Wavelet estimation using Bayesian basis selection and basis averaging

Wavelet shrinkage methods are widely recognized as a useful tool for nonpar ametric regression and signal recovery, while Bayesian approaches to choosi ng the shrinkage method in wavelet smoothing are known to be effective. In this paper we extend the Bayesian methodology to include choice among wavel et bases (and the Fourier basis), and averaging of the regression function estimates over different bases. This results in improved function estimates .