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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. We 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 particularlydoi:10.1214/09-ejs466 fatcat:osp3dpblareyfa6kc4udjzc5z4