Advanced

Sufficient conditions for Bayesian consistency

Xing, Yang LU and Bo, Ranneby (2009) In Journal of Statistical Planning and Inference 139(7). p.2479-2489
Abstract
We introduce the Hausdorff α-entropy to study the strong Hellinger consistency of posterior distributions. We obtain general Bayesian consistency theorems which extend the well-known results of Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536–561] and Ghosal et al. [1999. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143–158] and Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043]. As an application we strengthen previous results on Bayesian consistency of the (normal) mixture models.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Infinite-dimensional model, Sieve, Posterior distribution, Hellinger consistency
in
Journal of Statistical Planning and Inference
volume
139
issue
7
pages
2479 - 2489
publisher
North-Holland
external identifiers
  • scopus:62049084447
ISSN
1873-1171
DOI
10.1016/j.jspi.2008.11.008
language
English
LU publication?
no
id
9f3000f6-98b6-4328-bdc7-969e147bb0b2 (old id 1465066)
alternative location
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V0M-4V1TXRG-2-1&_cdi=5650&_user=745831&_orig=search&_coverDate=07%2F01%2F2009&_sk=998609992&view=c&wchp=dGLzVtz-zSkWA&_valck=1&md5=26ae78f4b2906952bdac231182963eba&ie=/sdarticle.pdf
date added to LUP
2009-08-20 13:42:09
date last changed
2017-01-01 05:08:48
@article{9f3000f6-98b6-4328-bdc7-969e147bb0b2,
  abstract     = {We introduce the Hausdorff α-entropy to study the strong Hellinger consistency of posterior distributions. We obtain general Bayesian consistency theorems which extend the well-known results of Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536–561] and Ghosal et al. [1999. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143–158] and Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043]. As an application we strengthen previous results on Bayesian consistency of the (normal) mixture models.},
  author       = {Xing, Yang and Bo, Ranneby},
  issn         = {1873-1171},
  keyword      = {Infinite-dimensional model,Sieve,Posterior distribution,Hellinger consistency},
  language     = {eng},
  number       = {7},
  pages        = {2479--2489},
  publisher    = {North-Holland},
  series       = {Journal of Statistical Planning and Inference},
  title        = {Sufficient conditions for Bayesian consistency},
  url          = {http://dx.doi.org/10.1016/j.jspi.2008.11.008},
  volume       = {139},
  year         = {2009},
}