Bayesian inference with wavelets: Density estimation

We propose a prior probability model in the wavelet coefficient space. The proposed model implements wavelet coefficient thresholding by full posterio r inference in a coherent probability model. We introduce a prior probabili ty model with mixture priors for the wavelet coefficients. The prior includ es a positive prior probability mass at zero which leads to a posteriori th resholding and generally to a posteriori shrinkage on the coefficients. We discuss an efficient posterior simulation scheme to implement inference in the proposed model. The discussion is focused on the density estimation pro blem. However, the introduced prior probability model on the wavelet coeffi cient space and the Markov chain Monte Carlo scheme are general.