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We investigate the frequentist coverage properties of Bayesian credible sets in a general, adaptive, nonparametric framework.
On the Bernsteinñ-von Mises phenomenon for nonparametric bayes procedures
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Asymptotic Methods in Statistical Decision Theory
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Ghosal, S., Ghosh, J. K., and van der Vaart, A. (2000) · 2000
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Picard, D. and Tribouley, K. (2000) · 2000
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An adaptation theory for nonparametric confidence intervals
Cai, T. and Low, M. (2004) · 2004
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Adaptive nonparametric confidence sets
Robins, J. and van der Vaart, A. (2006) · 2006
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Convergence rates of posterior distributions for non iid observations
Ghosal, S. and van der Vaart, A. (2007) · 2007
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Approximating interval hypotheses: p-values and Bayes factors
Rousseau, J. (2007) · 2007
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On rates of convergence for bayesian density estimation
Scricciolo, C. (2007) · 2007
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Lower bounds for posterior rates with Gaussian process priors
Castillo, I. (2008) · 2008
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An Introduction to Nonparametric Estimation
Tsybakov, A. (2008) · 2008
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Rates of contraction of posterior distributions based on Gaussian process priors
van der Vaart, A. W. and van Zanten, J. H. (2008) · 2008
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Bayesian goodness-of-fit testing with mixtures of triangular distributions
McVinish, R., Rousseau, J., and Mengersen, K. (2009) · 2009
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Confidence bands in density estimation
Giné, E. and Nickl, R. (2010) · 2010
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On adaptive inference and confidence bands
Hoffmann, M. and Nickl, R. (2011) · 2011
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Knapik, B., van der Vaart, A. W., and van Zanten, J. H. (2011) · 2011
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Adaptive Bayesian credible sets in regression with a Gaussian process prior
Sniekers, S. and van der Vaart, A. (2015) · 2015
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Frequentist coverage of adaptive nonparametric Bayesian credible sets
Szabo, B. T., van der Vaart, A. W., and van Zanten, J. H. (2015) · 2015
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Rate exact bayesian adaptation with modified block priors
Gao, C. and Zhou, H. H. (2016) · 2016
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Mathematical foundations of infinite-dimensional statistical models
Giné, E. and Nickl, R. (2016) · 2016
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A sharp adaptive confidence ball for self-similar functions
Nickl, R. and Szabo, B. (2016) · 2016
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Adaptive confidence bands for markov chains and diffusions: Estimating the invariant measure and the drift
Söhl, J. and Trabs, M. (2016) · 2016
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Adaptive confidence sets in lˆ 2
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Asymptotic behaviour of the empirical bayes posteriors associated to maximum marginal likelihood estimator: supplementary material
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Nonparametric Bernsteinñ-von Mises theorems in gaussian white noise
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