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Convergence rates of posterior distributions

- S. Ghosal, J. Ghosh, A. V. D. Vaart
- Mathematics
- 1 April 2000

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… Expand

POSTERIOR CONSISTENCY OF DIRICHLET MIXTURES IN DENSITY ESTIMATION

- S. Ghosal, J. Ghosh, R. Ramamoorthi
- Mathematics
- 1 March 1999

A Dirichlet mixture of normal densities is a useful choice for a prior distribution on densities in the problem of Bayesian density estimation. In the recent years, efficient Markov chain Monte Carlo… Expand

Convergence rates of posterior distributions for non-i.i.d. observations

- S. Ghosal, A. V. D. Vaart
- Mathematics
- 1 February 2007

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general… Expand

Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities

- S. Ghosal, A. V. D. Vaart
- Mathematics
- 1 October 2001

We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of… Expand

Convergence rates for density estimation with Bernstein polynomials

- S. Ghosal
- Mathematics
- 1 October 2001

Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible… Expand

CONVERGENCE RATES OF POSTERIOR DISTRIBUTIONS FOR NONIID OBSERVATIONS By

- S. Ghosal
- Mathematics
- 2018

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general… Expand

Fundamentals of Nonparametric Bayesian Inference

- S. Ghosal, A. V. D. Vaart
- Computer Science
- 26 June 2017

TLDR

Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables

- T. K. Chandra, S. Ghosal
- Mathematics
- 1 December 1996

TESTING MONOTONICITY OF REGRESSION By

- S. Ghosal
- Mathematics
- 1998

We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We… Expand

Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution

- E. Belitser, S. Ghosal
- Mathematics
- 1 April 2003

We consider the problem of estimating the mean of an infinite-break dimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a… Expand

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