On adaptive Bayesian inference
| dc.creator | Xing, Yang | |
| dc.date | 2008-05-23 | |
| dc.date | 2008-09-23 | |
| dc.date.accessioned | 2026-07-07T10:04:13Z | |
| dc.date.available | 2026-07-07T10:04:13Z | |
| dc.description | 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 $n^{-γ/(2γ+1)}$ of convergence if the true density of the observations belongs to the Hölder space $C^γ[0,1]$. 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. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-EJS244 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0805.3584 | |
| dc.identifier | http://arxiv.org/abs/0805.3584 | |
| dc.identifier | Electronic Journal of Statistics 2008, Vol. 2, 848-862 | |
| dc.identifier | doi:10.1214/08-EJS244 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169585 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G07, 62G20 (Primary) 62C10 (Secondary) | |
| dc.title | On adaptive Bayesian inference | |
| dc.type | text |