On adaptive Bayesian inference

dc.creatorXing, Yang
dc.date2008-05-23
dc.date2008-09-23
dc.date.accessioned2026-07-07T10:04:13Z
dc.date.available2026-07-07T10:04:13Z
dc.descriptionWe 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.descriptionPublished 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.identifierhttps://arxiv.org/abs/0805.3584
dc.identifierhttp://arxiv.org/abs/0805.3584
dc.identifierElectronic Journal of Statistics 2008, Vol. 2, 848-862
dc.identifierdoi:10.1214/08-EJS244
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169585
dc.subjectStatistics Theory
dc.subject62G07, 62G20 (Primary) 62C10 (Secondary)
dc.titleOn adaptive Bayesian inference
dc.typetext

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