Convergence rates of posterior distributions

Convergence rates of posterior distributions (2000)

Cached

Download Links

by Subhashis Ghosal , Jayanta K. Ghosh , Aad W. Van Der Vaart

Venue:	Ann. Statist
Citations:	26 - 8 self

BibTeX

@ARTICLE{Ghosal00convergencerates,
    author = {Subhashis Ghosal and Jayanta K. Ghosh and Aad W. Van Der Vaart},
    title = {Convergence rates of posterior distributions},
    journal = {Ann. Statist},
    year = {2000},
    pages = {500--531}
}

Years of Citing Articles

Bookmark

OpenURL

Abstract

We consider the asymptotic behavior of posterior distributions and Bayes estimators for infinite-dimensional statistical models. We give general results on the rate of convergence of the posterior measure. These are applied to several examples, including priors on finite sieves, log-spline models, Dirichlet processes and interval censoring. 1. Introduction. Suppose

Citations

818	A Practical Guide to Splines - Boor - 1978
488	T.S.: A Bayesian analysis of some nonparametric problems - Ferguson - 1973
442	Time Series: Theory and Methods - Brockwell, Davis - 1991
417	Markov chains and stochastic stability - Meyn, Tweedie - 1993
239	Weak Convergence and Empirical Processes - VAART, A - 1996
182	Weak Convergence and Empirical Processes with Applications to Statistics - Vaart, Wellner - 1996
175	Asymptotic methods in statistical decision theory - Cam - 1986
167	Statistical Estimation: Asymptotic Theory - Ibragimov, Hasminskii - 1981
131	Prior distributions on spaces of probability measures - Ferguson - 1974
121	Polynomial Splines and their Tensor Products in Extended Linear Modeling (with discussion - Stone, Hansen, et al. - 1997
112	Probability Theory - Chow, Teicher - 1978
83	Empirical processes: theory and applications - Pollard - 1990
68	A course on empirical processes - Dudley - 1984
55	On the asymptotic behavior of Bayes estimates in the discrete - FREEDMAN - 1963
55	On Bayes procedures - SCHWARTZ - 1965
53	The consistency of posterior distributions in nonparametric problems - Barron, Schervis, et al. - 1999
53	Rates of convergence for minimum contrast estimators - BIRGE, MASSART - 1993
52	Approximation dans les espaces métriques et théorie de l’estimation - Birgé - 1983
48	Minimum Contrast Estimators on Sieves: Exponential Bounds and - Birgé, Massart - 1998
47	Posterior consistency of Dirichlet mixtures in density estimation - Ghosal, Ghosh, et al. - 1999
47	Asymptotics in Statistics: Some Basic Concepts - LeCam, Yang - 1990
46	From model selection to adaptive estimation - BIRGÉ, MASSART - 1997
44	The dimensionality reduction principle for generalized additive models - Stone - 1986
43	Some limit theorems for stationary processes - Ibragimov - 1962
40	Probability inequalities for likelihood ratios and convergence rates of sieve mles Ann - Wong, Shen - 1995
29	Convergence of estimates under dimensionality restrictions - CAM - 1973
27	Rates of convergence of posterior distributions - Shen, Wasserman - 2001
23	Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities. The Annals of Statistics - Ghosal, Vaart - 2001
22	On the consistency of Bayes estimates (with discussion - Diaconis, Freedman - 1986
21	Application of the theory of martingales - Doob - 1948
20	Model selection via testing : an alternative to (penalized) maximum likelihood estimators. Ann. Inst. Henri Poincaré Probab. et Statist - BIRGÉ
18	From model selection to adaptive estimation. Festschrift for Lucien Le Cam, 55–87 - Birgé, Massart - 1997
15	Large-sample inference for log-spline models - Stone - 1990
15	Asymptotic properties of nonparametric Bayesian procedures - WASSERMAN - 1998
15	Posterior consistency for semi-parametric regression problems - Amewou-Atisso, Ghosal, et al. - 2003
14	Posterior convergence rates for Dirichlet mixtures at smooth densities - Ghosal, Vaart - 2007
13	Convergence rates for density estimation with Bernstein polynomials - Ghosal - 2001
13	Asymptotic normality of semiparametric and nonparametric posterior distributions - Shen - 2002
12	Bayesian density estimation using Bernstein polynomials - Petrone - 1999
11	Consistency issues in Bayesian nonparametrics - Ghosal, Ghosh, et al. - 1999
11	Empirical spectral processes and their applications to time series analysis. Stochastic Process - Dahlhaus - 1988
11	Bayesian aspects of some nonparametric problems. Ann. Statist. 28 532–552. MR1790008 Istituto di Metodi Quantitativi Università “L. Bocconi,” Milano Viale Isonzo 25 I-20135 Milano Italy E-mail: catia.scricciolo@uni-bocconi.it - Zhao - 2000
10	Bayesian estimation of the spectral density of a time series - Choudhuri, Ghosal, et al. - 2004
10	On convergence of posterior distributions - Ghosal, Ghosh, et al. - 1995
9	On local and global properties in the theory of asymptotic normality of experiments - CAM - 1975
8	Non-informative priors via sieves and packing numbers - Ghosal, Ghosh, et al. - 1997
7	Epsilon- entropy and epsiloncapacity of sets in funktional spaces - Kolmogorov, Tihomirov - 1959
7	Sur un théorème de minimax et son application aux tests - BIRGÉ - 1984
6	On bayes procedures. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 4 - Schwartz - 1965
6	On universal Bayesian adaptation - Lember, Vaart - 2007