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Activity Number: 286 - Advances in Bayesian Nonparametric Methods and Its Applications
Type: Topic Contributed
Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #305290 Presentation
Title: Adaptive Bayesian Density Estimation in Sup-Norm
Author(s): Zacharie Naulet*
Keywords: bayesian; density estimation; supremum norm; adaptation

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.

Authors who are presenting talks have a * after their name.

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