• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Adaptive Bayesian Density Estimation with Location-Scale Mixtures

Thumbnail
Date
2009-05
Link to item file
http://hal.archives-ouvertes.fr/hal-00389343/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Rate-adaptive density estimation; Bayesian density estimation; Nonparametric density estimation; Convergence Rates; Location-Scale Mixtures
Conference name
7th Workshop on Bayesian Nonparametrics
Conference date
06-2009
Conference city
Moncalieri
Conference country
Italie
URI
https://basepub.dauphine.fr/handle/123456789/2955
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Kruijer, Willem
Rousseau, Judith
Van Der Vaart, Aad
Type
Communication / Conférence
Abstract (EN)
We study convergence rates of Bayesian density estimators based on finite location-scale mixtures of a kernel $C_p \exp\{-|x|^p\}$. We construct a finite mixture approximation of densities whose logarithm is locally $\beta$-H\"older, with squared integrable H\"older constant. Under additional tail and moment conditions, the approximation is minimax for both the supremum-norm and the Kullback-Leibler divergence. We use this approximation to establish convergence rates for a Bayesian mixture model with priors on the weights, locations, and the number of components. Regarding these priors, we provide general conditions under which the posterior converges at a near optimal rate, and is rate-adaptive with respect to the smoothness of $\log f_0$. Examples of priors which satisfy these conditions include Dirichlet and Polya-tree priors for the weights, and Poisson processes for the locations.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.