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Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution.
Empirical priors for prediction in sparse high-dimensional linear regression
Martin, R. and Tang, Y. (2019) · 1903
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General framework for projection structures
Nurushev, N. and Belitser, E. (2019) · 1904
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Honest confidence regions for nonparametric regression
Li, K.-C. (1989) · 1989
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Minimax risk over l p l_{p} -balls for l q l_{q} -error
Donoho, D. L. and Johnstone, I. M. (1994) · 1994
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Optimal predictive model selection
Barbieri, M. M. and Berger, J. O. (2004) · 2004
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Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences
Johnstone, I. M. and Silverman, B. W. (2004) · 2004
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An Introduction to Bayesian Analysis
Ghosh, J. K., Delampady, M., and Samanta, T. (2006) · 2006
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A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing
Bogdan, M., Ghosh, J. K., and Tokdar, S. T. (2008) · 2008
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General maximum likelihood empirical Bayes estimation of normal means
Jiang, W. and Zhang, C.-H. (2009) · 2009
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The horseshoe estimator for sparse signals
Carvalho, C. M., Polson, N. G., and Scott, J. G. (2010) · 2010
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Asymptotic Bayes-optimality under sparsity of some multiple testing procedures
Bogdan, M., Chakrabarti, A., Frommlet, F., and Ghosh, J. K. (2011) · 2011
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Asymptotic properties of Bayes risk for the horseshoe prior
Datta, J. and Ghosh, J. K. (2013) · 2013
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Estimation and variable selection with exponential weights
Arias-Castro, E. and Lounici, K. (2014) · 2014
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Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector
Martin, R. and Walker, S. G. (2014) · 2014
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Concentration rate and consistency of the posterior distribution for selected priors under monotonicity constraints
Salomond, J.-B. (2014) · 2014
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The horseshoe estimator: posterior concentration around nearly black vectors
van der Pas, S. L., Kleijn, B. J. K., and van der Vaart, A. W. (2014) · 2014
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Ghosh, P. and Chakrabarti, A. (2015) · 2015
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Invited comment on the article by van der Pas, Szabó, and van der Vaart
Martin, R. (2017) · 2017
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Empirical Bayes posterior concentration in sparse high-dimensional linear models
Martin, R., Mess, R., and Walker, S. G. (2017) · 2017
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Bayesian linear regression with sparse priors
Castillo, I., Schmidt-Hieber, J., and van der Vaart, A. (2015) · 2018
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Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior
Liu, C., Yang, Y., Bondell, H., and Martin, R. (2018) · 2018
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Empirical priors and posterior concentration rates for a monotone density
Martin, R. (2018) · 2018
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horseshoe: Implementation of the Horseshoe Prior
van der Pas, S., Scott, J., Chakraborty, A., and Bhattacharya, A. (2016) · 2016
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On coverage and local radial rates of credible sets
Belitser, E. (2017) · 2017
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Needles and straw in a haystack: robust confidence for possibly sparse sequences
Belitser, E. and Nurushev, N. (2017) · 2017
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Faster rates for general unbounded loss functions: from ERM to generalized Bayes
Grünwald, P. and Mehta, N. (2017) · 2017
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Inconsistency of Bayesian inference for misspecified linear models, and a proposal for repairing it
Grünwald, P. and van Ommen, T. (2017) · 2017
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Holmes, C. C. and Walker, S. G. (2017) · 2017
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Empirical Bayes oracle uncertainty quantification
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Spike and slab empirical Bayes sparse credible sets
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Data-dependent priors and their posterior concentration rates
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Calibrating general posterior credible regions
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Needles and straw in a haystack: posterior concentration for possibly sparse sequences
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