Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems, Stochastic Processes and their Applications, vol.123, issue.10, pp.3828-3860, 2013. ,
DOI : 10.1016/j.spa.2013.05.001
Abstract., Journal of Inverse and Ill-posed Problems, vol.22, issue.3, pp.297-321, 2014. ,
DOI : 10.1515/jip-2012-0071
Bayesian optimal adaptive estimation using a sieve prior. Scand, J. Stat, vol.40, issue.3, pp.549-570, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01203280
The consistency of posterior distributions in nonparametric problems, Ann. Statist, vol.27, issue.2, pp.536-561, 1999. ,
The exponential convergence of posterior probabilities with implications for Bayes estimators of density functions, 1988. ,
On coverage and local radial rates of credible sets, The Annals of Statistics, vol.45, issue.3 ,
DOI : 10.1214/16-AOS1477SUPP
Adaptive Bayesian inference on the mean of an infinitedimensional normal distribution, Ann. Statist, vol.31, issue.2, pp.536-559, 2003. ,
Asymptotic equivalence of nonparametric regression and white noise, The Annals of Statistics, vol.24, issue.6, pp.2384-2398, 1996. ,
DOI : 10.1214/aos/1032181159
On Bayesian supremum norm contraction rates, The Annals of Statistics, vol.42, issue.5, pp.2058-2091, 2014. ,
DOI : 10.1214/14-AOS1253
URL : http://arxiv.org/pdf/1304.1761
Bayesian linear regression with sparse priors, The Annals of Statistics, vol.43, issue.5, pp.1986-2018, 2015. ,
DOI : 10.1214/15-AOS1334SUPP
URL : https://hal.archives-ouvertes.fr/hal-01226832
Needles and Straw in a Haystack: Posterior concentration for possibly sparse sequences, The Annals of Statistics, vol.40, issue.4, pp.2069-2101, 2012. ,
DOI : 10.1214/12-AOS1029SUPP
Nonparametric statistical inverse problems, Inverse Problems, vol.24, issue.3, p.34004, 2008. ,
DOI : 10.1088/0266-5611/24/3/034004
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.5900
A practical guide to splines, 1978. ,
Adaptive nonparametric Bayesian inference using location-scale mixture priors, The Annals of Statistics, vol.38, issue.6, pp.3300-3320, 2010. ,
DOI : 10.1214/10-AOS811
Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors, Electronic Journal of Statistics, vol.6, issue.0, pp.1984-2001, 2012. ,
DOI : 10.1214/12-EJS735
Posterior concentration rates for empirical Bayes procedures, with applications to Dirichlet Process mixtures. arXiv preprint, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01007554
Geometrizing Rates of Convergence, II, The Annals of Statistics, vol.19, issue.2, pp.633-667, 1991. ,
DOI : 10.1214/aos/1176348114
Regularization of inverse problems, 1996. ,
On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems, The Annals of Statistics, vol.19, issue.3, pp.1257-1272, 1991. ,
DOI : 10.1214/aos/1176348248
Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior, Journal of Econometrics, vol.170, issue.2, pp.458-475, 2012. ,
DOI : 10.1016/j.jeconom.2012.05.016
URL : https://hal.archives-ouvertes.fr/hal-00922877
Regularized posteriors in linear ill-posed inverse problems. Scand, J. Stat, vol.39, issue.2, pp.214-235, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00922879
Posterior consistency of Dirichlet mixtures in density estimation, Ann. Statist, vol.27, issue.1, pp.143-158, 1999. ,
Convergence rates of posterior distributions, The Annals of Statistics, vol.28, issue.2, pp.500-531, 2000. ,
DOI : 10.1214/aos/1016218228
Convergence rates of posterior distributions for noniid observations, The Annals of Statistics, vol.35, issue.1, pp.192-223, 2007. ,
DOI : 10.1214/009053606000001172
Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities, Ann. Statist, vol.29, issue.5, pp.1233-1263, 2001. ,
On adaptive posterior concentration rates, The Annals of Statistics, vol.43, issue.5, pp.2259-2295, 2015. ,
DOI : 10.1214/15-AOS1341
URL : https://hal.archives-ouvertes.fr/hal-01251098
Bayes procedures for adaptive inference in inverse problems for the white noise model, Probability Theory and Related Fields, vol.28, issue.2, pp.771-813, 2016. ,
DOI : 10.1214/aos/1016218229
Bayesian inverse problems with Gaussian priors, The Annals of Statistics, vol.39, issue.5, pp.2626-2657, 2011. ,
DOI : 10.1214/11-AOS920
URL : http://doi.org/10.1214/11-aos920
Bayesian Recovery of the Initial Condition for the Heat Equation, Communications in Statistics - Theory and Methods, vol.35, issue.2, p.42, 2013. ,
DOI : 10.1017/S0962492910000061
Adaptive Bayesian density estimation with location-scale mixtures, Electronic Journal of Statistics, vol.4, issue.0, pp.1225-1257, 2010. ,
DOI : 10.1214/10-EJS584
URL : https://hal.archives-ouvertes.fr/hal-00389343
Asymptotic equivalence of functional linear regression and a white noise inverse problem, The Annals of Statistics, vol.39, issue.3, pp.1471-1495, 2011. ,
DOI : 10.1214/10-AOS872
Asymptotic equivalence of density estimation and Gaussian white noise, The Annals of Statistics, vol.24, issue.6, pp.2399-2430, 1996. ,
DOI : 10.1214/aos/1032181160
Bayesian inverse problems with non-conjugate priors, Electronic Journal of Statistics, vol.7, issue.0, pp.2516-2549, 2013. ,
DOI : 10.1214/13-EJS851
URL : http://doi.org/10.1214/13-ejs851
Rates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the density, The Annals of Statistics, vol.38, issue.1, pp.146-180, 2010. ,
DOI : 10.1214/09-AOS703
Asymptotic behaviour of the posterior distribution in overfitted mixture models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.6, issue.5, pp.689-710, 2011. ,
DOI : 10.1214/aos/1176344136
URL : https://hal.archives-ouvertes.fr/hal-00641475
Real and complex analysis, 1987. ,
Concentration rate and consistency of the posterior distribution for selected priors under monotonicity constraints, Electronic Journal of Statistics, vol.8, issue.1, pp.1380-1404, 2014. ,
DOI : 10.1214/14-EJS929
URL : https://hal.archives-ouvertes.fr/hal-01065564
On Bayes procedures, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.20, issue.1, pp.10-26, 1965. ,
DOI : 10.1007/BF00535479
Adaptive Bayesian Density Estimation in $L^{p}$ -metrics with Pitman-Yor or Normalized Inverse-Gaussian Process Kernel Mixtures, Bayesian Analysis, vol.9, issue.2, pp.475-520, 2014. ,
DOI : 10.1214/14-BA863
Adaptive Bayesian Procedures Using Random Series Priors, Scandinavian Journal of Statistics, vol.37, issue.5B, pp.1194-1213, 2015. ,
DOI : 10.1214/08-AOS678
URL : http://arxiv.org/abs/1403.0625
Adaptive Bayesian multivariate density estimation with Dirichlet mixtures, Biometrika, vol.100, issue.3, pp.623-640, 2013. ,
DOI : 10.1093/biomet/ast015
URL : http://arxiv.org/abs/1109.6406
Rates of convergence of posterior distributions, Ann. Statist, vol.29, issue.3, pp.687-714, 2001. ,
Frequentist coverage of adaptive nonparametric Bayesian credible sets, The Annals of Statistics, vol.43, issue.4, pp.1391-1428, 2015. ,
DOI : 10.1214/14-AOS1270
Posterior consistency for Bayesian inverse problems through stability and regression results, Inverse Problems, vol.29, issue.12, p.125011, 2013. ,
DOI : 10.1088/0266-5611/29/12/125011
URL : http://arxiv.org/pdf/1302.4101
Bayesian aspects of some nonparametric problems, The Annals of Statistics, vol.28, issue.2, pp.532-552, 2000. ,
DOI : 10.1214/aos/1016218229