Adaptive Bayesian density estimation with location-scale mixtures

Abstract

We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of exponential power distributions. We construct approximations of β-Hölder densities be continuous mixtures of exponential power distributions, leading to approximations of the β-Hölder densities by finite mixtures. These results are then used to derive posterior concentration rates, with priors based on these mixture models. The rates are minimax (up to a logn term) and since the priors are independent of the smoothness the rates are adaptive to the smoothness.