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• W3100176265 abstract "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." @default.
• W3100176265 created "2020-11-23" @default.
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• W3100176265 date "2013-08-01" @default.
• W3100176265 modified "2023-10-16" @default.
• W3100176265 title "Nonparametric Bernstein–von Mises theorems in Gaussian white noise" @default.
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• W3100176265 doi "https://doi.org/10.1214/13-aos1133" @default.
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