On Adaptive Bayesian Inference
(2008) In Electronic Journal of Statistics 2. p.848-863- 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 $n^{-\gamma/(2\gamma+1)}$ of convergence if the true density of the observations belongs to the H\"{o}lder space $C^{\gamma}[0,1]$. This strengthens a result in [1; 2]. We also study consistency of posterior... (More)
- 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 $n^{-\gamma/(2\gamma+1)}$ of convergence if the true density of the observations belongs to the H\"{o}lder space $C^{\gamma}[0,1]$. 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1465047
- author
- Xing, Yang LU
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- log spline density., density function, posterior distribution, rate of convergence, Adaptation
- in
- Electronic Journal of Statistics
- volume
- 2
- pages
- 848 - 863
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- scopus:85006570606
- ISSN
- 1935-7524
- DOI
- 10.1214/08-EJS244
- language
- English
- LU publication?
- no
- id
- b3be2546-40ce-4f8f-9c1f-ead354b36240 (old id 1465047)
- date added to LUP
- 2016-04-01 14:14:05
- date last changed
- 2022-03-14 04:47:06
@article{b3be2546-40ce-4f8f-9c1f-ead354b36240,
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 $n^{-\gamma/(2\gamma+1)}$ of convergence if the true density of the observations belongs to the H\"{o}lder space $C^{\gamma}[0,1]$. 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.}},
author = {{Xing, Yang}},
issn = {{1935-7524}},
keywords = {{log spline density.; density function; posterior distribution; rate of convergence; Adaptation}},
language = {{eng}},
pages = {{848--863}},
publisher = {{Institute of Mathematical Statistics}},
series = {{Electronic Journal of Statistics}},
title = {{On Adaptive Bayesian Inference}},
url = {{http://dx.doi.org/10.1214/08-EJS244}},
doi = {{10.1214/08-EJS244}},
volume = {{2}},
year = {{2008}},
}