Abstract (EN)

We study the Bayes estimation of an infinite dimensional parameter from a Sobolev smoothness class. We propose a family of sieve priors whose resulting Bayes estimators are adaptive optimal, both in posterior concentration rate and in risk convergence for the inherent distance of the model, denoted dn (e.g. the Hellinger distance). This result is applied to several examples, including white noise model, regression function and density model.