Adaptive Bayesian semiparametric density estimation in sup-norm


We investigate the problem of deriving adaptive posterior rates of contraction on uniform balls in density estimation. Although it is known that log-density priors can achieve optimal rates when the true density is sufficiently smooth, adaptive rates were still to be proven. Recent works have shown that the so called spike-and-slab priors can achieve optimal rates of contraction under loss in white-noise regression and multivariate regression with normal errors. Here we show that a spike-and-slab prior on the log-density also allows for (nearly) optimal rates of contraction in density estimation under uniform loss. Interestingly, our results hold without lower bound on the smoothness of the true density.

arXiv preprint arXiv:1805.06816