The present paper investigates theoretical performance of various Bayesian
wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors
which are not necessarily normally distributed. The main purpose is comparison
of various Bayesian models in terms of their frequentist asymptotic optimality
in Sobolev and Besov spaces. We establish a relationship between
hyperparameters, verify that the majority of Bayesian models studied so far
achieve theoretical optimality, state which Bayesian models cannot achieve
optimal convergence rate and explain why it happens.Comment: Published at http://dx.doi.org/10.1214/009053606000000128 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
