On Adaptive Bayesian Inference

Research output: Contribution to journalArticle

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.

Details

Authors
External organisations
  • External Organization - Unknown
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • log spline density., density function, posterior distribution, rate of convergence, Adaptation
Original languageEnglish
Pages (from-to)848-863
JournalElectronic Journal of Statistics
Volume2
Publication statusPublished - 2008
Publication categoryResearch
Peer-reviewedYes
Externally publishedYes