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2008 On adaptive Bayesian inference
Yang Xing
Electron. J. Statist. 2: 848-862 (2008). DOI: 10.1214/08-EJS244

Abstract

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general in-probability theorems on the rate of convergence of the resulting posterior distributions. We extend their results to almost sure assertions. As an application we study log spline densities with a finite number of models and obtain that the Bayes procedure achieves the optimal minimax rate nγ/(2γ+1) of convergence if the true density of the observations belongs to the Hölder space Cγ[0,1]. This strengthens a result in [1; 2]. We also study consistency of posterior distributions of the model index and give conditions ensuring that the posterior distributions concentrate their masses near the index of the best model.

Citation

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Yang Xing. "On adaptive Bayesian inference." Electron. J. Statist. 2 848 - 862, 2008. https://doi.org/10.1214/08-EJS244

Information

Published: 2008
First available in Project Euclid: 23 September 2008

zbMATH: 1320.62083
MathSciNet: MR2443199
Digital Object Identifier: 10.1214/08-EJS244

Subjects:
Primary: 62G07 , 62G20
Secondary: 62C10

Keywords: Adaptation , density function , log spline density , posterior distribution , rate of convergence

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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