The Annals of Statistics
- Ann. Statist.
- Volume 42, Number 5 (2014), 2058-2091.
On Bayesian supremum norm contraction rates
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.
Ann. Statist., Volume 42, Number 5 (2014), 2058-2091.
First available in Project Euclid: 11 September 2014
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Castillo, Ismaël. On Bayesian supremum norm contraction rates. Ann. Statist. 42 (2014), no. 5, 2058--2091. doi:10.1214/14-AOS1253. https://projecteuclid.org/euclid.aos/1410440634