| Title | On Adaptive Bayesian Inference |
| Authors | Yang Xing |
| Alternative Location | http://dx.doi.org/10.1214/0... |
| Publication | Electronic Journal of Statistics |
| Year | 2008 |
| Volume | 2 |
| Pages | 848 - 863 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Institute of Mathematical Statistics |
| Abstract English | 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. |
| Keywords | log spline density., density function, posterior distribution, rate of convergence, Adaptation, |
| ISBN/ISSN/Other | ISSN: 1935-7524 |
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