Xing, Yang
- Department of Forest Economics, Swedish University of Agricultural Sciences
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 Holder 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
Adaptation; rate of convergence; posterior distribution; density function; log spline density
Published in
Electronic Journal of Statistics
2008, volume: 2, pages: 848-862
SLU Authors
UKÄ Subject classification
Probability Theory and Statistics
Publication identifier
- DOI: https://doi.org/10.1214/08-EJS244
Permanent link to this page (URI)
https://res.slu.se/id/publ/18938