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October 2014 On Bayesian supremum norm contraction rates
Ismaël Castillo
Ann. Statist. 42(5): 2058-2091 (October 2014). DOI: 10.1214/14-AOS1253

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.

Citation

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Ismaël Castillo. "On Bayesian supremum norm contraction rates." Ann. Statist. 42 (5) 2058 - 2091, October 2014. https://doi.org/10.1214/14-AOS1253

Information

Published: October 2014
First available in Project Euclid: 11 September 2014

zbMATH: 1305.62189
MathSciNet: MR3262477
Digital Object Identifier: 10.1214/14-AOS1253

Subjects:
Primary: 62G20
Secondary: 62G05 , 62G07

Keywords: Bayesian nonparametrics , contraction rates , supremum norm

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 5 • October 2014
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