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August 2013 Nonparametric Bernstein–von Mises theorems in Gaussian white noise
Ismaël Castillo, Richard Nickl
Ann. Statist. 41(4): 1999-2028 (August 2013). DOI: 10.1214/13-AOS1133


Bernstein–von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete nonparametric problems. Particularly Bayesian credible sets are constructed that have asymptotically exact $1-\alpha$ frequentist coverage level and whose $L^{2}$-diameter shrinks at the minimax rate of convergence (within logarithmic factors) over Hölder balls. Other applications include general classes of linear and nonlinear functionals and credible bands for auto-convolutions. The assumptions cover nonconjugate product priors defined on general orthonormal bases of $L^{2}$ satisfying weak conditions.


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Ismaël Castillo. Richard Nickl. "Nonparametric Bernstein–von Mises theorems in Gaussian white noise." Ann. Statist. 41 (4) 1999 - 2028, August 2013.


Published: August 2013
First available in Project Euclid: 23 October 2013

zbMATH: 1285.62052
MathSciNet: MR3127856
Digital Object Identifier: 10.1214/13-AOS1133

Primary: 62G20
Secondary: 62G08 , 62G15

Keywords: Bayesian inference , efficiency , plug-in property

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 4 • August 2013
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