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We investigate Bernstein-von Mises theorems for adaptive nonparametric Bayesian procedures in the canonical Gaussian white noise model.
On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures
Castillo, I., and Nickl, R · 1969
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On the consistency of Bayes estimates
Diaconis, P., and Freedman, D · 1986
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Asymptotic methods in statistical decision theory
Le Cam, L · 1986
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Chow, Y. S., and Teicher, H · 1988
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Meyer, Y · 1990
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Cox, D. D · 1993
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Abramovich, F., Sapatinas, T., and Silverman, B. W · 1998
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A complement to Le Cam’s theorem
Low, M. G., and Zhou, H. H · 2007
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Castillo, I · 2008
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A Bernstein-von Mises theorem for discrete probability distributions
Boucheron, S., and Gassiat, E · 2009
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Giné, E., and Nickl, R · 2010
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Castillo, I · 2015
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A Bernstein–von Mises theorem for smooth functionals in semiparametric models
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Mathematical foundations of infinite-dimensional statistical models
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On adaptive posterior concentration rates
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Low, M. G., and Ma, Z · 2015
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