Open Access
February 2007 Convergence rates of posterior distributions for noniid observations
Subhashis Ghosal, Aad van der Vaart
Ann. Statist. 35(1): 192-223 (February 2007). DOI: 10.1214/009053606000001172


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 results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We apply our general results to several examples of infinite-dimensional statistical models including nonparametric regression with normal errors, binary regression, Poisson regression, an interval censoring model, Whittle estimation of the spectral density of a time series and a nonlinear autoregressive model.


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Subhashis Ghosal. Aad van der Vaart. "Convergence rates of posterior distributions for noniid observations." Ann. Statist. 35 (1) 192 - 223, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62060
MathSciNet: MR2332274
Digital Object Identifier: 10.1214/009053606000001172

Primary: 62G20
Secondary: 62G08

Keywords: covering numbers , Hellinger distance , independent nonidentically distributed observations , Infinite dimensional model , Markov chains , posterior distribution , rate of convergence , tests

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • February 2007
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