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arXiv · 1304.1761

On Bayesian supremum norm contraction rates

Ismaël Castillo
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Abstract

Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when "strong" measures of distances, such as the sup-norm, are considered. In particular, we show that likelihood methods can achieve optimal minimax sup-norm rates in density estimation on the unit interval. The introduced methodology is used to prove that commonly used families of prior distributions on densities, namely log-density priors and dyadic random density histograms, can indeed achieve optimal sup-norm rates of convergence. New results are also derived in the Gaussian white noise model as a further illustration of the presented techniques.

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Ismaël Castillo. 2014-10-14. On Bayesian supremum norm contraction rates. https://doi.org/10.1214/14-aos1253

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