integration Theory, Volume 26 of de Gruyter Studies in Mathematics. Berlin: Walter de Gruyter & Co. Translated from the German by Robert B., Burckel.
Beal, M., and Z., Ghahramani (2003). The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures. In Bayesian Statistics, 7 (Tenerife, 2002), pp. 453– 463. New York: Oxford Univ. Press.
Begun, J., W., Hall W.-M., Huang, and J., Wellner (1983). Information and asymptotic efficiency in parametric–nonparametric models. Ann. Statist. 11(2), 432–452.CrossRefGoogle Scholar
Belitser, E., and S., Ghosal (2003). Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution. Ann. Statist. 31(2), 536–559. Dedicated to the memory of Herbert E. Robbins.CrossRefGoogle Scholar
Bennett, B. (1962). On multivariate sign tests. J. Roy. Statist. Soc. Ser. B 24, 161–.Google Scholar
Berger, J., and A., Guglielmi (2001). Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives. J. Amer. Statist. Assoc. 96(453), 174–184.CrossRefGoogle Scholar
Bernardo, J., and A., Smith (1994). Bayesian Theory. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. Chichester: John Wiley & Sons Ltd.CrossRef
Bertoin, J. (1996). Lévy Processes, Volume 121 of Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press.
Bhattacharya, A., and D., Dunson (2010). Nonparametric Bayesian density estimation on manifolds with applications to planar shapes. Biometrika 97(4), 851–865.CrossRefGoogle Scholar
Bickel, P., C., Klaassen Y., Ritov and J., Wellner (1998). Efficient and Adaptive Estimation for Semiparametric Models. New York: Springer-Verlag. Reprint of the 1993 original.
Bickel, P., and B., Kleijn (2012). The semiparametric Bernstein–von Mises theorem. Ann. Statist. 40(1), 206–237.CrossRefGoogle Scholar
Bickel, P., and M., Rosenblatt (1973). On some global measures of the deviations of density function estimates. Ann. Statist. 1, 1095–.CrossRefGoogle Scholar
Billingsley, P. (1968). Convergence of Probability Measures. New York: John Wiley & Sons Inc.
Billingsley, P. (1979). Probability and Measure. New York–Chichester–Brisbane: John Wiley & Sons. Wiley Series in Probability and Mathematical Statistics.
Birgé, L. (1979). Sur les tests de deux ensembles convexes compacts de probabilités. C. R. Acad. Sci. Paris Sér. A-B 289(3), A237–A240.Google Scholar
Birgé, L. (1983a). Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahrsch. Verw. Gebiete 65(2), 181–237.Google Scholar
Birgé, L. (1983b). Robust testing for independent nonidentically distributed variables and Markov chains. In Specifying Statistical Models (Louvain-la-Neuve, 1981), Volume 16 of Lecture Notes in Statist., pp. 134–162. New York: Springer.
Blackwell, D. (1973). Discreteness of Ferguson selections. Ann. Statist. 1, 358–.CrossRefGoogle Scholar
Blackwell, D., and L., Dubins (1962). Merging of opinions with increasing information. Ann. Math. Statist. 33, 886–.CrossRefGoogle Scholar
Blackwell, D., and J., MacQueen (1973). Ferguson distributions via Pólya urn schemes. Ann. Statist. 1, 355–.CrossRefGoogle Scholar
Blei, D., and M., Jordan (2006). Variational inference for Dirichlet process mixtures. Bayesian Anal. 1(1), 121–143 (electronic).CrossRefGoogle Scholar
Borell, C. (1975). The Brunn–Minkowski inequality in Gauss space. Invent. Math. 30(2), 207–216.CrossRefGoogle Scholar
Breiman, L., L. Le, Cam, and L., Schwartz (1964). Consistent estimates and zero-one sets. Ann. Math. Statist. 35, 161–.CrossRefGoogle Scholar
Brown, L., and M., Low (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24(6), 2384–2398.CrossRefGoogle Scholar
Brunner, L. (1992). Bayesian nonparametric methods for data from a unimodal density. Statist. Probab. Lett. 14(3), 195–199.CrossRefGoogle Scholar
Brunner, L., and A., Lo (1989). Bayes methods for a symmetric unimodal density and its mode. Ann. Statist. 17(4), 1550–1566.CrossRefGoogle Scholar
Carter, C., and R., Kohn (1997). Semiparametric Bayesian inference for time series with mixed spectra. J. Roy. Statist. Soc. Ser. B 59(1), 255–268.CrossRefGoogle Scholar
Castillo, I. (2008). Lower bounds for posterior rates with Gaussian process priors. Electron. J. Stat. 2, 1299–.CrossRefGoogle Scholar
Castillo, I. (2012a). Semiparametric Bernstein–von Mises theorem and bias, illustrated with Gaussian process priors. Sankhya A 74(2), 194–221.Google Scholar
Castillo, I. (2012b). A semiparametric Bernstein–von Mises theorem for Gaussian process priors. Probab. Theory Related Fields 152(1–2), 53–99.Google Scholar
Castillo, I. (2014). On Bayesian supremum norm contraction rates. Ann. Statist. 42(5), 2058–2091.CrossRefGoogle Scholar
Castillo, I., and R., Nickl (2013). Nonparametric Bernstein–von Mises theorems in Gaussian white noise. Ann. Statist. 41(4), 1999–2028.CrossRefGoogle Scholar
Castillo, I., and R., Nickl (2014). On the Bernstein–von Mises phenomenon for nonparametric Bayes procedures. Ann. Statist. 42(5), 1941–1969.CrossRefGoogle Scholar
Castillo, I., and J., Rousseau (2015). A general Bernstein–von Mises theorem in semiparametric models. Ann. Statist. 43(6), 2353–2383.CrossRefGoogle Scholar
Catoni, O. (2004). Statistical Learning Theory and Stochastic Optimization, Volume 1851 of Lecture Notes in Mathematics. Berlin: Springer-Verlag. Lecture notes from the 31st Summer School on Probability Theory held in Saint-Flour, July 8–25, 2001.
Cerquetti, A. (2007). A note on Bayesian nonparametric priors derived from exponentially tilted Poisson– Kingman models. Statist. Probab. Lett. 77(18), 1705–1711.CrossRefGoogle Scholar
Cerquetti, A. (2008). On a Gibbs characterization of normalized generalized gamma processes. Statist. Probab. Lett. 78(18), 3123–3128.CrossRefGoogle Scholar
Chen, L. (1975). Poisson approximation for dependent trials. Ann. Probab. 3(3), 534–545.CrossRefGoogle Scholar
Chen, L., L., Goldstein and Q.-M., Shao (2011). Normal Approximation by Stein's Method. Probability and Its Applications. New York, Heidelberg: Springer.CrossRef
Choi, T., and R., Ramamoorthi (2008). Remarks on consistency of posterior distributions. In Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, Volume 3 of Inst.Math. Stat. Collect., pp. 170–186. Beachwood, OH: Inst. Math. Statist.CrossRef
Choi, T., and M., Schervish (2007). On posterior consistency in nonparametric regression problems. J. Multivariate Anal. 98(10), 1969–1987.CrossRefGoogle Scholar
Choudhuri, N. (1998). Bayesian bootstrap credible sets for multidimensional mean functional. Ann. Statist. 26(6), 2104–2127.CrossRefGoogle Scholar
Choudhuri, N., S., Ghosal and A., Roy (2004a). Bayesian estimation of the spectral density of a time series. J. Amer. Statist. Assoc. 99(468), 1050–1059.Google Scholar
Choudhuri, N., S., Ghosal and A., Roy (2004b). Contiguity of the Whittle measure for a Gaussian time series. Biometrika 91(1), 211–218.Google Scholar
Choudhuri, N., S., Ghosal and A., Roy (2007). Nonparametric binary regression using a Gaussian process prior. Stat. Methodol. 4(2), 227–243.Google Scholar
Chung,, K.-L. (2001). A Course in Probability Theory (Third ed.). San Diego, CA: Academic Press Inc.
Chung, Y., and D., Dunson (2011). The local Dirichlet process. Ann. Inst. Statist. Math. 63(1), 59–80.Google Scholar
Cifarelli, D., and E., Regazzini (1978). Problemi statistici non parametrici in condizioni di scambiabilita parziale e impiego di medie associative. Quad. Istit. Mat. Finanz. Univ. Torino 3, 13–.Google Scholar
Cifarelli, D., and E., Regazzini (1990). Distribution functions of means of a Dirichlet process. Ann. Statist. 18(1), 429–442.CrossRefGoogle Scholar
Cohen, A., I., Daubechies and P., Vial (1993). Wavelets on the interval and fast wavelet transforms. Applied and Computational Harmonic Analysis 1(1), 54–81.CrossRefGoogle Scholar
Connor, R., and J., Mosimann (1969). Concepts of independence for proportions with a generalization of the Dirichlet distribution. J. Amer. Statist. Assoc. 64, 206–.CrossRefGoogle Scholar
Coram, M., and S., Lalley (2006). Consistency of Bayes estimators of a binary regression function. Ann. Statist. 34(3), 1233–1269.CrossRefGoogle Scholar
Cox, D., D. (1993). An analysis of Bayesian inference for nonparametric regression. Ann. Statist. 21(2), 903–923.CrossRefGoogle Scholar
Cox, D., R. (1972). Regression models and life-tables. J. Roy. Statist. Soc. Ser. B 34, 220–. With discussion by F., Downton, R., Peto, D., Bartholomew, D., Lindley, P., Glassborow, D., Barton, S., Howard, B., Benjamin, J., Gart, L., Meshalkin, A., Kagan, M., Zelen, R., Barlow, J., Kalbfleisch, R., Prentice and N., Breslow, and a reply by D. R., Cox.Google Scholar
Cseke, B., and T., Heskes (2011). Approximate marginals in latent Gaussian models. J. Mach. Learn. Res. 12, 454–.Google Scholar
Csörgʺo, M., and P., Révész (1975). A new method to prove Strassen type laws of invariance principle. I, II. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 31, 259–.Google Scholar
Csörgʺo, M., and P., Révész (1981). Strong Approximations in Probability and Statistics. Probability and Mathematical Statistics. New York: Academic Press Inc.
Dalal, S. (1979). Dirichlet invariant processes and applications to nonparametric estimation of symmetric distribution functions. Stochastic Process. Appl. 9(1), 99–107.CrossRefGoogle Scholar
Daley, D., J., and D., Vere-Jones (2003). An Introduction to the Theory of Point Processes. Vol. I (Second ed.). Probability and Its Applications (New York). Springer-Verlag, New York. Elementary theory and methods.
Daley, D., J., and D., Vere-Jones (2008). An Introduction to the Theory of Point Processes. Vol. II (Second ed.). Probability and Its Applications (New York). New York: Springer. General theory and structure.CrossRef
Damien, P., P., Laud, and A., Smith (1995). Approximate random variate generation from infinitely divisible distributions with applications to Bayesian inference. J. Roy. Statist. Soc., Ser. B. 57(3), 547–563.Google Scholar
Damien, P., P., Laud, and A., Smith (1996). Implementation of Bayesian non-parametric inference based on beta processes. Scand. J. Statist. 23(1), 27–36.Google Scholar
Dass, S., and J., Lee (2004). A note on the consistency of Bayes factors for testing point null versus nonparametric alternatives. J. Statist. Plann. Inference 119(1), 143–152.Google Scholar
Daubechies, I. (1992). Ten Lectures on Wavelets, Volume 61 of CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
de Acosta, A. (1983). Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm. Ann. Probab. 11(1), 78–101.Google Scholar
De Blasi, P., S., Favaro, A., Lijoi, R., Mena, I., Prünster, and M., Ruggiero (2015). Are Gibbs-type priors the most natural generalization of the Dirichlet process? IEEE Trans. Pattern Anal. Machine Intell. 37, 229–.Google Scholar
De Blasi, P., A., Lijoi, and I., Prünster (2013). An asymptotic analysis of a class of discrete nonparametric priors. Statistica Sinica 23(3), 1299–1321.Google Scholar
De Blasi, P., G., Peccati, and I., Prünster (2009). Asymptotics for posterior hazards. Ann. Statist. 37(4), 1906–1945.CrossRefGoogle Scholar
de Boor, C. (1978). A Practical Guide to Splines, Volume 27 of Applied Mathematical Sciences. New York: Springer-Verlag.CrossRef
de Boor, C., and J., Daniel (1974). Splines with nonnegative B-spline coefficients. Mathematics of Computation 28(126), 565–568.Google Scholar
de Finetti, B. (1937). La prévision: ses lois logiques, ses sources subjectives. Ann. Inst. H. Poincaré 7(1), 1–68.Google Scholar
de Jonge, R., and H. van, Zanten (2010). Adaptive nonparametric Bayesian inference using location-scale mixture priors. Ann. Statist. 38(6), 3300–3320.CrossRefGoogle Scholar
DeVore, R., A., and G. G., Lorentz (1993). Constructive Approximation, Volume 303 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer- Verlag.
Dey, D., P., Müller, and D., Sinha (1998). Practical Nonparametric and Semiparametric Bayesian Statistics. Springer Heidelberg.
Dey, J., R., Erickson, and R., Ramamoorthi (2003). Some aspects of neutral to right priors. Int. Stat. Rev. 71(2), 383–401.CrossRefGoogle Scholar
Diaconis, P., and D., Freedman (1986a). On inconsistent Bayes estimates of location. Ann. Statist. 14(1), 68–87.Google Scholar
Diaconis, P., and D., Freedman (1986b). On the consistency of Bayes estimates. Ann. Statist. 14(1), 1–67. With a discussion and a rejoinder by the authors.Google Scholar
Diaconis, P., and D., Freedman (1993). Nonparametric binary regression: a Bayesian approach. Ann. Statist. 21(4), 2108–2137.CrossRefGoogle Scholar
Diaconis, P., and J., Kemperman (1996). Some new tools for Dirichlet priors. In Bayesian Statistics, 5 (Alicante, 1994), Oxford Sci. Publ., pp. 97–106. New York: Oxford Univ. Press.
Doksum, K. (1974). Tail-free and neutral random probabilities and their posterior distributions. Ann. Probab. 2, 201–.Google Scholar
Doksum, K., and A., Lo (1990). Consistent and robust Bayes procedures for location based on partial information. Ann. Statist. 18(1), 443–453.Google Scholar
Doob, J. (1949). Application of the theory of martingales. In Le Calcul des probabilités et ses applications, Colloques Internationaux du Centre National de la Recherche Scientifique, no. 13, pp. 23–27. Paris: Centre National de la Recherche Scientifique.
Doss, H. (1985a). Bayesian nonparametric estimation of the median. I. Computation of the estimates. Ann. Statist. 13(4), 1432–1444.Google Scholar
Doss, H. (1985b). Bayesian nonparametric estimation of the median. II. Asymptotic properties of the estimates. Ann. Statist. 13(4), 1445–1464.Google Scholar
Doss, H., and T., Sellke (1982). The tails of probabilities chosen from a Dirichlet prior. Ann. Statist. 10(4), 1302–1305.CrossRefGoogle Scholar
Drăghici, L., and R., Ramamoorthi (2000). A note on the absolute continuity and singularity of Pólya tree priors and posteriors. Scand. J. Statist. 27(2), 299–303.CrossRefGoogle Scholar
Drăghici, L., and R., Ramamoorthi (2003). Consistency of Dykstra–Laud priors. Sankhyā 65(2), 464–481.Google Scholar
Dubins, L., and D., Freedman (1963). Random distribution functions. Bull. Amer. Math. Soc. 69, 551–.Google Scholar
Dudley, R. (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Functional Analysis 1, 330–.Google Scholar
Dudley, R. (2002). Real Analysis and Probability, Volume 74 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press. Revised reprint of the 1989 original.
Dudley, R., M. (1984). A course on empirical processes. In École d'été de probabilités de Saint-Flour, XII—1982, Volume 1097 of Lecture Notes in Math., pp. 1–142. Berlin: Springer.
Dudley, R., M. (2014). Uniform Central Limit Theorems (Second ed.), Volume 142 of Cambridge Studies in Advanced Mathematics. New York: Cambridge University Press.
Dunson, D., and J.-H., Park (2008). Kernel stick-breaking processes. Biometrika 95(2), 307–323.Google Scholar
Dykstra, R., and P., Laud (1981). A Bayesian nonparametric approach to reliability. Ann. Statist. 9(2), 356–367.CrossRefGoogle Scholar
Edmunds, D., and H., Triebel (1996). Function Spaces, Entropy Numbers, Differential Operators, Volume 120 of Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press.
Efroĭmovich, S., and M., Pinsker (1984). A self-training algorithm for nonparametric filtering. Avtomat. i Telemekh. (11), 58–65.Google Scholar
Eichelsbacher, P., and A., Ganesh (2002). Moderate deviations for Bayes posteriors. Scand. J. Statist. 29(1), 153–167.CrossRefGoogle Scholar
Escobar, M. (1994). Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89(425), 268–277.CrossRefGoogle Scholar
Escobar, M., and M., West (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90(430), 577–588.Google Scholar
Fabius, J. (1964). Asymptotic behavior of Bayes' estimates. Ann. Math. Statist. 35, 856–.CrossRefGoogle Scholar
Favaro, S., A., Lijoi, R., Mena, and I., Prünster (2009). Bayesian non-parametric inference for species variety with a two-parameter Poisson–Dirichlet process prior. J. Roy. Stat. Soc. Ser. B 71(5), 993–1008.CrossRefGoogle Scholar
Favaro, S., A., Lijoi, and I., Prünster (2012a). Asymptotics for a Bayesian nonparametric estimator of species variety. Bernoulli 18(4), 1267–1283.Google Scholar
Favaro, S., A., Lijoi, and I., Prünster (2012b). On the stick-breaking representation of normalized inverse Gaussian priors. Biometrika 99(3), 663–674.Google Scholar
Favaro, S., and Y., Teh (2013). MCMC for normalized random measure mixture models. Stat. Sci 28, 335– 350.Google Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications. Vol. I. (Third ed.). New York: John Wiley & Sons Inc.
Feller, W. (1971). An Introduction to Probability Theory and Its Applications. Vol. II. (Second ed.). New York: John Wiley & Sons Inc.
Feng, S. (2010). The Poisson–Dirichlet Distribution and Related Topics:Models and Asymptotic Behaviors. Probability and its Applications. New York, Heidelberg: Springer.CrossRef
Ferguson, T. (1967). Mathematical Statistics: A Decision Theoretic Approach. Probability and Mathematical Statistics, Vol. 1. New York: Academic Press.
Ferguson, T. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 230–.Google Scholar
Ferguson, T. (1974). Prior distributions on spaces of probability measures. Ann. Statist. 2, 629–.CrossRefGoogle Scholar
Ferguson, T. (1983). Bayesian density estimation by mixtures of normal distributions. In Recent Advances in Statistics, pp. 287–302. New York: Academic Press.
Ferguson, T., and M., Klass (1972). A representation of independent increment processes without Gaussian components. Ann. Math. Statist. 43, 1643–.CrossRefGoogle Scholar
Ferguson, T., and E., Phadia (1979). Bayesian nonparametric estimation based on censored data. Ann. Statist. 7(1), 163–186.Google Scholar
Freedman, D. (1963). On the asymptotic behavior of Bayes' estimates in the discrete case. Ann. Math. Statist. 34, 1403–.Google Scholar
Freedman, D. (1965). On the asymptotic behavior of Bayes estimates in the discrete case. II. Ann. Math. Statist. 36, 456–.Google Scholar
Freedman, D. (1999). On the Bernstein–von Mises theorem with infinite-dimensional parameters. Ann. Statist. 27(4), 1119–1140.Google Scholar
Freedman, D., and P., Diaconis (1982). On inconsistent M-estimators. Ann. Statist. 10(2), 454–461.CrossRefGoogle Scholar
Fristedt, B., and W., Pruitt (1971). Lower functions for increasing random walks and subordinators. Z. Wahrsch. Verw. Gebiete 18, 182–.CrossRefGoogle Scholar
Gaenssler, P., P., Molnár, and D., Rost (2007). On continuity and strict increase of the CDF for the supfunctional of a Gaussian process with applications to statistics. Results Math. 51(1–2), 51–60.Google Scholar
Ganesh, A., and N., O'Connell (2000). A large-deviation principle for Dirichlet posteriors. Bernoulli 6(6), 1021–1034.CrossRefGoogle Scholar
Gangopadhyay, A., B., Mallick, and D., Denison (1999). Estimation of spectral density of a stationary time series via an asymptotic representation of the periodogram. J. Statist. Plann. Inference 75(2), 281–290.Google Scholar
Gasparini, M. (1996). Bayesian density estimation via Dirichlet density processes. J. Nonparametr. Statist. 6(4), 355–366.Google Scholar
Gelfand, A., and A., Kottas (2002). A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. J. Comput. Graph. Statist. 11(2), 289–305.CrossRefGoogle Scholar
Ghorai, J., and H., Rubin (1982). Bayes risk consistency of nonparametric Bayes density estimates. Austral. J. Statist. 24(1), 51–66.Google Scholar
Ghosal, S. (2001). Convergence rates for density estimation with Bernstein polynomials. Ann. Statist. 29(5), 1264–1280.CrossRefGoogle Scholar
Ghosal, S., J., Ghosh, and R., Ramamoorthi (1997). Non-informative priors via sieves and packing numbers. In Advances in Statistical Decision Theory and Applications, Stat. Ind. Technol., pp. 119–132. Boston, MA: Birkhäuser Boston.CrossRef
Ghosal, S., J., Ghosh, and R., Ramamoorthi (1999a). Consistent semiparametric Bayesian inference about a location parameter. J. Statist. Plann. Inference 77(2), 181–193.Google Scholar
Ghosal, S., J., Ghosh, and R., Ramamoorthi (1999b). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27(1), 143–158.Google Scholar
Ghosal, S., J., Ghosh, and T., Samanta (1995). On convergence of posterior distributions. Ann. Statist. 23(6), 2145–2152.Google Scholar
Ghosal, S., J., Ghosh, and A. van der, Vaart (2000). Convergence rates of posterior distributions. Ann. Statist. 28(2), 500–531.Google Scholar
Ghosal, S., J., Lember, and A. van der, Vaart (2003). On Bayesian adaptation. In Proceedings of the Eighth Vilnius Conference on Probability Theory and Mathematical Statistics, Part II (2002), Volume 79, pp. 165–175.Google Scholar
Ghosal, S., J., Lember, and A. van der, Vaart (2008). Nonparametric Bayesian model selection and averaging. Electron. J. Stat. 2, 89–.Google Scholar
Ghosal, S., and A., Roy (2006). Posterior consistency of Gaussian process prior for nonparametric binary regression. Ann. Statist. 34(5), 2413–2429.Google Scholar
Ghosal, S., A., Roy, and Y., Tang (2008). Posterior consistency of Dirichlet mixtures of beta densities in estimating positive false discovery rates. In Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, Volume 1 of Inst. Math. Stat. Collect., pp. 105–115. Beachwood, OH: Inst. Math. Statist.CrossRef
Ghosal, S., and Y., Tang (2006). Bayesian consistency for Markov processes. Sankhyā 68(2), 227–239.Google Scholar
Ghosal, S., and A. van der, Vaart (2001). Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities. Ann. Statist. 29(5), 1233–1263.Google Scholar
Ghosal, S., and A. van der, Vaart (2003). Discussion of “new tools for consistency in Bayesian nonparametrics” by Gabriella Salinetti. In Bayesian Statistics, 7 (Tenerife, 2002), pp. 382. New York: Oxford Univ. Press.
Ghosal, S., and A. van der, Vaart (2007a). Convergence rates of posterior distributions for non-i.i.d. observations. Ann. Statist. 35(1), 192–223.Google Scholar
Ghosal, S., and A. van der, Vaart (2007b). Posterior convergence rates of Dirichlet mixtures at smooth densities. Ann. Statist. 35(2), 697–723.Google Scholar
Ghosh, J., S., Ghosal, and T., Samanta (1994). Stability and convergence of the posterior in non-regular problems. In Statistical Decision Theory and Related Topics, V (West Lafayette, IN, 1992), pp. 183–199. New York: Springer.
Ghosh, J., and R., Ramamoorthi (1995). Consistency of Bayesian inference for survival analysis with or without censoring. In Analysis of Censored Data (Pune, 1994/1995), Volume 27 of IMS Lecture Notes Monogr. Ser., pp. 95–103. Hayward, CA: Inst. Math. Statist.CrossRef
Ghosh, J., and R., Ramamoorthi (2003). Bayesian Nonparametrics. Springer Series in Statistics. New York: Springer-Verlag.
Ghosh, J., and S., Tokdar (2006). Convergence and consistency of Newton's algorithm for estimating mixing distribution. In Frontiers in Statistics, pp. 429–443. London: Imp. Coll. Press.
Gilks, W., A., Thomas, and D., Spiegelhalter (1994). A language and program for complex Bayesian modelling. The Statistician, 169–177.CrossRef
Gill, R., and S., Johansen (1990). A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18(4), 1501–1555.CrossRefGoogle Scholar
Giné, E., and R., Nickl (2015). Mathematical Foundations of Infinite-Dimensional Statistical Models. Cambridge University Press.
Gnedin, A. (2010). A species sampling model with finitely many types. Electron. Commun. Probab. 15, 88–.Google Scholar
Gnedin, A., and J., Pitman (2006). Exchangeable Gibbs partitions and Stirling triangles. Journal of Mathematical Sciences 138(3), 5674–5685.Google Scholar
Grenander, U. (1981). Abstract Inference. New York: John Wiley & Sons Inc. Wiley Series in Probability and Mathematical Statistics.
Griffin, J., and M., Steel (2006). Order-based dependent Dirichlet processes. J. Amer. Statist. Assoc. 101(473), 179–194.Google Scholar
Griffiths, T., and Z., Ghahramani (2006). Infinite latent feature models and the indian buffet process. Volume 18 of Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press.
Gu, J., and S., Ghosal (2008). Strong approximations for resample quantile processes and application to ROC methodology. J. Nonparametr. Stat. 20(3), 229–240.Google Scholar
Gurland, J. (1948). Inversion formulae for the distribution of ratios. Ann. Math. Statist. 19, 237–.Google Scholar
Hansen, B., and J., Pitman (2000). Prediction rules for exchangeable sequences related to species sampling. Statist. Probab. Lett. 46(3), 251–256.Google Scholar
Hanson, T., and W., Johnson (2002). Modeling regression error with a mixture of Pólya trees. J. Amer. Statist. Assoc. 97(460), 1020–1033.CrossRefGoogle Scholar
Härdle, W., G., Kerkyacharian, A., Tsybakov, and D., Picard (1998). Wavelets, Approximation and Statistical Applications. New York: Springer-Verlag.CrossRef
Helson, H. (1983). Harmonic Analysis. Reading, MA: Addison-Wesley Publishing Company Advanced Book Program.
Hesthaven, J., S., Gottlieb, and D., Gottlieb (2007). Spectral Methods for Time Dependent Problems. Cambridge, UK: Cambridge University Press.
Hjort, N. (1990). Nonparametric Bayes estimators based on beta processes in models for life history data. Ann. Statist. 18(3), 1259–1294.CrossRefGoogle Scholar
Hjort, N. (1996). Bayesian approaches to non- and semiparametric density estimation. In Bayesian Statistics, 5 (Alicante, 1994), Oxford Sci. Publ., pp. 223–253. New York: Oxford University Press.
Hoppe, F. (1984). Pólya-like urns and the Ewens' sampling formula. J. Math. Biol. 20(1), 91–94.CrossRefGoogle Scholar
Huang, T.-M. (2004). Convergence rates for posterior distributions and adaptive estimation. Ann. Statist. 32(4), 1556–1593.Google Scholar
Ibragimov, I. (1962). On stationary Gaussian processes with a strong mixing property. Dokl. Akad. Nauk SSSR 147, 1282–1284.Google Scholar
Ibragimov, I., and R., Has'minskiĭ (1981). Statistical Estimation: Asymptotic Theory, Volume 16 of Applications of Mathematics. New York: Springer-Verlag. Translated from the Russian by Samuel Kotz.
Ibragimov, I., and R., Has'minskiĭ (1982). An estimate of the density of a distribution belonging to a class of entire functions. Teor. Veroyatnost. i Primenen. 27(3), 514–524.Google Scholar
Ishwaran, H., and L., James (2001). Gibbs sampling methods for stick-breaking priors. J. Amer. Statist. Assoc. 96(453), 161–173.Google Scholar
Ishwaran, H., and M., Zarepour (2002). Dirichlet prior sieves in finite normal mixtures. Statist. Sinica 12(3), 941–963.Google Scholar
Jackson, D. (1912). On approximation by trigonometric sums and polynomials. Trans. Amer. Math. Soc. 13(4), 491–515.CrossRefGoogle Scholar
Jacobsen, M. (1989). Existence and unicity of MLEs in discrete exponential family distributions. Scand. J. Statist. 16(4), 335–349.Google Scholar
Jacod, J., and A., Shiryaev (2003). Limit Theorems for Stochastic Processes (Second ed.), Volume 288 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag.
James, I., and J., Mosimann (1980). A new characterization of the Dirichlet distribution through neutrality. Ann. Statist. 8(1), 183–189.Google Scholar
James, L. (2005). Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages. Ann. Statist. 33(4), 1771–1799.Google Scholar
James, L. (2008). Large sample asymptotics for the two-parameter Poisson-Dirichlet process. In Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, Volume 3 of Inst. Math. Stat. Collect., pp. 187–199. Beachwood, OH: Institute of Mathematical Statistics.
James, L., A., Lijoi, and I., Prünster (2006). Conjugacy as a distinctive feature of the Dirichlet process. Scand. J. Statist. 33(1), 105–120.Google Scholar
James, L., A., Lijoi, and I., Prünster (2008). Distributions of linear functionals of two parameter Poisson- Dirichlet random measures. Ann. Appl. Probab. 18(2), 521–551.Google Scholar
James, L., A., Lijoi, and I., Prünster (2009). Posterior analysis for normalized random measures with independent increments. Scand. J. Stat. 36(1), 76–97.Google Scholar
James, L., A., Lijoi, and I., Prünster (2010). On the posterior distribution of classes of random means. Bernoulli 16(1), 155–180.Google Scholar
Jang, G., J. Lee, and S. Lee (2010). Posterior consistency of species sampling priors. Statist. Sinica 20(2), 581–593.Google Scholar
Jara, A. (2007). Applied Bayesian non-and semi-parametric inference using dppackage. R News 7, 26–.Google Scholar
Jara, A., T., Hanson, F., Quintana, P., Müller, and G., Rosner (2015). Package dppackage.
Jiang, W. (2007). Bayesian variable selection for high dimensional generalized linear models: convergence rates of the fitted densities. Ann. Statist. 35(4), 1487–1511.Google Scholar
Kalbfleisch, J. (1978). Non-parametric Bayesian analysis of survival time data. J. Roy. Statist. Soc. Ser. B 40(2), 214–221.Google Scholar
Kallenberg, O. (1986). Random Measures (Fourth ed.). Berlin: Akademie-Verlag.
Karlin, S. (1967). Central limit theorems for certain infinite urn schemes. J. Math. Mech. 17, 401–.CrossRefGoogle Scholar
Kim, Y. (1999). Nonparametric Bayesian estimators for counting processes. Ann. Statist. 27(2), 562–588.Google Scholar
Kim, Y. (2001). Mixtures of beta processes priors for right censored survival data. J. Korean Statist. Soc. 30(1), 127–138.Google Scholar
Kim, Y. (2006). The Bernstein–von Mises theorem for the proportional hazard model. Ann. Statist. 34(4), 1678–1700.CrossRefGoogle Scholar
Kim, Y., and J., Lee (2001). On posterior consistency of survival models. Ann. Statist. 29(3), 666–686.Google Scholar
Kim, Y., and J., Lee (2003a). Bayesian analysis of proportional hazard models. Ann. Statist. 31(2), 493–511. Dedicated to the memory of Herbert E. Robbins.Google Scholar
Kim, Y., and J., Lee (2003b). Bayesian bootstrap for proportional hazards models. Ann. Statist. 31(6), 1905– 1922.Google Scholar
Kim, Y., and J., Lee (2004). A Bernstein–von Mises theorem in the nonparametric right-censoring model. Ann. Statist. 32(4), 1492–1512.CrossRefGoogle Scholar
Kimeldorf, G., and G., Wahba (1970). A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Ann. Math. Statist. 41, 502–.Google Scholar
Kingman, J. (1967). Completely random measures. Pacific J. Math. 21, 78–.Google Scholar
Kingman, J. (1975). Random discrete distribution. J. Roy. Statist. Soc. Ser. B 37, 22–. With a discussion by S. J., Taylor, A. G., Hawkes, A. M., Walker, D. R., Cox, A. F. M., Smith, B. M., Hill, P. J., Burville, T., Leonard, and a reply by the author.Google Scholar
Kingman, J. (1978). The representation of partition structures. J. London Math. Soc. (2) 18(2), 374–380.Google Scholar
Kingman, J. (1982). The coalescent. Stochastic Process. Appl. 13(3), 235–248.Google Scholar
Kingman, J. (1993). Poisson Processes, Volume 3 of Oxford Studies in Probability. New York: The Clarendon Press Oxford University Press. Oxford Science Publications.
Kleijn, B., and A. van der, Vaart (2006). Misspecification in infinite-dimensional Bayesian statistics. Ann. Statist. 34(2), 837–877.CrossRefGoogle Scholar
Knapik, B., T., B. T., Szabó, A. W. van der, Vaart, and J. H. van, Zanten (2016). Bayes procedures for adaptive inference in inverse problems for the white noise model. Probab. Theory Related Fields 164(3-4), 771–813.CrossRefGoogle Scholar
Knapik, B., A. van der, Vaart, and H. van, Zanten (2011). Bayesian inverse problems with Gaussian priors. Ann. Statist. 39(5), 2626–2657.CrossRefGoogle Scholar
Kolmogorov, A., and V., Tihomirov (1961). ε-entropy and ε-capacity of sets in functional space. Amer.Math. Soc. Transl. (2) 17, 364–.Google Scholar
Komlós, J., P., Major, and G., Tusnády (1975). An approximation of partial sums of independent RVs and the sample DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 32, 131–.Google Scholar
Korwar, R., and M., Hollander (1973). Contributions to the theory of Dirichlet processes. Ann. Probab. 1, 711–.CrossRefGoogle Scholar
Kraft, C. (1964). A class of distribution function processes which have derivatives. J. Appl. Probab. 1, 388–.Google Scholar
Kruijer, W., J., Rousseau, and A. van der, Vaart (2010). Adaptive Bayesian density estimation with locationscale mixtures. Electron. J. Stat. 4, 1257–.Google Scholar
Kruijer, W., and A. van der, Vaart (2008). Posterior convergence rates for Dirichlet mixtures of beta densities. J. Statist. Plann. Inference 138(7), 1981–1992.Google Scholar
Kruijer, W., and A. van der, Vaart (2013). Analyzing posteriors by the information inequality. In From Probability to Statistics and Back: High-Dimensional Models and Processes – A Festschrift in Honor of Jon A. Wellner. IMS.
Kuelbs, J., and W., Li (1993). Metric entropy and the small ball problem for Gaussian measures. J. Funct. Anal. 116(1), 133–157.CrossRefGoogle Scholar
Kuelbs, J., W., Li, and W., Linde (1994). The Gaussian measure of shifted balls. Probab. Theory Related Fields 98(2), 143–162.CrossRefGoogle Scholar
Kuo, L. (1986). Computations of mixtures of Dirichlet processes. SIAM J. Sci. Statist. Comput. 7(1), 60–71.Google Scholar
Lavine, M. (1992). Some aspects of Pólya tree distributions for statistical modelling. Ann. Statist. 20(3), 1222–1235.Google Scholar
Lavine, M. (1994). More aspects of Pólya tree distributions for statistical modelling. Ann. Statist. 22(3), 1161–1176.CrossRefGoogle Scholar
Le Cam, L. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates. Univ. California Publ. Statist. 1, 329–.Google Scholar
Le Cam, L. (1986). Asymptotic Methods in Statistical Decision Theory. Springer Series in Statistics. New York: Springer-Verlag.
Leahu, H. (2011). On the Bernstein–von Mises phenomenon in the Gaussian white noise model. Electron. J. Stat. 5, 404–.CrossRefGoogle Scholar
Ledoux, M., and M., Talagrand (1991). Probability in Banach spaces, Volume 23. Berlin: Springer-Verlag.CrossRef
Lee, J. (2007). Sampling methods of neutral to the right processes. J. Comput. Graph. Statist. 16(3), 656–671.CrossRefGoogle Scholar
Lee, J., and Y., Kim (2004). A new algorithm to generate beta processes. Comput. Statist. Data Anal. 47(3), 441–453.Google Scholar
Lee, J., F., Quintana, P., Müller, and L., Trippa (2013). Defining predictive probability functions for species sampling models. Stat. Sci. 28(2), 209–222.Google Scholar
Lember, J., and A. van der, Vaart (2007). On universal Bayesian adaptation. Statist. Decisions 25(2), 127–152.CrossRefGoogle Scholar
Lenk, P. (1988). The logistic normal distribution for Bayesian, nonparametric, predictive densities. J. Amer. Statist. Assoc. 83(402), 509–516.CrossRefGoogle Scholar
Leonard, T. (1978). Density estimation, stochastic processes and prior information. J. Roy. Statist. Soc. Ser. B 40(2), 113–146. With discussion.Google Scholar
Li, W., and W., Linde (1998). Existence of small ball constants for fractional Brownian motions. C. R. Acad. Sci. Paris Sér. I Math. 326(11), 1329–1334.Google Scholar
Muliere, P., and L., Tardella (1998). Approximating distributions of random functionals of Ferguson- Dirichlet priors. Canad. J. Statist. 26(2), 283–297.Google Scholar
Müller, P., F., Quintana, A., Jara, and T., Hanson (2015). Bayesian Nonparametric Data Analysis. Cambridge: Springer.
Murphy, S., and A. van der, Vaart (2000). On profile likelihood. J. Amer. Statist. Assoc. 95(450), 449–485. With comments and a rejoinder by the authors.CrossRefGoogle Scholar
Neal, R. (2000). Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Statist. 9(2), 249–265.Google Scholar
Newton, M. (2002). On a nonparametric recursive estimator of the mixing distribution. Sankhyā Ser. A 64(2), 306–322. Selected articles from San Antonio Conference in honour of C. R. Rao (San Antonio, TX, 2000).
Newton, M., F., Quintana, and Y., Zhang (1998). Nonparametric Bayes methods using predictive updating. In Practical Nonparametric and Semiparametric Bayesian Statistics, Volume 133 of Lecture Notes in Statistics, pp. 45–61. New York: Springer.CrossRef
Newton, M., and Y., Zhang (1999). A recursive algorithm for nonparametric analysis with missing data. Biometrika 86(1), 15–26.CrossRefGoogle Scholar
Nieto-Barajas, L., I., Prünster, and S., Walker (2004). Normalized random measures driven by increasing additive processes. Ann. Statist. 32(6), 2343–2360.Google Scholar
Nussbaum, M. (1996). Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24(6), 2399–2430.CrossRefGoogle Scholar
Panzar, L., and H. van, Zanten (2009). Nonparametric Bayesian inference for ergodic diffusions. J. Statist. Plann. Inference 139(12), 4193–4199.CrossRefGoogle Scholar
Parthasarathy, K. (2005). Probability Measures on Metric Spaces. AMS Chelsea Publishing, Providence, RI. Reprint of the 1967 original.
Peccati, G., and I., Prünster (2008). Linear and quadratic functionals of random hazard rates: an asymptotic analysis. Ann. Appl. Probab. 18(5), 1910–1943.CrossRefGoogle Scholar
Perman, M., J., Pitman, and M., Yor (1992). Size-biased sampling of Poisson point processes and excursions. Probab. Theory Related Fields 92(1), 21–39.Google Scholar
Petrone, S. (1999a). Bayesian density estimation using Bernstein polynomials. Canad. J. Statist. 27(1), 105–126.Google Scholar
Petrone, S. (1999b). Random Bernstein polynomials. Scand. J. Statist. 26(3), 373–393.Google Scholar
Petrone, S., and P., Veronese (2010). Feller operators and mixture priors in Bayesian nonparametrics. Statist. Sinica 20(1), 379–404.Google Scholar
Petrone, S., and L., Wasserman (2002). Consistency of Bernstein polynomial posteriors. J. Roy. Stat. Soc. Ser. B, Stat. Methodol. 64(1), 79–100.CrossRefGoogle Scholar
Pinsker, M. (1980). Optimal filtration of square-integrable signals in Gaussian noise. Problems Inform. Transmission 16.
Pitman, J. (1995). Exchangeable and partially exchangeable random partitions. Probab. Theory Related Fields 102(2), 145–158.CrossRefGoogle Scholar
Pitman, J. (1996a). Random discrete distributions invariant under size-biased permutation. Adv. in Appl. Probab. 28(2), 525–539.Google Scholar
Pitman, J. (1996b). Some developments of the Blackwell-MacQueen urn scheme. In Statistics, Probability and Game Theory, Volume 30 of IMS Lecture Notes Monogr. Ser., pp. 245–267. Hayward, CA: Institute of Mathematical Statistics.
Pitman, J. (2003). Poisson-Kingman partitions. In Statistics and Science: a Festschrift for Terry Speed, Volume 40 of IMS Lecture Notes Monogr. Ser., pp. 1–34. Beachwood, OH: Institute of Mathematical Statistics.
Pitman, J. (2006). Combinatorial Stochastic Processes, Volume 1875 of Lecture Notes in Mathematics. Berlin: Springer-Verlag. Lectures from the 32nd Summer School on Probability Theory held in Saint- Flour, July 7–24, 2002. With a foreword by Jean Picard.
Pitman, J., and M., Yor (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25(2), 855–900.CrossRefGoogle Scholar
Pollard, D. (1984). Convergence of Stochastic Processes. Springer Series in Statistics. New York: Springer- Verlag.
Præstgaard, J., and J., Wellner (1993). Exchangeably weighted bootstraps of the general empirical process. Ann. Probab. 21(4), 2053–2086.CrossRefGoogle Scholar
Prünster, I. (2012). Proof of conjugacy of neutral to the right processes for censored data.
Ramamoorthi, R., L., Drăghici, and J., Dey (2002). Characterizations of tailfree and neutral to the right priors. In Advances on theoretical and methodological aspects of probability and statistics (Hamilton, ON, 1998), pp. 305–316. London: Taylor & Francis.
Rasmussen, C., and C., Williams (2006). Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning. Cambridge, MA: MIT Press.
Ray, K. (2014). Adaptive Bernstein–von Mises theorems in Gaussian white noise. arXiv:1407.3397.
Regazzini, E., A., Guglielmi, and G. Di, Nunno (2002). Theory and numerical analysis for exact distributions of functionals of a Dirichlet process. Ann. Statist. 30(5), 1376–1411.Google Scholar
Regazzini, E., A., Lijoi, and I., Prünster (2003). Distributional results for means of normalized random measures with independent increments. Ann. Statist. 31(2), 560–585. Dedicated to the memory of Herbert E. Robbins.Google Scholar
Rivoirard, V., and J., Rousseau (2012). Bernstein–von Mises theorem for linear functionals of the density. Ann. Statist. 40(3), 1489–1523.Google Scholar
Rodríguez, A., and D., Dunson (2011). Nonparametric Bayesian models through probit stick-breaking processes. Bayesian Anal. 6(1), 145–177.CrossRefGoogle Scholar
Rodríguez, A., D., Dunson, and A., Gelfand (2008). The nested Dirichlet process. J. Amer. Statist. Assoc. 103(483), 1131–1144.Google Scholar
Rousseau, J. (2010). Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparametric estimation of the density. Ann. Statist. 38(1), 146–180.CrossRefGoogle Scholar
Roy, A., S., Ghosal, and W., Rosenberger (2009). Convergence properties of sequential Bayesian D-optimal designs. J. Statist. Plann. Inference 139(2), 425–440.Google Scholar
Rubin, D. (1981). The Bayesian bootstrap. Ann. Statist. 9(1), 130–134.CrossRefGoogle Scholar
Rudin, W. (1973). Functional Analysis. New York: McGraw-Hill Book Co. McGraw-Hill Series in Higher Mathematics.
Rue, H., S., Martino, and N., Chopin (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. Roy. Stat. Soc. Ser. B Stat. Methodol. 71(2), 319–392.Google Scholar
Salinetti, G. (2003). New tools for consistency in Bayesian nonparametrics. In Bayesian Statistics, 7 (Tenerife, 2002), pp. 369–384. New York: Oxford Univ. Press.With discussions by J. K., Ghosh, S., Ghosal and A. van der, Vaart, and a reply by the author.
Schervish, M. (1995). Theory of Statistics. Springer Series in Statistics. New York: Springer-Verlag.
Schumaker, L. (2007). Spline Functions: Basic Theory (Third ed.). Cambridge Mathematical Library. Cambridge: Cambridge University Press.
Schwartz, L. (1965). On Bayes procedures. Z. Wahrsch. Verw. Gebiete 4, 26–.CrossRefGoogle Scholar
Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6(2), 461–464.CrossRefGoogle Scholar
Scricciolo, C. (2006). Convergence rates for Bayesian density estimation of infinite-dimensional exponential families. Ann. Statist. 34(6), 2897–2920.Google Scholar
Scricciolo,, C. (2007). On rates of convergence for Bayesian density estimation. Scand. J. Statist. 34(3), 626–642.Google Scholar
Scricciolo, C. (2014). Adaptive Bayesian density estimation in L p -metrics with Pitman-Yor or normalized inverse-Gaussian process kernel mixtures. Bayesian Anal. 9(2), 475–520.CrossRefGoogle Scholar
Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4(2), 639–650.Google Scholar
Sethuraman, J., and R., Tiwari (1982). Convergence of Dirichlet measures and the interpretation of their parameter. In Statistical Decision Theory and Related Topics, III, Vol. 2 (West Lafayette, Ind., 1981), pp. 305–315. New York: Academic Press.
Shen, W., and S. Ghosal (2015). Adaptive Bayesian procedures using random series prior. Scand. J. Statist. 42, 1213–.Google Scholar
Shen, W., S., Tokdar, and S., Ghosal (2013). Adaptive Bayesian multivariate density estimation with Dirichlet mixtures. Biometrika 100(3), 623–640.CrossRefGoogle Scholar
Shen, X., and L., Wasserman (2001). Rates of convergence of posterior distributions. Ann. Statist. 29(3), 687–714.Google Scholar
Shively, T., R., Kohn, and S., Wood (1999). Variable selection and function estimation in additive nonparametric regression using a data-based prior. J. Amer. Statist. Assoc. 94(447), 777–806. With comments and a rejoinder by the authors.CrossRefGoogle Scholar
Skorohod, A. (1974). Integration in Hilbert space. New York: Springer-Verlag. Translated from the Russian by Kenneth Wickwire, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 79.
Sniekers, S., and A. van der, Vaart (2015a). Adaptive Bayesian credible sets in regression with a Gaussian process prior. Electron. J. Stat. 9(2), 2475–2527.Google Scholar
Sniekers, S., and A. van der, Vaart (2015b). Credible sets in the fixed design model with Brownian motion prior. J. Statist. Plann. Inference 166, 86–.Google Scholar
Srivastava, S. (1998). A Course on Borel Sets, Volume 180 of Graduate Texts in Mathematics. New York: Springer-Verlag.CrossRef
Stein, E. (1970). Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, No. 30. Princeton, N.J.: Princeton University Press.
Stone, C. (1990). Large-sample inference for log-spline models. Ann. Statist. 18(2), 717–741.CrossRefGoogle Scholar
Stone, C. (1994). The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22(1), 118–184. With discussion by A., Buja and T., Hastie and a rejoinder by the author.Google Scholar
Strasser, H. (1985). Mathematical Theory of Statistics, Volume 7 of de Gruyter Studies in Mathematics. Berlin: Walter de Gruyter & Co. Statistical experiments and asymptotic decision theory.
Susarla, V., and J. Van, Ryzin (1976). Nonparametric Bayesian estimation of survival curves from incomplete observations. J. Amer. Statist. Assoc. 71(356), 897–902.Google Scholar
Szabó, B., A. van der, Vaart, and H. van, Zanten (2013). Empirical Bayes scaling of Gaussian priors in the white noise model. Electron. J. Statist. 7, 1018–.Google Scholar
Szabó, B., A.W. van der, Vaart, and J. H. van, Zanten (2015). Frequentist coverage of adaptive nonparametric Bayesian credible sets. Ann. Statist. 43(4), 1391–1428.Google Scholar
Talagrand, M. (1987). Regularity of Gaussian processes. Acta Math. 159(1-2), 99–149.Google Scholar
Talagrand, M. (1992). A simple proof of the majorizing measure theorem. Geom. Funct. Anal. 2(1), 118–125.CrossRefGoogle Scholar
Tang, Y., and S., Ghosal (2007a). A consistent nonparametric Bayesian procedure for estimating autoregressive conditional densities. Comput. Statist. Data Anal. 51(9), 4424–4437.Google Scholar
Tang, Y., and S., Ghosal (2007b). Posterior consistency of Dirichlet mixtures for estimating a transition density. J. Statist. Plann. Inference 137(6), 1711–1726.Google Scholar
Teh, Y., D., Görür, and Z., Ghahramani (2007). Stick-breaking construction for the Indian buffet process. In International Conference on Artificial Intelligence and Statistics, pp. 556–563.
Teh, Y., M., Jordan, M., Beal, and D., Blei (2006). Hierarchical Dirichlet processes. J. Amer. Statist. Assoc. 101(476), 1566–1581.CrossRefGoogle Scholar
Teicher, H. (1961). Identifiability of mixtures. Ann. Math. Statist. 32, 248–.CrossRefGoogle Scholar
Thibaux, R., and M., Jordan (2007). Hierarchical beta processes and the Indian buffet process. In International Conference on Artificial Intelligence and Statistics, pp. 564–571.
Tierney, L., and J., Kadane (1986). Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81(393), 82–86.CrossRefGoogle Scholar
Tokdar, S. (2006). Posterior consistency of Dirichlet location-scale mixture of normals in density estimation and regression. Sankhyā 68(1), 90–110.Google Scholar
Tokdar, S. (2007). Towards a faster implementation of density estimation with logistic Gaussian process priors. J. Comput. Graph. Statist. 16(3), 633–655.CrossRefGoogle Scholar
Tokdar, S., and J., Ghosh (2007). Posterior consistency of logistic Gaussian process priors in density estimation. J. Statist. Plann. Inference 137(1), 34–42.CrossRefGoogle Scholar
Tokdar, S., R., Martin, and J., Ghosh (2009). Consistency of a recursive estimate of mixing distributions. Ann. Statist. 37(5A), 2502–2522.CrossRefGoogle Scholar
Tsiatis, A. (1981). A large sample study of Cox's regression model. Ann. Statist. 9(1), 93–108.CrossRefGoogle Scholar
van der Meulen, F., A. van der, Vaart, and H. van, Zanten (2006). Convergence rates of posterior distributions for Brownian semimartingale models. Bernoulli 12(5), 863–888.CrossRefGoogle Scholar
van der Vaart, A. (1991). On differentiable functionals. Ann. Statist. 19(1), 178–204.CrossRefGoogle Scholar
van der Vaart,, A. (1998). Asymptotic Statistics, Volume 3 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press.
van der Vaart, A. (2010). Bayesian regularization. In Proceedings of the International Congress of Mathematicians. Volume IV, pp. 2370–2385. Hindustan Book Agency, New Delhi.
van der Vaart,, A., and H. van, Zanten (2007). Bayesian inference with rescaled Gaussian process priors. Electron. J. Stat. 1, 433–448 (electronic).CrossRefGoogle Scholar
van der Vaart, A., and H. van, Zanten (2008a). Rates of contraction of posterior distributions based on Gaussian process priors. Ann. Statist. 36(3), 1435–1463.Google Scholar
van der Vaart, A., and H. van, Zanten (2008b). Reproducing kernel Hilbert spaces of Gaussian priors. In Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, Volume 3 of Inst. Math. Stat. Collect., pp. 200–222. Beachwood, OH: Institute of Mathematical Statistics.
van der Vaart, A., and H. van, Zanten (2009). Adaptive Bayesian estimation using a Gaussian random field with inverse gamma bandwidth. Ann. Statist. 37(5B), 2655–2675.CrossRefGoogle Scholar
van der Vaart, A., and H. van, Zanten (2011). Information rates of nonparametric Gaussian process methods. J. Mach. Learn. Res. 12, 2119–.Google Scholar
van der Vaart, A., and J., Wellner (1996). Weak Convergence and Empirical Processes. Springer Series in Statistics. New York: Springer-Verlag. With applications to statistics.CrossRef
van der Vaart, A., and J., Wellner (2017).Weak Convergence and Empirical Processes (Second ed.). Springer Series in Statistics. New York: Springer-Verlag. With applications to statistics.
vanWaaij, J., and H. van, Zanten (2016). Gaussian process methods for one-dimensional diffusions: optimal rates and adaptation. Electron. J. Statist. 10(1), 628–645.CrossRefGoogle Scholar
Verdinelli, I., and L., Wasserman (1998). Bayesian goodness-of-fit testing using infinite-dimensional exponential families. Ann. Statist. 26(4), 1215–1241.CrossRefGoogle Scholar
Vershik, A., M., Yor, and N., Tsilevich (2001). The Markov-Kreĭn identity and the quasi-invariance of the gamma process. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 283(Teor. Predst. Din. Sist. Komb. i Algoritm. Metody. 6), 21–36, 258.
Wahba, G. (1978). Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. Roy. Statist. Soc. Ser. B 40(3), 364–372.Google Scholar
Walker, S. (2003). On sufficient conditions for Bayesian consistency. Biometrika 90(2), 482–488.CrossRefGoogle Scholar
Walker, S. (2004). New approaches to Bayesian consistency. Ann. Statist. 32(5), 2028–2043.CrossRefGoogle Scholar
Walker, S. (2007). Sampling the Dirichlet mixture model with slices. Comm. Statist. Simulation Comput. 36(1-3), 45–54.CrossRefGoogle Scholar
Walker, S., and N., Hjort (2001). On Bayesian consistency. J. Roy. Statist. Soc. Ser. B 63(4), 811–821.CrossRefGoogle Scholar
Walker, S., A., Lijoi, and I., Prünster (2005). Data tracking and the understanding of Bayesian consistency. Biometrika 92(4), 765–778.CrossRefGoogle Scholar
Walker, S., A., Lijoi, and I., Prünster (2007). On rates of convergence for posterior distributions in infinitedimensional models. Ann. Statist. 35(2), 738–746.CrossRefGoogle Scholar
Walker, S., and P., Muliere (1997). Beta-Stacy processes and a generalization of the Pólya-urn scheme. Ann. Statist. 25(4), 1762–1780.CrossRefGoogle Scholar
Watson, G. (1995). A treatise on the theory of Bessel functions. Cambridge: Cambridge University Press.
Whitney, H. (1934). Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc. 36(1), 63–89.CrossRefGoogle Scholar
Whittle, P. (1957). Curve and periodogram smoothing. J. Roy. Statist. Soc. Ser. B. 19, 38–47 (discussion 47–63).Google Scholar
Williamson, R. (1956). Multiply monotone functions and their Laplace transforms. Duke Math. J. 23, 207–.CrossRefGoogle Scholar
Wolpert, R., and K., Ickstadt (1998). Simulation of Lévy random fields. In Practical Nonparametric and Semiparametric Bayesian Statistics, pp. 227–242. New York: Springer.CrossRef
Wong, W., and X., Shen (1995). Probability inequalities for likelihood ratios and convergence rates of sieve MLEs. Ann. Statist. 23(2), 339–362.CrossRefGoogle Scholar
Wood, S., and R., Kohn (1998). A Bayesian approach to robust nonparametric binary regression. J. Amer. Statist. Assoc. 93, 213–.CrossRefGoogle Scholar
Wu, Y., and S., Ghosal (2008a). Kullback-Leibler property of kernel mixture priors in Bayesian density estimation. Electron. J. Stat. 2, 331–.Google Scholar
Wu, Y., and S., Ghosal (2008b). Posterior consistency for some semi-parametric problems. Sankhyā, Ser. A 70(2), 267–313.Google Scholar
Wu, Y., and S., Ghosal (2010). The L1-consistency of Dirichlet mixtures in multivariate Bayesian density estimation. J. Multivariate Anal. 101(10), 2411–2419.CrossRefGoogle Scholar
Xing, Y. (2008). On adaptive Bayesian inference. Electron. J. Stat. 2, 862–.CrossRefGoogle Scholar
Xing, Y. (2010). Rates of posterior convergence for iid observations. Comm. Statist. Theory Methods 39(19), 3389–3398.CrossRefGoogle Scholar
Xing, Y., and B., Ranneby (2009). Sufficient conditions for Bayesian consistency. J. Statist. Plann. Inference 139(7), 2479–2489.CrossRefGoogle Scholar
Yamato, H. (1984). Expectations of functions of samples from distributions chosen from Dirichlet processes. Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem. (17), 1–8.Google Scholar
Yang, Y., and A., Barron (1999). Information-theoretic determination of minimax rates of convergence. Ann. Statist. 27(5), 1564–1599.Google Scholar
Yang, Y., and S. T., Tokdar (2015). Minimax-optimal nonparametric regression in high dimensions. Ann. Statist. 43(2), 652–674.CrossRefGoogle Scholar
Zhang, T. (2006). From ɛ-entropy to KL-entropy: analysis of minimum information complexity density estimation. Ann. Statist. 34(5), 2180–2210.CrossRefGoogle Scholar
Zhao, L. (2000). Bayesian aspects of some nonparametric problems. Ann. Statist. 28(2), 532–552.CrossRefGoogle Scholar
Zygmund, A. (2002). Trigonometric series. Vol. I, II (Third ed.). Cambridge Mathematical Library. Cambridge University Press, Cambridge. With a foreword by Robert A., Fefferman. peacoke

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  • References
  • Subhashis Ghosal, North Carolina State University, Aad van der Vaart, Universiteit Leiden
  • Book: Fundamentals of Nonparametric Bayesian Inference
  • Online publication: 22 July 2017
  • Chapter DOI: https://doi.org/10.1017/9781139029834.029
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  • References
  • Subhashis Ghosal, North Carolina State University, Aad van der Vaart, Universiteit Leiden
  • Book: Fundamentals of Nonparametric Bayesian Inference
  • Online publication: 22 July 2017
  • Chapter DOI: https://doi.org/10.1017/9781139029834.029
Available formats
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  • References
  • Subhashis Ghosal, North Carolina State University, Aad van der Vaart, Universiteit Leiden
  • Book: Fundamentals of Nonparametric Bayesian Inference
  • Online publication: 22 July 2017
  • Chapter DOI: https://doi.org/10.1017/9781139029834.029
Available formats
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