Bayesian Inference with Wavelets: Density Estimation

We propose a prior probability model in the wavelet coeecient space. The proposed model implements wavelet coeecient thresholding by full posterior inference in a coherent probability model. We introduce a prior probability model with mixture priors for the wavelet coeecients. The prior includes a positive prior probability mass at zero which leads to a posteriori threshold-ing and generally to a posteriori shrinkage on the coeecients. We discuss an eecient posterior simulation scheme to implement inference in the proposed model. The discussion is focused on the density estimation problem. However , the introduced prior probability model on the wavelet coeecient space and the Markov chain Monte Carlo scheme are general.