Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 2 (2008), 848-862.
On adaptive Bayesian inference
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  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 n−γ/(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.
Electron. J. Statist., Volume 2 (2008), 848-862.
First available in Project Euclid: 23 September 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G07: Density estimation 62G20: Asymptotic properties
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures
Xing, Yang. On adaptive Bayesian inference. Electron. J. Statist. 2 (2008), 848--862. doi:10.1214/08-EJS244. https://projecteuclid.org/euclid.ejs/1222175445