|
Abstract:
|
We investigate the problem of deriving adaptive posterior rates of contraction on sup-norm 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 sup-norm 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 optimal rates of contraction in density estimation under sup-norm loss. Interestingly, our results hold without lower bound on the smoothness of the true density, and use adaptation of rather classical techniques, in contrast with previous results.
|
