  In this paper we deal with the regression problem in a random design setting.
We investigate asymptotic optimality under minimax point of view of various
Bayesian rules based on warped wavelets and show that they nearly attain
optimal minimax rates of convergence over the Besov smoothness class
considered. Warped wavelets have been introduced recently, they offer very good
computable and easy-to-implement properties while being well adapted to the
statistical problem at hand. We particularly put emphasis on Bayesian rules
leaning on small and large variance Gaussian priors and discuss their
simulation performances comparing them with a hard thresholding procedure.
