Bayesian optimal adaptive estimation using a sieve prior - Archive ouverte HAL Access content directly
Journal Articles Scandinavian Journal of Statistics Year : 2013

Bayesian optimal adaptive estimation using a sieve prior

Abstract

We derive rates of contraction of posterior distributions on non-parametric models resulting from sieve priors. The aim of the study was to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter is, for example, a Sobolev class. The conditions employed, although standard in the literature, are combined in a different way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual l2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the l2 loss is strongly suboptimal and we provide a lower bound on the rate.
Fichier principal
Vignette du fichier
arxived version.pdf (699.68 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01203280 , version 1 (24-09-2015)

Identifiers

Cite

Julyan Arbel, Ghislaine Gayraud, Judith Rousseau. Bayesian optimal adaptive estimation using a sieve prior. Scandinavian Journal of Statistics, 2013, ⟨10.1002/sjos.12002⟩. ⟨hal-01203280⟩
250 View
126 Download

Altmetric

Share

Gmail Facebook X LinkedIn More